Recent works of Roughgarden (EC'21) and Chung and Shi (Highlights Beyond EC'22) initiate the study of a new decentralized mechanism design problem called transaction fee mechanism design (TFM). Unlike the classical mechanism design literature, in the decentralized environment, even the auctioneer (i.e., the miner) can be a strategic player, and it can even collude with a subset of the users facilitated by binding side contracts. Chung and Shi showed two main impossibility results that rule out the existence of a dream TFM. First, any TFM that provides incentive compatibility for individual users and miner-user coalitions must always have zero miner revenue, no matter whether the block size is finite or infinite. Second, assuming finite block size, no non-trivial TFM can simultaenously provide incentive compatibility for any individual user, and for any miner-user coalition. In this work, we explore what new models and meaningful relaxations can allow us to circumvent the impossibility results of Chung and Shi. Besides today’s model that does not employ cryptography, we introduce a new MPC-assisted model where the TFM is implemented by a joint multi-party computation (MPC) protocol among the miners. We prove several feasibility and infeasibility results for achieving strict and approximate incentive compatibility, respectively, in the plain model as well as the MPC-assisted model. We show that while cryptography is not a panacea, it indeed allows us to overcome some impossibility results pertaining to the plain model, leading to non-trivial mechanisms with useful guarantees that are otherwise impossible in the plain model. Our work is also the first to characterize the mathematical landscape of transaction fee mechanism design under approximate incentive compatibility, as well as in a cryptography-assisted model.
Ring signatures allow signers to produce verifiable signatures and remain anonymous within a set of signers (i.e., the ring) while doing so. They are well-suited to protocols that target anonymity as a primary goal, for example, anonymous cryptocurrencies. However, standard ring signatures do not ensure that signers are held accountable if they act maliciously. Fraser and Quaglia (CANS'21) introduced a ring signature variant that they called report and trace ring signatures which balances the anonymity guarantee of standard ring signatures with the need to hold signers accountable. In particular, report and trace ring signatures introduce a reporting system whereby ring members can report malicious message/signature pairs. A designated tracer can then revoke the signer's anonymity if, and only if, a ring member submits a report to the tracer. Fraser and Quaglia present a generic construction of a report and trace ring signature scheme and outline an instantiation for which it is claimed that the complexity of signing is linear in the size of the ring $|R|$. In this paper, we introduce a new instantiation of Fraser and Quaglia's generic report and trace ring signature construction. Our instantiation uses a pairing-based variant of ElGamal that we define. We demonstrate that our instantiation is more efficient. In fact, we highlight that the efficiency of Fraser and Quaglia's instantiation omits a scaling factor of $\lambda$ where $\lambda$ is a security parameter. As such, the complexity of signing for their instantiation grows linearly in $\lambda \cdot |R|$. Our instantiation, on the other hand, achieves signing complexity linear in $|R|$. We also introduce a new pairing-free report and trace ring signature construction reaching a similar signing complexity. Whilst this construction requires some additional group exponentiations, it can be instantiated over any prime order group for which the Decisional Diffie-Hellman assumption holds.
A Bloom filter is a data structure that maintains a succinct and probabilistic representation of a set $S\subseteq U$ of elements from a universe $U$. It supports approximate membership queries. The price of the succinctness is allowing some error, namely false positives: for any $x\notin S$, it might answer `Yes' but with a small (non-negligible) probability. When dealing with such data structures in adversarial settings, we need to define the correctness guarantee and formalize the requirement that bad events happen infrequently and those false positives are appropriately distributed. Recently, several papers investigated this topic, suggesting different robustness definitions. In this work we unify this line of research and propose several robustness notions for Bloom filters that allow the adaptivity of queries. The goal is that a robust Bloom filter should behave like a random biased coin even against an adaptive adversary. The robustness definitions are expressed by the type of test that the Bloom filter should withstand. We explore the relationships between these notions and highlight the notion of Bet-or-Pass as capturing the desired properties of such a data structure.
The paper introduces a new AEAD-mode called sMGM (strong Multilinear Galois Mode). The proposed construction can be treated as an extension of the Russian standardized MGM mode and its modification MGM2 mode presented at the CTCrypt'21 conference. The distinctive feature of the new mode is that it provides an interface allowing one to choose specific security properties required for a certain application case. Namely, the mode has additional parameters allowing to switch on/off misuse-resistance or re-keying mechanisms. The sMGM mode consists of two main "building blocks" that are a CTR-style gamma generation function with incorporated re-keying and a multilinear function that lies in the core of the original MGM mode. Different ways of using these functions lead to achieving different sets of security properties. Such an approach to constructing parameterizable AEAD-mode allows for reducing the code size which can be crucial for constrained devices. We provide security bounds for the proposed mode. We focus on proving the misuse-resistance of the sMGM mode, since the standard security properties were already analyzed during the development of the original MGM and MGM2 modes.
With the advancement of blockchain technology, hundreds of cryptocurrencies have been deployed. The bloom of heterogeneous blockchain platforms brings a new emerging problem: typically, various blockchains are isolated systems, how to securely identify and/or transfer digital properties across blockchains? There are three main kinds of cross-chain approaches: sidechains/relays, notaries, and hashed time-lock contracts. Among them, notary-based cross-chain solutions have the best compatibility and user-friendliness, but they are typically centralized. To resolve this issue, we present Bool Network -- an open, distributed, secure cross-chain notary platform powered by MPC-based distributed key management over evolving hidden committees. More specifically, to protect the identities of the committee members, we propose a Ring verifiable random function (Ring VRF) protocol, where the real public key of a VRF instance can be hidden among a ring, which may be of independent interest to other cryptographic protocols. Furthermore, all the key management procedures are executed in the TEE, such as Intel SGX, to ensure the privacy and integrity of partial key components. A prototype of the proposed Bool Network is implemented in Rust language, using Polkadot Substrate.
Isogeny-based cryptography suffers from a long-running time due to its requirement of a great amount of large integer arithmetic. The Residue Number System (RNS) can compensate for that drawback by making computation more efficient via parallelism. However, performing a modular reduction by a large prime which is not part of the RNS base is very expensive. In this paper, we propose a new fast and efficient modular reduction algorithm using RNS. Our method reduces the number of required multiplications by 40\% compared to RNS Montgomery modular reduction algorithm. Also, we evaluate our modular reduction method by realizing a cryptoprocessor for isogeny-based SIDH key exchange. On a Xilinx Ultrascale+ FPGA, the proposed cryptoprocessor consumes 151,009 LUTs, 143,171 FFs and 1,056 DSPs. It achieves 250 MHz clock frequency and finishes the key exchange for SIDH in 3.8 and 4.9 ms.
We give round-optimal {\em black-box} constructions of two-party and multiparty protocols in the common random/reference string (CRS) model, with security against malicious adversaries, based on any two-round oblivious transfer (OT) protocol in the same model. Specifically, we obtain two types of results. \begin{enumerate} \item {\bf Two-party protocol.} We give a (two-round) {\it two-sided NISC} protocol that makes black-box use of two-round (malicious-secure) OT in the CRS model. In contrast to the standard setting of non-interactive secure computation (NISC), two-sided NISC allows communication from both parties in each round and delivers the output to both parties at the end of the protocol. Prior black-box constructions of two-sided NISC relied on idealized setup assumptions such as OT correlations, or were proven secure in the random oracle model. \item {\bf Multiparty protocol.} We give a three-round secure multiparty computation protocol for an arbitrary number of parties making black-box use of a two-round OT in the CRS model. The round optimality of this construction follows from a black-box impossibility proof of Applebaum et al. (ITCS 2020). Prior constructions either required the use of random oracles, or were based on two-round malicious-secure OT protocols that satisfied additional security properties. \end{enumerate}
Let $P(x, y)$ be a bivariate polynomial with coefficients in $\mathbb{C}$. Form the $n \times n$ matrices $L_n$ whose elements are defined by $P(i, j)$. Define the matrices $M_n = I_n - L_n $. We show that $\mu_n = \det(M_n)$ is a polynomial in $n$, thus answering a conjecture of Naccache and Yifrach.
ZEBRA is an Anonymous Credential (AC) scheme, supporting auditability and revocation, that provides practical on-chain verification for the first time. It realizes efficient access control on permissionless blockchains while achieving both privacy and accountability. In all prior solutions, users either pay exorbitant fees or lose privacy since authorities granting access can map users to their wallets. Hence, ZEBRA is the first to enable DeFi platforms to remain compliant with imminent regulations without compromising user privacy. We evaluate ZEBRA and show that it reduces the gas cost incurred on the Ethereum Virtual Machine (EVM) by 11.8x when compared to Coconut [NDSS 2019], the state-of-the-art AC scheme for blockchains. This translates to a reduction in transaction fees from 94 USD to 8 USD on Ethereum in August 2022. However, 8 USD is still high for most applications, and ZEBRA further drives down credential verification costs through batched verification. For a batch of 512 layer-1 and layer-2 wallets, the gas cost is reduced by 35x and 641x on EVM, and the transaction fee is reduced to just 0.23 USD and 0.0126 USD on Ethereum, respectively. For perspective, these costs are comparable to the minimum transaction costs on Ethereum.
Registration-based encryption (Garg, Hajiabadi, Mahmoody, Rahimi, TCC'18) aims to offer what identity-based encryption offers without the key-escrow problem, which refers to the ability of the private-key generator to obtain parties' decryption keys at wish. In RBE, parties generate their own secret and public keys and register their public keys to the key curator (KC) who updates a compact public parameter after each registration. The updated public parameter can then be used to securely encrypt messages to registered identities. A major drawback of RBE, compared with IBE, is that in order to decrypt, parties might need to periodically request so-called decryption updates from the KC. Current RBE schemes require $\Omega(\log n)$ number of updates after $n$ registrations, while the public parameter is of length $\text{poly}(\log n)$. Clearly, it would be highly desirable to have RBEs with only, say, a constant number of updates. This leads to the following natural question: are so many (logarithmic) updates necessary for RBE schemes, or can we decrease the frequency of updates significantly? In this paper, we prove an almost tight lower bound for the number of updates in RBE schemes, as long as the times that parties receive updates only depend on the registration time of the parties, which is a natural property that holds for all known RBE constructions. More generally, we prove a trade-off between the number of updates in RBEs and the length of the public parameter for any scheme with fixed update times. Indeed, we prove that for any such RBE scheme, if there are $n \geq \binom{k+d}{d+1}$ identities that receive at most $d$ updates, the public parameter needs to be of length $\Omega(k)$. As a corollary, we find that RBE systems with fixed update times and public parameters of length $\text{poly} (\log n)$, require $\Omega(\log n/\text{loglog}\ n)$ decryption updates, which is optimal up to a $O(\text{loglog}\ n)$ factor.
We propose a novel variant of functional encryption which supports ciphertext updates, dubbed ciphertext updatable functional encryption (CUFE). Such a feature further broadens the practical applicability of the functional encryption paradigm and is carried out via so-called update tokens. However, allowing update tokens requires some care for the security definition as we want that updates can be done by any semi-trusted third party and only on ciphertexts. Our contribution is three-fold: a) We define our new primitive with a security notion in the indistinguishability setting. Within CUFE, functional decryption keys and ciphertexts are labeled with tags such that only if the tag of the decryption key and the ciphertext match, then decryption succeeds. Furthermore, we allow ciphertexts to switch their tags to any other tag via update tokens. Such tokens are generated by the holder of the main secret key and can only be used in the desired direction. b) We present a generic construction of CUFE for any functionality as well as predicates different from equality testing on tags, which relies on the existence of (probabilistic) indistinguishability obfuscation (iO). c) We present a practical construction of CUFE for the inner-product functionality from standard assumptions (i.e., LWE) in the random-oracle model. On the technical level, we build on the recent functional encryption schemes with fine-grained access control and linear operations on encrypted data (Abdalla et al., AC'20) and introduce an additional ciphertext updatability feature. Proving security for such a construction turned out to be non-trivial, particularly when revealing keys for the updated challenge ciphertext is allowed. Overall, such construction enriches the set of known inner-product functional-encryption schemes with the additional updatability feature of ciphertexts.
This note describes the implementation of the Castryck-Decru key recovery attack on SIDH using the computer algebra system, SageMath. We describe in detail alternate computation methods for the isogeny steps of the original attack ($(2,2)$-isogenies from a product of elliptic curves and from a Jacobian), using explicit formulas to compute values of these isogenies at given points, motivated by both performance considerations and working around SageMath limitations. A performance analysis is provided, with focus given to the various algorithmic and SageMath specific improvements made during development, which in total accumulated in approximately an eight-fold performance improvement compared with a naïve reimplementation of the proof of concept.
Recent works on key rank estimation methods claim that algorithmic key rank estimation is too slow, and suggest two new ideas: replacing repeat attacks with simulated attacks (PS-TH-GE rank estimation), and a shortcut rank estimation method that works directly on distinguishing vector distributions (GEEA). We take these ideas and provide a comprehensive comparison between them and a performant implementation of a classical, algorithmic ranking approach, as well as some earlier work on estimating distinguisher distributions. Our results show, in contrast to the recent work, that the algorithmic ranking approach outperforms GEEA, and that simulation based ranks are unreliable.
Vehicle-to-everything (V2X) communication is the key enabler for emerging intelligent transportation systems. Applications built on top of V2X require both authentication and privacy protection for the vehicles. The common approach to meet both requirements is to use pseudonyms which are short-term identities. However, both industrial standards and state-of-the-art research are not designed for resource-constrained environments. In addition, they make a strong assumption about the security of the vehicle's on-board computation units. In this paper, we propose a lightweight auto-refreshing pseudonym protocol LARP for V2X. LARP supports efficient operations for resource-constrained devices, and provides security even when parts of the vehicle are compromised. We provide formal security proof showing that the protocol is secure. We conduct experiments on a Raspberry Pi 4. The results demonstrate that LARP is feasible and practical.
Time-based One-Time Password (TOTP) provides a strong second factor for user authentication. In TOTP, a prover authenticates to a verifier by using the current time and a secret key to generate an authentication token (or password) which is valid for a short time period. Our goal is to extend TOTP to the group setting, and to provide both authentication and privacy. To this end, we introduce a new authentication scheme, called Group TOTP (GTOTP), that allows the prover to prove that it is a member of an authenticated group without revealing its identity. We propose a novel construction that transforms any asymmetric TOTP scheme into a GTOTP scheme. Our approach combines Merkle tree and Bloom filter to reduce the verifier's states to constant sizes. As a promising application of GTOTP, we show that GTOTP can be used to construct an efficient privacy-preserving Proof of Location (PoL) scheme. We utilize a commitment protocol, a privacy-preserving location proximity scheme, and our GTOTP scheme to build the PoL scheme, in which GTOTP is used not only for user authentication but also as a tool to glue up other building blocks. In the PoL scheme, with the help of some witnesses, a user can prove its location to a verifier, while ensuring the identity and location privacy of both the prover and witnesses. Our PoL scheme outperforms the alternatives based on group digital signatures. We evaluate our schemes on Raspberry Pi hardware, and demonstrate that they achieve practical performance. In particular, the password generation and verification time are in the order of microseconds and milliseconds, respectively, while the computation time of proof generation is less than $1$ second.
In CRYPTO 2019, Gohr successfully applied deep learning to differential cryptanalysis against the NSA block cipher Speck32/64, achieving higher accuracy than traditional differential distinguishers. Until now, the improvement of neural differential distinguishers is a mainstream research direction in neuralaided cryptanalysis. But the current development of training data formats for neural distinguishers forms barriers: (1) The source of data features is limited to linear combinations of ciphertexts, which does not provide more learnable features to the training samples for improving the neural distinguishers. (2) Lacking breakthroughs in constructing data format for network training from the deep learning perspective. In this paper, considering both the domain knowledge about deep learning and information on differential cryptanalysis, we use the output features of the penultimate round to proposing a two-dimensional and non-realistic input data generation method of neural differential distinguishers. Then, we validate that the proposed new input data format has excellent features through experiments and theoretical analysis. Moreover, combining the idea of multiple ciphertext pairs, we generate two specific models for data input construction: MRMSP(Multiple Rounds Multiple Splicing Pairs) and MRMSD(Multiple Rounds Multiple Splicing Differences) and then build new neural distinguishers against Speck and Simon family, which effectively improve the performance compared with the previous works. To the best of our knowledge, our neural distinguishers achieve the longest rounds and the higher accuracy for NSA block ciphers Speck and Simon.
Garbling schemes, a formalization of Yao's garbled circuit protocol, are useful cryptographic primitives both in privacy-preserving protocols and for secure two-party computation. In projective garbling schemes, $n$ values are assigned to each wire in the circuit. Current state-of-the-art schemes project two values. More concretely, we present a projective garbling scheme that assigns $2^n$ values to wires in a circuit comprising XOR and unary projection gates. A generalization of FreeXOR allows the XOR of wires with $2^n$ values to be very efficient. We then analyze the performance of our scheme by evaluating substitution-permutation ciphers. Using our proposal, we measure high-speed evaluation of the ciphers with a moderate increased cost in garbling and bandwidth. Theoretical analysis suggests that for evaluating the nine examined ciphers, one can expect a 4- to 70-fold increase in evaluation with at most a 4-fold increase in garbling cost and, at most, an 8-fold increase in communication cost when compared to state-of-the-art garbling schemes. In an offline/online setting, such as secure function evaluation as a service, the circuit garbling and communication to the evaluator can proceed before the input phase. Thus our scheme offers a fast online phase. Furthermore, we present efficient computation formulas for the S-boxes of TWINE and Midori64 in Boolean circuits. To our knowledge, our formulas give the smallest number of AND gates for the S-boxes of these two ciphers.
Classic McEliece is a code-based quantum-resistant public-key scheme characterized with relative high encapsulation/decapsulation speed and small cipher- texts, with an in-depth analysis on its security. However, slow key generation with large public key size make it hard for wider applications. Based on this observation, a high-throughput key generator in hardware, is proposed to accelerate the key generation in Classic McEliece based on algorithm-hardware co-design. Meanwhile the storage overhead caused by large-size keys is also minimized. First, compact large-size GF(2) Gauss elimination is presented by adopting naive processing array, singular matrix detection-based early abort, and memory-friendly scheduling strategy. Second, an optimized constant-time hardware sorter is proposed to support regular memory accesses with less comparators and storage. Third, algorithm-level pipeline is enabled for high-throughput processing, allowing for concurrent key generation based on decoupling between data access and computation.
In this paper, we introduce a second-order masking of the AES using the minimal number of shares and a total of 1268 bits of randomness including the sharing of the plaintext and key. The masking of the S-box is based on the tower field decomposition of the inversion over bytes where the changing of the guards technique is used in order to re-mask the middle branch of the decomposition. The sharing of the S-box is carefully crafted such that it achieves first-order probing security without the use of randomness and such that the sharing of its output is uniform. Multi-round security is achieved by re-masking the state where we use a theoretical analysis based on the propagation of probed information to reduce the demand for fresh randomness per round. The result is a second-order masked AES which competes with the state-of-the-art in terms of latency and area, but reduces the randomness complexity over eight times over the previous known works. In addition to the corresponding theoretical analysis and proofs for the security of our masked design, it has been implemented on FPGA and evaluated via lab analysis.
The notion of distributed authenticated encryption was formally introduced by Agrawal et al. in ACM CCS 2018. In their work, they propose the DiSE construction building upon a distributed PRF (DPRF), a commitment scheme and a PRG. We show that most of their constructions do not meet some of the claimed security guarantees. In fact, all the concrete instantiations of DiSE, as well as multiple follow-up papers (one accepted at ACM CCS 2021), fail to satisfy their strongly-secure definitions. We give simple fixes for these constructions and prove their security. We also propose a new construction DiAE using an encryptment instead of a commitment. This modification dispenses with the need to buffer the entire message throughout the encryption protocol, which in turn enables implementations with constant RAM footprint and online message encryption. This is particularly interesting for constrained IoT devices. Finally, we implement and benchmark DiAE and show that it performs similarly to the original DiSE construction.
The question whether one way functions (i.e., functions that are easy to compute but hard to invert) exist is arguably one of the central problems in complexity theory, both from theoretical and practical aspects. While proving that such functions exist could be hard, there were quite a few attempts to provide functions which are one way "in practice", namely, they are easy to compute, but there are no known polynomial time algorithms that compute their (generalized) inverse (or that computing their inverse is as hard as notoriously difficult tasks, like factoring very large integers). In this paper we study a different approach. We provide a simple heuristic, called self masking, which converts a given polynomial time computable function $f$ into a self masked version $[{f}]$, which satisfies the following: for a random input $x$, $[{f}]^{-1}([{f}](x))=f^{-1}(f(x))$ w.h.p., but a part of $f(x)$, which is essential for computing $f^{-1}(f(x))$ is masked in $[{f}](x)$. Intuitively, this masking makes it hard to convert an efficient algorithm which computes $f^{-1}$ to an efficient algorithm which computes $[{f}]^{-1}$, since the masked parts are available to $f$ but not to $[{f}]$. We apply this technique on variants of the subset sum problem which were studied in the context of one way functions, and obtain functions which, to the best of our knowledge, cannot be inverted in polynomial time by published techniques.
This note describes an observation discovered during a failed cryptanalysis attempt. Let $P(x,y)$ be a bivariate polynomial with coefficients in $\mathbb{C}$. Form the $n\times n$ matrices $L(n)$ whose elements are defined by $P(i,j)$. Define the matrices $M(n)=L(n)-\mbox{ID}_n$. It appears that $\mu(n)=(-1)^n\det(M_n)$ is a polynomial in $n$ that we did not characterize. We provide a numerical example.
One of the most fundamental results in game theory is that every finite strategic game has a Nash equilibrium, an assignment of (randomized) strategies to players with the stability property that no individual player can benefit from deviating from the assigned strategy. It is not known how to efficiently compute such a Nash equilibrium --- the computational complexity of this task is characterized by the class PPAD, but the relation of PPAD to other problems and well-known complexity classes is not precisely understood. In recent years there has been mounting evidence, based on cryptographic tools and techniques, showing the hardness of PPAD. We continue this line of research by showing that PPAD is as hard as learning with errors (LWE) and the iterated squaring (IS) problem, two standard problems in cryptography. Our work improves over prior hardness results that relied either on (1) sub-exponential assumptions, or (2) relied on ``obfustopia,'' which can currently be based on a particular combination of three assumptions. Our work additionally establishes public-coin hardness for PPAD (computational hardness for a publicly sampleable distribution of instances) that seems out of reach of the obfustopia approach. Following the work of Choudhuri et al. (STOC 2019) and subsequent works, our hardness result is obtained by constructing an unambiguous and incrementally-updatable succinct non-interactive argument for IS, whose soundness relies on polynomial hardness of LWE. The result also implies a verifiable delay function with unique proofs, which may be of independent interest.
Modern SVD computation dates back to work in the 1960s that proposed the basis for the eigensystem package and linear algebra package routines. As a result of a long history of research, SVD is now widely applied in various scenarios, such as recommendation system and principal component analysis. Furthermore, federated SVD has emerged as a prevalent privacy-preserving technique. For example, the raw data are not required to be exchanged among different parties; instead, each party trains and processes locally and shares intermediate result. In general, there are two main categories: SVD over horizontally and vertically partitioned data. Imagine a dataset matrix M, where each row stands for a record from a data subject, and the columns stand for the attributes/features of the records. In the horizontally partitioned setting, each party holds a disjoint subset of the rows of M. While in the vertically partitioned setting, each party has a disjoint subset of the columns of M for all the rows. In real-world applications, the horizontally partitioned setting is much more common than the vertically partitioned setting. In this paper, we have proposed a privacy-preserving federated SVD scheme with secure aggregation. The proposed scheme can aggregate SVD results (eigenspace) from different devices and synchronise the aggregation result with all devices while maintaining privacy protection.
The current gold standard of cryptographic software is to write efficient libraries with systematic protections against timing attacks. In order to meet this goal, cryptographic engineers increasingly use high-assurance cryptography tools. These tools guide programmers and provide rigorous guarantees that can be verified independently by library users. However, high-assurance tools reason about overly simple execution models that elide micro-architectural leakage. Thus, implementations validated by high-assurance cryptography tools remain potentially vulnerable to micro-architectural attacks such as Spectre or Meltdown. Moreover, proposed countermeasures are not used in practice due to performance overhead. We propose, analyze, implement and evaluate an approach for writing efficient cryptographic implementations that are protected against Spectre v1 attacks. Our approach ensures speculative constant-time, an information flow property which guarantees that programs are protected against Spectre v1. Speculative constant-time is enforced by means of a (value-dependent) information flow type system. The type system tracks security levels depending on whether execution is misspeculating. We implement our approach in the Jasmin framework for high assurance cryptography, and use it for protecting all implementations of an experimental cryptographic library that includes highly optimized implementations of symmetric primitives, of elliptic-curve cryptography, and of Kyber, a lattice-based KEM recently selected by NIST for standardization. The performance impact of our protections is very low; for example, less than 1% for Kyber and essentially zero for X25519.
In recent years, functional encryption (FE) has established itself as one of the fundamental primitives in cryptography. The choice of model of computation to represent the functions associated with the functional keys plays a critical role in the complexity of the algorithms of an FE scheme. Historically, the functions are represented as circuits. However, this results in the decryption time of the FE scheme growing proportional to not only the worst case running time of the function but also the size of the input, which in many applications can be quite large. In this work, we present the first construction of a public-key collusion-resistant FE scheme, where the functions, associated with the keys, are represented as random access machines (RAMs). We base the security of our construction on the existence of: (i) public-key collusion- resistant FE for circuits and, (ii) public-key doubly-efficient private-information retrieval [Boyle et al., Canetti et al., TCC 2017]. Our scheme enjoys many nice efficiency properties, including input-specific decryption time. We also show how to achieve FE for RAMs in the bounded-key setting with weaker efficiency guarantees from laconic oblivious transfer, which can be based on standard cryptographic assumptions. En route to achieving our result, we present conceptually simpler constructions of succinct garbling for RAMs [Canetti et al., Chen et al., ITCS 2016] from weaker assumptions.
In this paper, we follow the line of existing study on cryptographic enforcement of Role-Based Access Control (RBAC). Inspired by the study of the relation between the existing security definitions for such system, we identify two different types of attacks which cannot be captured by the existing ones. Therefore, we propose two new security definitions towards the goal of appropriately modelling cryptographic enforcement of Role-Based Access Control policies and study the relation between our new definitions and the existing ones. In addition, we show that the cost of supporting dynamic policy update is inherently expensive by presenting two lower bounds for such systems which guarantee correctness and secure access.
In most homomorphic encryption schemes based on the RLWE, the native plaintexts are represented as polynomials in a ring $Z_t[x]/x^N+1$ where $t$ is a plaintext modulus and $x^N+1$ is a cyclotomic polynomial with degree power of two. An encoding scheme should be used to transform some natural data types(such as integers and rational numbers) into polynomials in the ring. After a homomorphic computation on the polynomial is finished, the decoding procedure is invoked to obtain the result. However, conditions for decoding correctly are strict in a way. For example, the overflows of computation modulo both the plaintext modulus $t$ and the cyclotomic polynomial $x^N+1$ will result in a unexpected result for decoding. The reason is that decoding the part which is discarded by modular reduction is not 0. We combine number theory transformation with Hensel Codes to construct a scheme. Intuitively, decoding the discarded part will yield 0 so the limitations are overcome naturally in our scheme. On the other hand, rational numbers can be handled with high precision in parallel.
Broadcast is an essential primitive for secure computation. We focus in this paper on optimal resilience (i.e., when the number of corrupted parties $t$ is less than a third of the computing parties $n$), and with no setup or cryptographic assumptions. While broadcast with worst case $t$ rounds is impossible, it has been shown [Feldman and Micali STOC'88, Katz and Koo CRYPTO'06] how to construct protocols with expected constant number of rounds in the private channel model. However, those constructions have large communication complexity, specifically $\mathcal{O}(n^2L+n^6\log n)$ expected number of bits transmitted for broadcasting a message of length $L$. This leads to a significant communication blowup in secure computation protocols in this setting. In this paper, we substantially improve the communication complexity of broadcast in constant expected time. Specifically, the expected communication complexity of our protocol is $\mathcal{O}(nL+n^4\log n)$. For messages of length $L=\Omega(n^3 \log n)$, our broadcast has no asymptotic overhead (up to expectation), as each party has to send or receive $\mathcal{O}(n^3 \log n)$ bits. We also consider parallel broadcast, where $n$ parties wish to broadcast $L$ bit messages in parallel. Our protocol has no asymptotic overhead for $L=\Omega(n^2\log n)$, which is a common communication pattern in perfectly secure MPC protocols. For instance, it is common that all parties share their inputs simultaneously at the same round, and verifiable secret sharing protocols require the dealer to broadcast a total of $\mathcal{O}(n^2\log n)$ bits. As an independent interest, our broadcast is achieved by a packed verifiable secret sharing, a new notion that we introduce. We show a protocol that verifies $\mathcal{O}(n)$ secrets simultaneously with the same cost of verifying just a single secret. This improves by a factor of $n$ the state-of-the-art.
Ring signatures allow a user to sign messages on behalf of an ad hoc set of users - a ring - while hiding her identity. The original motivation for ring signatures was whistleblowing [Rivest et al. ASIACRYPT'01]: a high government employee can anonymously leak sensitive information while certifying that it comes from a reliable source, namely by signing the leak. However, essentially all known ring signature schemes require the members of the ring to publish a structured verification key that is compatible with the scheme. This creates somewhat of a paradox since, if a user does not want to be framed for whistleblowing, they will stay clear of signature schemes that support ring signatures. In this work, we formalize the concept of universal ring signatures (URS). A URS enables a user to issue a ring signature with respect to a ring of users, independently of the signature schemes they are using. In particular, none of the verification keys in the ring need to come from the same scheme. Thus, in principle, URS presents an effective solution for whistleblowing. The main goal of this work is to study the feasibility of URS, especially in the standard model (i.e. no random oracles or common reference strings). We present several constructions of URS, offering different trade-offs between assumptions required, the level of security achieved, and the size of signatures: * Our first construction is based on superpolynomial hardness assumptions of standard primitives. It achieves compact signatures. That means the size of a signature depends only logarithmically on the size of the ring and on the number of signature schemes involved. * We then proceed to study the feasibility of constructing URS from standard polynomially-hard assumptions only. We construct a non-compact URS from witness encryption and additional standard assumptions. * Finally, we show how to modify the non-compact construction into a compact one by relying on indistinguishability obfuscation.
Key Transparency (KT) systems allow end-to-end encrypted service providers (messaging, calls, etc.) to maintain an auditable directory of their users’ public keys, producing proofs that all participants have a consistent view of those keys, and allowing each user to check updates to their own keys. KT has lately received a lot of attention, in particular its privacy preserving variants, which also ensure that users and auditors do not learn anything beyond what is necessary to use the service and keep the service provider accountable. Abstractly, the problem of building such systems reduces to constructing so-called append-only Zero-Knowledge Sets (aZKS). Unfortunately, existing aZKS (and KT) solutions do not allow to adequately restore the privacy guarantees after a server compromise, a form of Post-Compromise Security (PCS), while maintaining the auditability properties. In this work we address this concern through the formalization of an extension of aZKS called Rotatable ZKS (RZKS). In addition to providing PCS, our notion of RZKS has several other attractive features, such as a stronger (extractable) soundness notion, and the ability for a communication party with out-of-date data to efficiently “catch up” to the current epoch while ensuring that the server did not erase any of the past data. Of independent interest, we also introduce a new primitive called a Rotatable Verifiable Random Function (VRF), and show how to build RZKS in a modular fashion from a rotatable VRF, ordered accumulator, and append-only vector commitment schemes.
We revisit the well-studied problem of preventing steganographic communication in multi-party communications. While this is known to be a provably impossible task, we propose a new model that allows circumventing this impossibility. In our model, the parties first publish a single message during an honest non-interactive pre-processing phase and then later interact in an execution phase. We show that in this model, it is indeed possible to prevent any steganographic communication in zero-knowledge protocols. Our solutions rely on standard cryptographic assumptions.
This paper studies Batch Private Information Retrieval (BatchPIR), a variant of private information retrieval (PIR) where the client wants to retrieve multiple entries from the server in one batch. BatchPIR matches the use case of many practical applications and holds the potential for substantial efficiency improvements over PIR in terms of amortized cost per query. Existing BatchPIR schemes have achieved decent computation efficiency but have not been able to improve communication efficiency at all. In this paper, we present the first BatchPIR protocol that is efficient in both computation and communication for a variety of database configurations. Specifically, to retrieve a batch of 256 entries from a database with one million entries of 256 bytes each, the communication cost of our scheme is 7.2$\sim$75x better than state-of-the-art solutions.
We investigate the relationship between the classical RSA and factoring problems when preprocessing is considered. In such a model, adversaries can use an unbounded amount of precomputation to produce an "advice" string to then use during the online phase, when a problem instance becomes known. Previous work (e.g., [Bernstein, Lange ASIACRYPT '13]) has shown that preprocessing attacks significantly improve the runtime of the best-known factoring algorithms. Due to these improvements, we ask whether the relationship between factoring and RSA fundamentally changes when preprocessing is allowed. Specifically, we investigate whether there is a superpolynomial gap between the runtime of the best attack on RSA with preprocessing and on factoring with preprocessing. Our main result rules this out with respect to algorithms in a natural adaptation of the generic ring model to the preprocessing setting. In particular, in this setting we show the existence of a factoring algorithm (albeit in the random oracle model) with polynomially related parameters, for any setting of RSA parameters.
We provide a strong definition for committing authenticated-encryption (cAE), as well as a framework that encompasses earlier and weaker definitions. The framework attends not only to what is committed but also the extent to which the adversary knows or controls keys. We slot into our framework strengthened cAE-attacks on GCM and OCB. Our main result is a simple and efficient construction, CTX, that makes a nonce-based AE (nAE) scheme committing. The transformed scheme achieves the strongest security notion in our framework. Just the same, the added computational cost (on top of the nAE scheme's cost) is a single hash over a short string, a cost independent of the plaintext's length. And there is no increase in ciphertext length compared to the base nAE scheme. That such a thing is possible, let alone easy, upends the (incorrect) intuition that you can't commit to a plaintext or ciphertext without hashing one or the other. And it motivates a simple and practical tweak to AE-schemes to make them committing.
We address three main open problems concerning the use of radical isogenies, as presented by Castryck, Decru and Vercauteren at Asiacrypt 2020, in the computation of long chains of isogenies of fixed, small degree between elliptic curves over finite fields. Firstly, we present an interpolation method for finding radical isogeny formulae in a given degree $N$, which by-passes the need for factoring division polynomials over large function fields. Using this method, we are able to push the range for which we have formulae at our disposal from $N \leq 13$ to $N \leq 37$ (where in the range $18 \leq N \leq 37$ we have restricted our attention to prime powers). Secondly, using a combination of known techniques and ad-hoc manipulations, we derive optimized versions of these formulae for $N \leq 19$, with some instances performing more than twice as fast as their counterparts from 2020. Thirdly, we solve the problem of understanding the correct choice of radical when walking along the surface between supersingular elliptic curves over $\mathbb{F}_p$ with $p \equiv 7 \bmod 8$; this is non-trivial for even $N$ and was settled for $N = 2$ and $N = 4$ only, in the latter case by Onuki and Moriya at PKC 2022. We give a conjectural statement for all even $N$ and prove it for $N \leq 14$. The speed-ups obtained from these techniques are substantial: using $16$-isogenies, the computation of long chains of $2$-isogenies over $512$-bit prime fields can be accelerated by a factor $3$, and the previous implementation of CSIDH using radical isogenies can be sped up by about $12\%$.
We define the security notion of (strong) collision resistance for chameleon hash functions in the multi-user setting ((S-)MU-CR security). We also present three constructions, CHF_dl, CHF_rsa and CHF_fac, and prove their tight S-MU-CR security based on the discrete logarithm, RSA and factoring assumptions, respectively. In applications, our tightly S-MU-CR secure chameleon hash functions help us to lift a signature scheme from (weak) unforgeability to strong unforgeability in the multi-user setting, and the security reduction is tightness preserving. Furthermore, they can also be used to construct tightly secure online/offline signatures, chameleon signatures and proxy signatures, etc., in the multi-user setting.
One-time programs, originally formulated by Goldwasser et al. [CRYPTO'08], are a powerful cryptographic primitive with compelling applications. Known solutions for one-time programs, however, require specialized secure hardware that is not widely available (or, alternatively, access to blockchains and very strong cryptographic tools). In this work we investigate the possibility of realizing one-time programs from a recent and now more commonly available hardware functionality: the counter lockbox. A counter lockbox is a stateful functionality that protects an encryption key under a user-specified password, and enforces a limited number of incorrect guesses. Counter lockboxes have become widely available in consumer devices and cloud platforms. We show that counter lockboxes can be used to realize one-time programs for general functionalities. We develop a number of techniques to reduce the number of counter lockboxes required for our constructions, that may be of independent interest.
Homomorphic encryption (HE) has opened an entirely new world up in the privacy-preserving use of sensitive data by conducting computations on encrypted data. Amongst many HE schemes targeting computation in various contexts, Cheon--Kim--Kim--Song (CKKS) scheme is distinguished since it allows computations for encrypted real number data, which have greater impact in real-world applications. CKKS scheme is a levelled homomorphic encryption scheme, consuming one level for each homomorphic multiplication. When the level runs out, a special computational circuit called bootstrapping is required in order to conduct further multiplications. The algorithm proposed by Cheon et al. has been regarded as a standard way to do bootstrapping in the CKKS scheme, and it consists of the following four steps: ModRaise, CoeffToSlot, EvalMod and SlotToCoeff. However, the steps consume a number of levels themselves, and thus optimizing this extra consumption has been a major focus of the series of recent research. Among the total levels consumed in the bootstrapping steps, about a half of them is spent in CoeffToSlot and SlotToCoeff steps to scale up the real number components of DFT matrices and round them to the nearest integers. Each scale-up factor is very large so that it takes up one level to rescale it down. Scale-up factors can be taken smaller to save levels, but the error of rounding would be transmitted to EvalMod and eventually corrupt the accuracy of bootstrapping. EvalMod aims to get rid of the superfluous $qI$ term from a plaintext $pt + qI$ resulting from ModRaise, where $q$ is the bottom modulus and $I$ is a polynomial with small integer coefficients. EvalRound is referred to as its opposite, obtaining $qI$. We introduce a novel bootstrapping algorithm consisting of ModRaise, CoeffToSlot, EvalRound and SlotToCoeff, which yields taking smaller scale-up factors without the damage of rounding errors.
ZK-SNARKs (Zero Knowledge Succinct Noninteractive ARguments of Knowledge) are one of the most promising new applied cryptography tools: proofs allow anyone to prove a property about some data, without revealing that data. Largely spurred by the adoption of cryptographic primitives in blockchain systems, ZK-SNARKs are rapidly becoming computationally practical in real-world settings, shown by i.e. tornado.cash and rollups. These have enabled ideation for new identity applications based on anonymous proof-of-ownership. One of the primary technologies that would enable the jump from existing apps to such systems is the development of deterministic nullifiers. Nullifiers are used as a public commitment to a specific anonymous account, to forbid actions like double spending, or allow a consistent identity between anonymous actions. We identify a new deterministic signature algorithm that both uniquely identifies the keypair, and keeps the account identity secret. In this work, we will define the full DDH-VRF construction, and prove uniqueness, secrecy, and existential unforgeability. We will also demonstrate a proof of concept of the nullifier.
The Montgomery Ladder is widely used for implementing the scalar multiplication in elliptic curve cryptographic designs. This algorithm is efficient and provides a natural robustness against (simple) side-channel attacks. Previous works however showed that implementations of the Montgomery Ladder using Lopez-Dahab projective coordinates easily leak the value of the most significant bits of the secret scalar, which led to a full key recovery in an attack known as LadderLeak. In light of such leakage, we analyse further popular methods for implementing the Montgomery Ladder. We first consider open source software implementations of the X25519 protocol which implement the Montgomery Ladder based on the ladderstep algorithm from Düll et al. [15]. We confirm via power measurements that these implementations also easily leak the most significant scalar bits, even when implementing Z-coordinate ran- domisations. We thus propose simple modifications of the algorithm and its handling of the most significant bits and show the effectiveness of our modifications via experimental results. Particularly, our re-designs of the algorithm do not incurring significant efficiency penalties. As a second case study, we consider open source hardware implementations of the Montgomery Ladder based on the complete addition formulas for prime order elliptic curves, where we observe the exact same leakage. As we explain, the most significant bits in implementations of the complete addition formulas can be protected in an analogous way as we do for Curve25519 in our first case study.
Incompressibility is one of the most fundamental security goals in white-box cryptography. Given recent advances in the design of efficient and incompressible block ciphers such as SPACE, SPNbox and WhiteBlock, we demonstrate the feasibility of reducing incompressible AEAD modes to incompressible block ciphers. We first observe that several existing AEAD modes of operation, including CCM, GCM(-SIV), and OCB, would be all insecure against white-box adversaries even when used with an incompressble block cipher. This motivates us to revisit and formalize incompressibility-based security definitions for AEAD schemes and for block ciphers, so that we become able to design modes and reduce their security to that of the underlying ciphers. Our new security notion for AEAD, which we name whPRI, is an extension of the pseudo-random injection security in the black-box setting. Similar security notions are also defined for other cryptosystems such as privacy-only encryption schemes. We emphasize that whPRI ensures quite strong authenticity against white-box adversaries: existential unforgeability beyond leakage. This contrasts sharply with previous notions which have ensured either no authenticity or only universal unforgeability. For the underlying ciphers we introduce a new notion of whPRP, which extends that of PRP in the black-box setting. Interestingly, our incompressibility reductions follow from a variant of public indifferentiability. In particular, we show that a practical whPRI-secure AEAD mode can be built from a whPRP-secure block cipher: We present a SIV-like composition of the sponge construction (utilizing a block cipher as its underlying primitive) with the counter mode and prove that such a construction is (in the variant sense) public indifferentiable from a random injection. To instantiate such an AEAD scheme, we propose a 256-bit variant of SPACE, based on our conjecture that SPACE should be a whPRP-secure cipher.
Secure software leasing is a quantum cryptographic primitive that enables us to lease software to a user by encoding it into a quantum state. Secure software leasing has a mechanism that verifies whether a returned software is valid or not. The security notion guarantees that once a user returns a software in a valid form, the user no longer uses the software. In this work, we introduce the notion of secret-key functional encryption (SKFE) with secure key leasing, where a decryption key can be securely leased in the sense of secure software leasing. We also instantiate it with standard cryptographic assumptions. More specifically, our contribution is as follows. - We define the syntax and security definitions for SKFE with secure key leasing. - We achieve a transformation from standard SKFE into SKFE with secure key leasing without using additional assumptions. Especially, we obtain bounded collusion-resistant SKFE for $\mathsf{P/poly}$ with secure key leasing based on post-quantum one-way functions since we can instantiate bounded collusion-resistant SKFE for $\mathsf{P/poly}$ with the assumption. Some previous secure software leasing schemes capture only pirate software that runs on an honest evaluation algorithm (on a legitimate platform). However, our secure key leasing notion captures arbitrary attack strategies and does not have such a limitation. As an additional contribution, we introduce the notion of single-decryptor FE (SDFE), where each functional decryption key is copy-protected. Since copy-protection is a stronger primitive than secure software leasing, this notion can be seen as a stronger cryptographic primitive than FE with secure key leasing. More specifically, our additional contribution is as follows. - We define the syntax and security definitions for SDFE. - We achieve collusion-resistant single-decryptor PKFE for $\mathsf{P/poly}$ from post-quantum indistinguishability obfuscation and quantum hardness of the learning with errors problem.
We propose Flashproofs, a new type of efficient special honest verifier zero-knowledge arguments with a transparent setup in the discrete logarithm (DL) setting. First, we put forth gas-efficient range arguments that achieve $O(N^{\frac{2}{3}})$ communication cost, and involve $O(N^{\frac{2}{3}})$ group exponentiations for verification and a slightly sub-linear number of group exponentiations for proving with respect to the range $[0, 2^N-1]$, where $N$ is the bit length of the range. For typical confidential transactions on blockchain platforms supporting smart contracts, verifying our range arguments consumes only 237K and 318K gas for 32-bit and 64-bit ranges, which are comparable to 220K gas incurred by verifying the most efficient zkSNARK with a trusted setup (EUROCRYPT 16) at present. Besides, the aggregation of multiple arguments can yield further efficiency improvement. Second, we present polynomial evaluation arguments based on the techniques of Bayer & Groth (EUROCRYPT 13). We provide two zero-knowledge arguments, which are optimised for lower-degree ($D \in [3, 2^9]$) and higher-degree ($D > 2^9$) polynomials, where $D$ is the polynomial degree. Our arguments yield a non-trivial improvement in the overall efficiency. Notably, the number of group exponentiations for proving drops from $8\log D$ to $3(\log D+\sqrt{\log D})$. The communication cost and the number of group exponentiations for verification decrease from $7\log D$ to $(\log D + 3\sqrt{\log D})$. To the best of our knowledge, our arguments instantiate the most communication-efficient arguments of membership and non-membership in the DL setting among those not requiring trusted setups. More importantly, our techniques enable a significantly asymptotic improvement in the efficiency of communication and verification (group exponentiations) from $O(\log D)$ to $O(\sqrt{\log D})$ when multiple arguments satisfying different polynomials with the same degree and inputs are aggregated.
Differential Privacy (DP) is one of the gold standards of privacy. Nonetheless, when one is interested in mechanisms with theoretical guarantees, one has to either choose from a relatively small pallet of generic mechanisms, like Laplacian, Gaussian, and exponential, or develop a new, problem-specific mechanism and analyze its privacy. This makes it challenging for non-experts in security to utilize DP for preserving privacy in complex tasks in areas like machine learning, data science, and medicine, which are primary application domains of DP. Our work aims to address the above limitation. In a nutshell we devise a methodology for domain experts with limited knowledge of security to estimate the (differential) privacy of an arbitrary mechanism. Our Eureka moment is the utilization of a link---which we prove---between the problems of DP parameter-estimation and Bayes optimal classifiers in machine learning, which we believe can be of independent interest. Our estimator methodology uses this link to achieve two desirable properties: (1) it is black-box, i.e., does not require knowledge of the underlying mechanism, and (2) it has a theoretically-proven accuracy, which depends on the underlying classifier used. This allows domain experts to design mechanisms that they conjecture offer certain (differential) privacy guarantees---but maybe cannot prove it---and apply our method to confirm (or disprove) their conjecture. More concretely, we first prove a new impossibility result, stating that for the classical DP notion there is no black-box poly-time estimator of $(\epsilon,\delta)$-DP. This motivates a natural relaxation of DP, which we term relative DP. Relative DP preserves the desirable properties of DP---composition, robustness to post processing, and robustness to the discovery disclosure of new data---and applies in most practical settings where privacy is desired. We then devise a black-box poly-time $(\epsilon,\delta)$-relative DP estimator---the first to support mechanisms with large output spaces while having tight accuracy bounds. As a result of independent interest, we apply this theory to develop the first approximate estimator for the standard, i.e., non-relative, definition of Distributional Differential Privacy (DDP) -- aka noiseless privacy. To demonstrate both our theory and its potential for practical impact, we devised a proof-of-concept implementation of our estimator and benchmarked it against well-studied DP mechanisms. We show that in reasonable execution time our estimator can reproduce the tight, analytically computed $\epsilon, \delta$ trade-off of Laplacian and Gaussian mechanisms---to our knowledge, the first black box estimator to do so, and for the Sparse Vector Technique, our outputs are comparable to that of a more specialized state-of-the-art $(\epsilon, \delta)$-DP estimator.
Lyubashevsky’s signatures are based on the Fiat-Shamir with aborts paradigm, whose central ingredient is the use of rejection sampling to transform secret-dependent signature samples into samples from (or close to) a secret-independent target distribution. Several choices for the underlying distributions and for the rejection sampling strategy can be considered. In this work, we study Lyubashevsky’s signatures through the lens of rejection sampling, and aim to minimize signature size given signing runtime requirements. Several of our results concern rejection sampling itself and could have other applications. We prove lower bounds for compactness of signatures given signing run- time requirements, and for expected runtime of perfect rejection sampling strategies. We also propose a Rényi-divergence-based analysis of Lyuba- shevsky’s signatures which allows for larger deviations from the target distribution, and show hyperball uniforms to be a good choice of distri- butions: they asymptotically reach our compactness lower bounds and offer interesting features for practical deployment. Finally, we propose a different rejection sampling strategy which circumvents the expected runtime lower bound and provides a worst-case runtime guarantee.
The task of achieving full security (with guaranteed output delivery) in secure multiparty computation (MPC) is a long-studied problem. Known impossibility results (Cleve, STOC 86) rule out general solutions in the dishonest majority setting. In this work, we consider solutions that use an external trusted party (TP) to bypass the impossibility results, and study the minimal requirements needed from this trusted party. In particular, we restrict ourselves to the extreme setting where the size of the TP is independent of the size of the functionality to be computed (called “small” TP) and this TP is invoked only once during the protocol execution. We present several positive and negative results for fully-secure MPC in this setting. -- For a natural class of protocols, specifically, those with a universal output decoder, we show that the size of the TP must necessarily be exponential in the number of parties. This result holds irrespective of the computational assumptions used in the protocol. The class of protocols to which our lower bound applies is broad enough to capture prior results in the area, implying that the prior techniques necessitate the use of an exponential-sized TP. We additionally rule out the possibility of achieving information-theoretic full security (without the restriction of using a universal output decoder) using a “small” TP in the plain model (i.e., without any setup). -- In order to get around the above negative result, we consider protocols without a universal output decoder. The main positive result in our work is a construction of such a fully-secure MPC protocol assuming the existence of a succinct Functional Encryption scheme. We also give evidence that such an assumption is likely to be necessary for fully-secure MPC in certain restricted settings. -- Finally, we explore the possibility of achieving full-security with a semi-honest TP that could collude with other malicious parties (which form a dishonest majority). In this setting, we show that even fairness is impossible to achieve regardless of the “small TP” requirement.
Homomorphic encryption (HE) is a cryptosystem that allows secure processing of encrypted data. One of the most popular HE schemes is the Brakerski-Fan-Vercauteren (BFV), which supports somewhat (SWHE) and fully homomorphic encryption (FHE). Since overly involved arithmetic operations of HE schemes are amenable to concurrent computation, GPU devices can be instrumental in facilitating the practical use of HE in real world applications thanks to their superior parallel processing capacity. This paper presents an optimized and highly parallelized GPU library to accelerate the BFV scheme. This library includes state-of-the-art implementations of Number Theoretic Transform (NTT) and inverse NTT that minimize the GPU kernel function calls. It makes an efficient use of the GPU memory hierarchy and computes 128 NTT operations for ring dimension of $2^{14}$ only in $176.1~\mu s$ on RTX~3060Ti GPU. To the best of our knowlede, this is the fastest implementation in the literature. The library also improves the performance of the homomorphic operations of the BFV scheme. Although the library can be independently used, it is also fully integrated with the Microsoft SEAL library, which is a well-known HE library that also implements the BFV scheme. For one ciphertext multiplication, for the ring dimension $2^{14}$ and the modulus bit size of $438$, our GPU implementation offers $\mathbf{63.4}$ times speedup over the SEAL library running on a high-end CPU. The library compares favorably with other state-of-the-art GPU implementations of NTT and the BFV operations. Finally, we implement a privacy-preserving application that classifies encrpyted genome data for tumor types and achieve speedups of $42.98$ and $5.7$ over a CPU implementations using single and 16 threads, respectively. Our results indicate that GPU implementations can facilitate the deployment of homomorphic cryptographic libraries in real world privacy preserving applications.
The permissionless clock synchronization problem asks how it is possible for a population of parties to maintain a system-wide synchronized clock, while their participation rate fluctuates --- possibly very widely --- over time. The underlying assumption is that parties experience the passage of time with roughly the same speed, but however they may disengage and engage with the protocol following arbitrary (and even chosen adversarially) participation patterns. This (classical) problem has received renewed attention due to the advent of blockchain protocols, and recently it has been solved in the setting of proof of stake, i.e., when parties are assumed to have access to a trusted PKI setup [Badertscher et al., Eurocrypt ’21]. In this work, we present the first proof-of-work (PoW)-based permissionless clock synchronization protocol. Our construction assumes a public setup (e.g., a CRS) and relies on an honest majority of computational power that, for the first time, is described in a fine-grain timing model that does not utilize a global clock that exports the current time to all parties. As a secondary result of independent interest, our protocol gives rise to the first PoW-based ledger consensus protocol that does not rely on an external clock for the time-stamping of transactions and adjustment of the PoW difficulty.
Cube attacks exploit the algebraic properties of symmetric ciphers by recovering a special polynomial, the superpoly, and subsequently the secret key. When the algebraic normal forms of the corresponding Boolean functions are not available, the division property based approach allows to recover the exact superpoly in a clever way. However, the computational cost to recover the superpoly becomes prohibitive as the number of rounds of the cipher increases. For example, the nested monomial predictions (NMP) proposed at ASIACRYPT 2021 stuck at round 845 for Trivium. To alleviate the bottleneck of the NMP technique, i.e., the unsolvable model due to the excessive number of monomial trails, we shift our focus to the so-called valuable terms of a specific middle round that contribute to the superpoly. Two new techniques are introduced, namely, Non-zero Bit-based Division Property (NBDP) and Core Monomial Prediction (CMP), both of which result in a simpler MILP model compared to the MILP model of MP. It can be shown that the CMP technique offers a substantial improvement over the monomial prediction technique in terms of computational complexity of recovering valuable terms. Combining the divide-and-conquer strategy with these two new techniques, we catch the valuable terms more effectively and thus avoid wasting computational resources on intermediate terms contributing nothing to the superpoly. As an illustration of the power of our techniques, we apply our framework to Trivium, Grain, Kreyvium and Acorn. As a result, the computational cost of earlier attacks can be significantly reduced and the exact ANFs of the superpolies for 846-, 847- and 848-round Trivium, 192-round Grain, 895-round Kreyvium and 776-round Acorn can be recovered in practical time, even though the superpoly of 848-round Trivium contains over 500 million terms; this corresponds to respectively 3, 1, 1 and 1 rounds more than the previous best results. Moreover, by investigating the internal properties of Möbius transformation, we show how to perform key recovery using superpolies involving full key bits, which leads to the best key recovery attacks on the targeted ciphers.
This document is an informal summary on the FRI low degree test [BSBHR18a], [BSCI+20], and DEEP algebraic linking from [BSGKS20]. Based on its most recent soundness analysis [BSCI+20], we discuss parameter settings for practical security levels, how FRI is turned into a polynomial commitment scheme, and the soundness of DEEP sampling in the list decoding regime. In particular, we illustrate the DEEP method applied to proving satisfiability of algebraic intermediate representations and prove a soundness error bound which slightly improves the one in [Sta21].
A major challenge for blockchain interoperability is having an on-chain light client protocol that is both efficient and secure. We present a protocol that provides short proofs about the state of a decentralised consensus protocol while being able to detect misbehaving parties. To do this naively, a verifier would need to maintain an updated list of all participants' public keys which makes the corresponding proofs long. In general, existing solutions either lack accountability or are not efficient. We define and design a committee key scheme with short proofs that do not include any of the individual participants' public keys in plain. Our committee key scheme, in turn, uses a custom designed SNARK which has a fast prover time. Moreover, using our committee key scheme, we define and design an accountable light client system as the main cryptographic core for building bridges between proof of stake blockchains. Finally, we implement a prototype of our custom SNARK for which we provide benchmarks.
Privacy-preserving protocols for matchings on general graphs can be used for applications such as online dating, bartering, or kidney donor exchange. In addition, they can act as a building blocks for more complex protocols. While privacy preserving protocols for matchings on bipartite graphs are a well-researched topic, the case of general graphs has experienced significantly less attention so far. We address this gap by providing the first privacy-preserving protocol for maximum weight matching on general graphs. We present two protocol variants, which both compute an $1/2-$approximation instead of an optimal solution in favor of scalability. For $N$ nodes, the first variant requires $\mathcal{O}(N \log^2 N)$ rounds and $\mathcal{O}(N^3\log N)$ communication, and the second variant requires only $\mathcal{O}(N \log N)$ rounds and $\mathcal{O}(N^3)$ communication. We implement both variants and find that the first variant runs in $14.9$ minutes for $N=300$ nodes, while the second variant requires only $5.1$ minutes for $N=300$, and $12.5$ minutes for $N=400$.
We present TRIFORS (TRIlinear FOrms Ring Signature), a logarithmic post-quantum (linkable) ring signature based on a novel assumption regarding equivalence of alternating trilinear forms. The basis of this work is the construction by Beullens, Katsumata and Pintore from Asiacrypt 2020 to obtain a linkable ring signature from a cryptographic group action. The group action on trilinear forms used here is the same employed in the signature presented by Tang et al. at Eurocrypt 2022. We first define a sigma protocol that, given a set of public keys, the ring, allows to prove the knowledge of a secret key corresponding to a public one in the ring. Furthermore, some optimisations are used to reduce the size of the signature: among others, we use a novel application of the combinatorial number system to the space of the challenges. Using the Fiat-Shamir transform, we obtain a (linkable) ring signature of competitive length with the state-of-the-art among post-quantum proposals for security levels 128 and 192.
In 3GPP mobile networks, application data is transferred between the phone and an access point over a wireless link. The mobile network wireless link is special since one channel endpoint is handed over from one access point to another as the phone physically moves. Key evolution during handover has been analyzed in various works, but these do not combine the analysis with analysis of the wireless-link application-data encryption protocol that uses the keys. To enable formal analysis of the 4G/5G wireless link, we develop a game-based security framework for such channels and define flexible key insulation security notions for application data transfer, including forward and backward security in the given adversary model. Our notions are modular and combine a bidirectional application data transfer channel with a generic framework for multiparty channel-evolution protocols. These two components interact, and the security of the channel-evolution protocol may rely on the security of the data transfer channel for some or all its messages. We also develop the first formal model of 4G/5G wireless link security including both handover key evolution and application data transfer, in the complexity theoretic setting. We prove the model secure w.r.t. our security notions. As a byproduct, we identify recommendations for improving the security of future mobile network standards to achieve key insulation. Specifically, we show that the current standards do not achieve forward secure encryption, even though this appears to be an explicit goal. We show how this can be rectified.
In the UC framework, protocols must be subroutine respecting; therefore, shared trusted setup might cause security issues. To address this drawback, Generalized UC (GUC) framework is introduced by Canetti \emph{et al.} (TCC 2007). In this work, we investigate the impossibility and feasibility of GUC-secure commitments using global random oracles (GRO) as the trusted setup. In particular, we show that it is impossible to have a 2-round (1-round committing and 1-round opening) GUC-secure commitment in the global observable RO model by Canetti \emph{et al.} (CCS 2014). We then give a new round-optimal GUC-secure commitment that uses only Minicrypt assumptions (i.e. the existence of one-way functions) in the global observable RO model. Furthermore, we also examine the complete picture on round complexity of the GUC-secure commitments in various global RO models.
Proving discrete log equality for groups of the same order is addressed by Chaum and Pedersen's seminal work. However, there has not been a lot of work in proving discrete log equality for groups of different orders. This paper presents an efficient solution, which leverages a technique we call delegated Schnorr. The discovery of this technique is guided by a design methodology that we call the inspection model, and we find it useful for protocol designs. We show two applications of this technique on the Findora blockchain: **Maxwell-Zerocash switching:** There are two privacy-preserving transfer protocols on the Findora blockchain, one follows the Maxwell construction and uses Pedersen commitments over Ristretto, one follows the Zerocash construction and uses Rescue over BLS12-381. We present an efficient protocol to convert assets between these two constructions while preserving the privacy. **Zerocash with secp256k1 keys:** Bitcoin, Ethereum, and many other chains do signatures on secp256k1. There is a strong need for ZK applications to not depend on special curves like Jubjub, but be compatible with secp256k1. Due to FFT unfriendliness of secp256k1, many proof systems (e.g., Groth16, Plonk, FRI) are infeasible. We present a solution using Bulletproofs over curve secq256k1 ("q") and delegated Schnorr which connects Bulletproofs to TurboPlonk over BLS12-381. We conclude the paper with (im)possibility results about Zerocash with only access to a deterministic ECDSA signing oracle, which is the case when working with MetaMask. This result shows the limitations of the techniques in this paper. This paper is under a bug bounty program through a grant from Findora Foundation.
Interactive oracle proofs (IOPs) are a generalization of probabilistically checkable proofs that can be used to construct succinct arguments. Improvements in the efficiency of IOPs lead to improvements in the efficiency of succinct arguments. Key efficiency goals include achieving provers that run in linear time and verifiers that run in sublinear time, where the time complexity is with respect to the arithmetic complexity of proved computations over a finite field $\mathbb{F}$. We consider the problem of constructing IOPs for any given finite field $\mathbb{F}$ with a linear-time prover and polylogarithmic query complexity. Several previous works have achieved these efficiency requirements with $O(1)$ soundness error for NP-complete languages. However, constrained by the soundness error of the sumcheck protocol underlying these constructions, the IOPs achieve linear prover time only for instances in fields of size $\Omega(\log n)$. Recent work (Ron-Zewi and Rothblum, STOC 2022) overcomes this problem, but with linear verification time. We construct IOPs for the algebraic automata problem over any finite field $\mathbb{F}$ with a linear-time prover, polylogarithmic query complexity, and sublinear verification complexity. We additionally prove a similar result to Ron-Zewi and Rothblum for the NP-complete language R1CS using different techniques. The IOPs imply succinct arguments for (nondeterministic) arithmetic computations over any finite field with linear-time proving (given black-box access to a linear-time collision-resistant hash function). Inspired by recent constructions of reverse-multiplication-friendly embeddings, our IOP constructions embed problem instances over small fields into larger fields and adapt previous IOP constructions to the new instances. The IOP provers are modelled as random access machines and use precomputation techniques to achieve linear prover time. In this way, we avoid having to replace the sumcheck protocol.
Verifiable random functions (Micali et al., FOCS'99) allow a key-pair holder to verifiably evaluate a pseudorandom function under that particular key pair. These primitives enable fair and verifiable pseudorandom lotteries, essential in proof-of-stake blockchains such as Algorand and Cardano, and are being used to secure billions of dollars of capital. As a result, there is an ongoing IRTF effort to standardize VRFs, with a proposed ECVRF based on elliptic-curve cryptography appearing as the most promising candidate. In this work, towards understanding the general security of VRFs and in particular the ECVRF construction, we provide an ideal functionality in the Universal Composability (UC) framework (Canetti, FOCS'01) that captures VRF security, and show that ECVRF UC-realizes this functionality. We further show how the range of a VRF can generically be extended in a modular fashion based on the above functionality. This observation is particularly useful for protocols such as Ouroboros since it allows to reduce the number of VRF evaluations (per slot) and VRF verifications (per block) from two to one at the price of additional (but much faster) hash-function evaluations. Finally, we study batch verification in the context of VRFs. We provide a UC-functionality capturing a VRF with batch-verification capability, and propose modifications to ECVRF that allow for this feature. We again prove that our proposal UC-realizes the desired functionality. We provide a performance analysis showing that verification can yield a factor-two speedup for batches with 1024 proofs, at the cost of increasing the proof size from 80 to 128 bytes.
Public key encryption with keyword search (PEKS) inherently suffers from the inside keyword guessing attack. To resist against this attack, Huang et al. proposed the public key authenticated encryption with keyword search (PAEKS), where the sender not only encrypts a keyword, but also authenticates it. To further resist against quantum attacks, Liu et al. proposed a generic construction of PAEKS and the first quantum-resistant PAEKS instantiation based on lattices. Later, Emura pointed out some issues in Liu et al.'s construction and proposed a new generic construction of PAEKS. The basic construction methodology of Liu et al. and Emura is the same, i.e., each keyword is converted into an extended keyword using the shared key calculated by a word-independent smooth projective hash functions (SPHF), and PEKS is used for the extended keyword. In this paper, we first analyze the schemes of Liu et al. and Emura, and point out some issues regarding their construction and security model. In short, in their lattice-based instantiations, the sender and receiver use a lattice-based word independent SPHF to compute the same shared key to authenticate keywords, leading to a super-polynomial modulus $q$; their generic constructions need a trusted setup assumption or the designated-receiver setting; Liu et al. failed to provide convincing evidence that their scheme satisfies their claimed security. Then, we propose two new lattice-based PAEKS schemes with totally different construction methodology from Liu et al. and Emura. Specifically, in our PAEKS schemes, instead of using the shared key calculated by SPHF, the sender and receiver achieve keyword authentication by using their own secret key to sample a set of short vectors related to the keyword. In this way, the modulus $q$ in our schemes could be of polynomial size, which results in much smaller size of the public key, ciphertext and trapdoor. In addition, our schemes need neither a trusted setup assumption nor the designated-receiver setting. Finally, our schemes can be proven secure in stronger security model, and thus provide stronger security guarantee for both ciphertext privacy and trapdoor privacy.
Zero-knowledge proof is a powerful cryptographic primitive that has found various applications in the real world. However, existing schemes with succinct proof size suffer from a high overhead on the proof generation time that is super-linear in the size of the statement represented as an arithmetic circuit, limiting their efficiency and scalability in practice. In this paper, we present Orion, a new zero-knowledge argument system that achieves $O(N)$ prover time of field operations and hash functions and $O(\log^2 N)$ proof size. Orion is concretely efficient and our implementation shows that the prover time is 3.09s and the proof size is 1.5MB for a circuit with $2^{20}$ multiplication gates. The prover time is the fastest among all existing succinct proof systems, and the proof size is an order of magnitude smaller than a recent scheme proposed in Golovnev et al. 2021. In particular, we develop two new techniques leading to the efficiency improvement. (1) We propose a new algorithm to test whether a random bipartite graph is a lossless expander graph or not based on the densest subgraph algorithm. It allows us to sample lossless expanders with an overwhelming probability. The technique improves the efficiency and/or security of all existing zero-knowledge argument schemes with a linear prover time. The testing algorithm based on densest subgraph may be of independent interest for other applications of expander graphs. (2) We develop an efficient proof composition scheme, code switching, to reduce the proof size from square root to polylogarithmic in the size of the computation. The scheme is built on the encoding circuit of a linear code and shows that the witness of a second zero-knowledge argument is the same as the message in the linear code. The proof composition only introduces a small overhead on the prover time.
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of information set decoders (ISD). A while ago, a generic decoding algorithm which does not belong to this family was proposed: statistical decoding. It is a randomized algorithm that requires the computation of a large set of parity-checks of moderate weight, and uses some kind of majority voting on these equations to recover the error. This algorithm was long forgotten because even the best variants of it performed poorly when compared to the simplest ISD algorithm. We revisit this old algorithm by using parity-check equations in a more general way. Here the parity-checks are used to get LPN samples with a secret which is part of the error and the LPN noise is related to the weight of the parity-checks we produce. The corresponding LPN problem is then solved by standard Fourier techniques. By properly choosing the method of producing these low weight equations and the size of the LPN problem, we are able to outperform in this way significantly information set decodings at code rates smaller than $0.3$. It gives for the first time after $60$ years, a better decoding algorithm for a significant range which does not belong to the ISD family.
In the light of NIST’s announced reopening of the call for digital signature proposals in 2023 due to lacking diversity, there is a strong need for constructions based on other established hardness assumptions. In this work we construct a new post-quantum secure digital signature scheme based on the $MinRank$ problem, a problem with a long history of applications in cryptanalysis that led to a strong belief in its hardness. Initially following a design by Courtois (Asiacrypt '01) based on the Fiat--Shamir transform, we make use of several recent developments in the design of sigma protocols to reduce signature size and improve efficiency. This includes the recently introduced $sigma \; protocol \; with \; helper$ paradigm (Eurocrypt '19) and combinations with $cut$-$and$-$choose$ techniques (CCS '18). Moreover, we introduce several improvements to the core of the scheme to further reduce its signature size.
Side-Channel Analysis (SCA) allows extracting secret keys manipulated by cryptographic primitives through leakages of their physical implementations. Supervised attacks, known to be optimal, can theoretically defeat any countermeasure, including masking, by learning the dependency between the leakage and the secret through the profiling phase. However, defeating masking is less trivial when it comes to unsupervised attacks. While classical strategies such as CPA or LRA have been extended to masked implementations, we show that these extensions only hold for Boolean and arithmetic schemes. Therefore, we propose a new unsupervised strategy, the Joint Moments Regression (JMR), able to defeat any masking schemes (multiplicative, affine, polynomial, inner product...), which are gaining popularity in real implementations. The main idea behind JMR is to directly regress the leakage model of the shares by fitting a system based on higher-order joint moments conditions. We show that this idea can be seen as part of a more general framework known as the Generalized Method of Moments (GMM). This offers mathematical foundations on which we rely to derive optimizations of JMR. Simulations results confirm the interest of JMR over state-of-the-art attacks, even in the case of Boolean and arithmetic masking. Eventually, we apply this strategy to provide, to the best of our knowledge, the first unsupervised attack on the protected AES implementation proposed by the ANSSI for SCA research, which embeds an affine masking and shuffling counter-measures.
This paper presents an approach to uncover and analyze power side-channel leakages on a processor cycle level precision. By carefully designing and evaluating the measurement setup, accurate trace timing is enabled, which is used to overlay the trace with the corresponding assembly code. This methodology allows to expose the sources of leakage on a processor cycle scale, which allows for evaluating new implementations. It also exposes that the default ChipWhisperer configuration for STM32F4 targets used in prior work includes wait cycles that are rarely used in real-world applications, but affect power side-channel leakage. As an application for our setup, we target the widely used Sign-Flip function of Gaussian sampling code used in multiple Post-Quantum Key-Exchange Mechanisms and Signature schemes. We propose new implementations for the Sign-Flip function based on our analysis on the original implementation and further evaluate their leakage. Our findings allow the conclusion that unmasked cryptographic implementations of schemes based on Gaussian random numbers for STM32F4 cannot be secure against power side-channel, and that masking just the Gaussian sampler is not a viable option.
We investigate the security of succinct arguments against quantum adversaries. Our main result is a proof of knowledge-soundness in the post-quantum setting for a class of multi-round interactive protocols, including those based on the recursive folding technique of Bulletproofs. To prove this result, we devise a new quantum rewinding strategy, the first that allows for rewinding across many rounds. This technique applies to any protocol satisfying natural multi-round generalizations of special soundness and collapsing. For our main result, we show that recent Bulletproofs-like protocols based on lattices satisfy these properties, and are hence sound against quantum adversaries.
The re-encryption mix-net (RMN) is a basic cryptographic tool that is widely used in the privacy protection domain and requires anonymity support; for example, it is used in electronic voting, web browsing, and location systems. To protect information about the relationship between senders and messages, a number of mix servers in RMNs shuffle and forward a list of input ciphertexts in a cascading manner. The output of the last mix server is decrypted to yield the set of original messages. The main downside of this approach is that the mixing process requires a number of rounds that is linear in the number of mix servers. This implies that a long round delay would cause network latency, which can dominate local computational latencies. To minimize the effect of network latency, RMN protocols with constant round complexity are more desirable. In this work, we propose a new RMN protocol that runs in $O(1)$ rounds in the number of mix servers and that UC-realizes a hybrid model with access to some functionalities for secure communication and zero-knowledge proof (ZKP). Interestingly, because our protocol does not require a ZKP protocol for a verifiable shuffle, we also achieve a considerable efficiency gain in terms of computation cost. Our main tools are secret sharing and an ElGamal encryption that is extended in the sense that it works on a multiplicative group under field extension. Importantly, this extended ElGamal encryption scheme acquires a new capability: it can efficiently decompose a decrypted message into unique values. We provide a detailed report on the theoretical performance and security analysis of this method.
We show that for many fundamental cryptographic primitives, proving classical security under the learning-with-errors (LWE) assumption, does not imply post-quantum security. This is despite the fact that LWE is widely believed to be post-quantum secure, and our work does not give any evidence otherwise. Instead, it shows that post-quantum insecurity can arise inside cryptographic constructions, even if the assumptions are post-quantum secure. Concretely, our work provides (contrived) constructions of pseudorandom functions, CPA-secure symmetric-key encryption, message-authentication codes, signatures, and CCA-secure public-key encryption schemes, all of which are proven to be classically secure under LWE via black-box reductions, but demonstrably fail to be post-quantum secure. All of these cryptosystems are stateless and non-interactive, but their security is defined via an interactive game that allows the attacker to make oracle queries to the cryptosystem. The polynomial-time quantum attacker can break these schemes by only making a few classical queries to the cryptosystem, and in some cases, a single query suffices. Previously, we only had examples of post-quantum insecurity under post-quantum assumptions for stateful/interactive protocols. Moreover, there appears to be a folklore belief that for stateless/non-interactive cryptosystems with black-box proofs of security, a quantum attack against the scheme should translate into a quantum attack on the assumption. This work shows otherwise. Our main technique is to carefully embed interactive protocols inside the interactive security games of the above primitives. As a result of independent interest, we also show a 3-round quantum disclosure of secrets (QDS) protocol between a classical sender and a receiver, where a quantum receiver learns a secret message in the third round but, assuming LWE, a classical receiver does not.
Certificate authorities in public key infrastructures typically require entities to prove possession of the secret key corresponding to the public key they want certified. While this is straightforward for digital signature schemes, the most efficient solution for public key encryption and key encapsulation mechanisms (KEMs) requires an interactive challenge-response protocol, requiring a departure from current issuance processes. In this work we investigate how to non-interactively prove possession of a KEM secret key, specifically for lattice-based KEMs, motivated by the recently proposed KEMTLS protocol which replaces signature-based authentication in TLS 1.3 with KEM-based authentication. Although there are various zero-knowledge (ZK) techniques that can be used to prove possession of a lattice key, they yield large proofs or are inefficient to generate. We propose a technique called verifiable generation, in which a proof of possession is generated at the same time as the key itself is generated. Our technique is inspired by the Picnic signature scheme and uses the multi-party-computation-in-the-head (MPCitH) paradigm; this similarity to a signature scheme allows us to bind attribute data to the proof of possession, as required by certificate issuance protocols. We show how to instantiate this approach for two lattice-based KEMs in Round 3 of the NIST post-quantum cryptography standardization project, Kyber and FrodoKEM, and achieve reasonable proof sizes and performance. Our proofs of possession are faster and an order of magnitude smaller than the previous best MPCitH technique for knowledge of a lattice key, and in size-optimized cases can be comparable to even state-of-the-art direct lattice-based ZK proofs for Kyber. Our approach relies on a new result showing the uniqueness of Kyber and FrodoKEM secret keys, even if the requirement that all secret key components are small is partially relaxed, which may be of independent interest for improving efficiency of zero-knowledge proofs for other lattice-based statements.
Quantum computing is considered among the next big leaps in the computer science. While a fully functional quantum computer is still in the future, there is an ever-growing need to evaluate the security of the secret-key ciphers against a potent quantum adversary. Keeping this in mind, our work explores the key recovery attack using the Grover's search on the three variants of AES (-128, -192, -256) with respect to the quantum implementation and the quantum key search using the Grover's algorithm. We develop a pool of implementations, by mostly reducing the circuit depth metrics. We consider various strategies for optimization, as well as make use of the state-of-the-art advancements in the relevant fields. In a nutshell, we present the least Toffoli depth and full depth implementations of AES, thereby improving from Zou et al.'s Asiacrypt'20 paper by more than 98 percent for all variants of AES. Our qubit count - Toffoli depth product is improved from theirs by more than 75 percent. Furthermore, we analyze the Jaques et al.'s Eurocrypt'20 implementations in details, fix its bugs and report corrected benchmarks. To the best of our finding, our work improves from all the previous works (including the recent Eprint'22 paper by Huang and Sun).
In "Optimal collision side-channel attacks" (https://eprint.iacr.org/2019/828) we studied, and derived an optimal distinguisher for key ranking. In this note we propose a heuristic estimation procedure for key ranking based on this distinguisher, and provide estimates of lower bounds for secret key ranks in collision side channel attacks.
In recent years, permisionless blockchains have received a lot of attention both from industry and academia, where substantial effort has been spent to develop consensus protocols that are secure under the assumption that less than half (or a third) of a given resource (e.g., stake or computing power) is controlled by corrupted parties. The security proofs of these consensus protocols usually assume the availability of a network functionality guaranteeing that a block sent by an honest party is received by all honest parties within some bounded time. To obtain an overall protocol that is secure under the same corruption assumption, it is therefore necessary to combine the consensus protocol with a network protocol that achieves this property under that assumption. In practice, however, the underlying network is typically implemented by flooding protocols that are not proven to be secure in the setting where a fraction of the considered total weight can be corrupted. This has led to many so-called eclipse attacks on existing protocols and tailor-made fixes against specific attacks. To close this apparent gap, we present the first practical flooding protocol that provably delivers sent messages to all honest parties after a logarithmic number of steps. We prove security in the setting where all parties are publicly assigned a positive weight and the adversary can corrupt parties accumulating up to a constant fraction of the total weight. This can directly be used in the proof-of-stake setting, but is not limited to it. To prove the security of our protocol, we combine known results about the diameter of Erdős–Rényi graphs with reductions between different types of random graphs. We further show that the efficiency of our protocol is asymptotically optimal. The practicality of our protocol is supported by extensive simulations for different numbers of parties, weight distributions, and corruption strategies. The simulations confirm our theoretical results and show that messages are delivered quickly regardless of the weight distribution, whereas protocols that are oblivious of the parties' weights completely fail if the weights are unevenly distributed. Furthermore, the average message complexity per party of our protocol is within a small constant factor of such a protocol.
One of the most successful applications of peer-to-peer communication networks is in the context of blockchain protocols, which—in Satoshi Nakamoto's own words—rely on the "nature of information being easy to spread and hard to stifle." Significant efforts were invested in the last decade into analyzing the security of these protocols, and invariably the security arguments known for longest-chain Nakamoto-style consensus use an idealization of this tenet. Unfortunately, the real-world implementations of peer-to-peer gossip-style networks used by blockchain protocols rely on a number of ad-hoc attack mitigation strategies that leave a glaring gap between the idealized communication layer assumed in formal security arguments for blockchains and the real world, where a wide array of attacks have been showcased. In this work we bridge this gap by presenting a Byzantine-resilient network layer for blockchain protocols. For the first time we quantify the problem of network-layer attacks in the context of blockchain security models, and we develop a design that thwarts resource restricted adversaries. Importantly, we focus on the proof-of-stake setting due to its vulnerability to Denial-of-Service (DoS) attacks stemming from the well-known deficiency (compared to the proof-of-work setting) known as nothing at stake. We present a Byzantine-resilient gossip protocol, and we analyze it in the Universal Composition framework. In order to prove security, we show novel results on expander properties of random graphs. Importantly, our gossip protocol can be based on any given bilateral functionality that determines a desired interaction between two "adjacent" peers in the networking layer and demonstrates how it is possible to use application-layer information to make the networking-layer resilient to attacks. Despite the seeming circularity, we demonstrate how to prove the security of a Nakamoto-style longest-chain protocol given our gossip networking functionality, and hence, we demonstrate constructively how it is possible to obtain provable security across protocol layers, given only bare-bone point-to-point networking, majority of honest stake, and a verifiable random function.
Currently, a vast majority of symmetric-key cryptographic schemes are built as block cipher modes. The block cipher is designed to be hard to distinguish from a random permutation and this is supported by cryptanalysis, while (good) modes can be proven secure if a random permutation takes the place of the block cipher. As such, block ciphers form an abstraction level that marks the border between cryptanalysis and security proofs. In this paper, we investigate a re-factored version of symmetric-key cryptography built not around the block ciphers but rather the deck function: a keyed function with arbitrary input and output length and incrementality properties. This allows for modes of use that are simpler to analyze and still very efficient thanks to the excellent performance of currently proposed deck functions. We focus on authenticated encryption (AE) modes with varying levels of robustness. Our modes have built-in support for sessions, but are also efficient without them. As a by-product, we define a new ideal model for AE dubbed the jammin cipher. Unlike the OAE2 security models, the jammin cipher is both a operational ideal scheme and a security reference, and addresses real-world use cases such as bi-directional communication and multi-key security.
We show how to backdoor the McEliece cryptosystem such that a backdoored public key is indistinguishable from a usual public key, but allows to efficiently retrieve the underlying secret key. For good cryptographic reasons, McEliece uses a small random seed 𝛅 that generates via some pseudo random generator (PRG) the randomness that determines the secret key. Our backdoor mechanism works by encoding an encryption of 𝛅 into the public key. Retrieving 𝛅 then allows to efficiently recover the (backdoored) secret key. Interestingly, McEliece can be used itself to encrypt 𝛅, thereby protecting our backdoor mechanism with strong post-quantum security guarantees. Our construction also works for the current Classic McEliece NIST standard proposal for non-compressed secret keys, and therefore opens the door for widespread maliciously backdoored implementations. Fortunately, our backdoor mechanism can be detected by the owner of the (backdoored) secret key if 𝛅 is stored after key generation as specified by the Classic McEliece proposal. Thus, our results provide strong advice for implementers to store 𝛅 inside the secret key and use 𝛅 to guard against backdoor mechanisms.
Pairing-based cryptographic protocols are typically vulnerable to small-subgroup attacks in the absence of protective measures. To thwart them, one of feasible measures is to execute subgroup membership testings, which are generally considered expensive. Recently, Scott proposed an efficient method of subgroup membership testings for $\mathbb{G}_1$, $\mathbb{G}_2$ and $\mathbb{G}_T$ on the BLS family. In this paper, we generalize this method proposed by Scott and show that the new technique is applicable to a large class of pairing-friendly curves. In addition, we also confirm that the new method leads to a significant speedup for membership testings on many popular pairing-friendly curves.
We show how the Weil pairing can be used to evaluate the assigned characters of an imaginary quadratic order $\mathcal{O}$ in an unknown ideal class $[\mathfrak{a}] \in \mathrm{Cl}(\mathcal{O})$ that connects two given $\mathcal{O}$-oriented elliptic curves $(E, \iota)$ and $(E', \iota') = [\mathfrak{a}](E, \iota)$. When specialized to ordinary elliptic curves over finite fields, our method is conceptually simpler and often faster than a recent approach due to Castryck, Sot\'akov\'a and Vercauteren, who rely on the Tate pairing instead. The main implication of our work is that it breaks the decisional Diffie–Hellman problem for practically all oriented elliptic curves that are acted upon by an even-order class group. It can also be used to better handle the worst cases in Wesolowski's recent reduction from the vectorization problem for oriented elliptic curves to the endomorphism ring problem, leading to a method that always works in sub-exponential time.
Hardware obfuscation through redundancy addition is a well-known countermeasure against reverse engineering. For FPGA designs, such a technique can be implemented with a small overhead, however, its effectiveness is heavily dependent on the stealthiness of the redundant elements. Hardware opaque predicates can provide adequately stealthy constant values that can be used for obfuscation. However, in this report, we show that such obfuscation schemes can be defeated by ensuring the full controllability of each active look-up table input in a design via iterative bitstream modifications. We present an algorithm that works directly on the bitstream and does not require the possession of a netlist. The feasibility of our approach is verified with the example of an obfuscated SNOW 3G design implemented in a Xilinx 7-series FPGA.
Mimblewimble is a cryptocurrency protocol that promises to overcome notorious blockchain scalability issues and provides user privacy. For a long time its wider adoption has been hindered by the lack of non-interactive transactions, that is, payments for which only the sender needs to be online. Yu proposed a way of adding non-interactive transactions to stealth addresses to Mimblewimble, but this turned out to be flawed. Building on Yu and integrating ideas from Burkett, we give a fixed scheme and provide a rigorous security analysis strenghtening the previous security model from Eurocrypt'19. Our protocol is considered for implementation by MimbleWimbleCoin and a variant is now deployed as MimbleWimble Extension Blocks (MWEB) in Litecoin.
We introduce a notion of round-robin secure sampling that captures several protocols in the literature, such as the "powers-of-tau" setup protocol for pairing-based polynomial commitments and zk-SNARKs, and certain verifiable mixnets. Due to their round-robin structure, protocols of this class inherently require $n$ sequential broadcast rounds, where $n$ is the number of participants. We describe how to compile them generically into protocols that require only $O(\sqrt{n})$ broadcast rounds. Our compiled protocols guarantee output delivery against any dishonest majority. This stands in contrast to prior techniques, which require $\Omega(n)$ sequential broadcasts in most cases (and sometimes many more). Our compiled protocols permit a certain amount of adversarial bias in the output, as all sampling protocols with guaranteed output must, due to Cleve's impossibility result (STOC'86). We show that in the context of the aforementioned applications, this bias is harmless.
Hybrid Homomorphic Encryption (HHE) reduces the amount of computation client-side and band- width usage in a Fully Homomorphic Encryption (FHE) framework. HHE requires the usage of specific sym- metric schemes that can be evaluated homomorphically efficiently. In this paper, we introduce the paradigm of Group Filter Permutator (GFP) as a generalization of the Improved Filter Permutator paradigm introduced by M ́eaux et al. From this paradigm, we specify Elisabeth , a family of stream cipher and give an instance: Elisabeth-4 . After proving the security of this scheme, we provide a Rust implementation of it and ensure its performance is comparable to state-of-the-art HHE. The true strength of Elisabeth lies in the available opera- tions server-side: while the best HHE applications were limited to a few multiplications server-side, we used data sent through Elisabeth-4 to homomorphically evaluate a neural network inference. Finally, we discuss the improvement and loss between the HHE and the FHE framework and give ideas to build more efficient schemes from the Elisabeth family
In this work, we study the security of sponge-based authenticated encryption schemes against quantum attackers. In particular, we analyse the sponge-based authenticated encryption scheme SLAE as put forward by Degabriele et al. (ASIACRYPT'19). We show that the scheme achieves security in the post-quantum (QS1) setting in the quantum random oracle model by using the one-way to hiding lemma. Furthermore, we analyse the scheme in a fully-quantum (QS2) setting. There we provide a set of attacks showing that SLAE does not achieve ciphertext indistinguishability and hence overall does not provide the desired level of security.
SHA-3 is considered to be one of the most secure standardized hash functions. It relies on the Keccak-f[1,600] permutation, which operates on an internal state of 1,600 bits, mostly represented as a $5\times5\times64{-}bit$ matrix. While existing implementations process the state sequentially in chunks of typically 32 or 64 bits, the Keccak-f[1,600] permutation can benefit a lot from speedup through parallelization. This paper is the first to explore the full potential of parallelization of Keccak-f[1,600] in RISC-V based processors through custom vector extensions on 32-bit and 64-bit architectures. We analyze the Keccak-f[1,600] permutation, composed of five different step mappings, and propose ten custom vector instructions to speed up the computation. We realize these extensions in a SIMD processor described in SystemVerilog. We compare the performance of our designs to existing architectures based on vectorized application-specific instruction set processors (ASIP). We show that our designs outperform all related work thanks to our carefully selected custom vector instructions.
The pseudorandom sampling of constant weight words, as it is currently implemented in cryptographic schemes like BIKE or HQC, is prone to the leakage of information on the seed being used for the pseudorandom number generation. This creates a vulnerability when the semantic security conversion requires a deterministic re-encryption. This observation was first made in [HLS21] about HQC and a timing attack was presented to recover the secret key. As suggested in [HLS21] a similar attack applies to BIKE and instances of such an attack were presented in an earlier version of this work [Sen21] and independently in [GHJ+22]. The timing attack stems from the variation of the amount of pseudorandom data to draw and process for sampling uniformly a constant weight word. We give here the exact distribution of this amount for BIKE. This will allow us to estimate precisely the cost of the natural countermeasure which consists in drawing always the same (large enough) amount of randomness for the sampler to terminate with probability overwhelmingly close to one. The main contribution of this work is to suggest a new approach for fixing the issue. It is first remarked that, contrary to what is done currently, the sampling of constant weight words doesn't need to produce a uniformly distributed output. If the distribution is close to uniform in the appropriate metric, the impact on security is negligible. Also, a new variant of the Fisher-Yates shuffle is proposed which is (1) very well suited for secure implementations against timing and cache attacks, and (2) produces constant weight words with a distribution close enough to uniform.
Trading goods lies at the backbone of the modern economy and the recent advent of cryptocurrencies has opened the door for trading decentralized (digital) assets: A large fraction of the value of cryptocurrencies comes from the inter-currency exchange and trading, which has been arguably the most successful application of decentralized money. The security issues observed with centralized, custodial cryptocurrency exchanges have motivated the design of atomic swaps, a protocol for coin exchanges between any two users. Yet, somewhat surprisingly, no atomic swap protocol exists that simultaneously satisfies the following simple but desired properties: (i) non-custodial, departing from a third party trusted holding the coins from users during the exchange; (ii) universal, that is, compatible with all (current and future) cryptocurrencies; (iii) multi-asset, supporting the exchange of multiple coins in a single atomic swap. From a theoretical standpoint, in this work we show a generic protocol to securely swap $n$ coins from any (possible multiple) currencies for $\tilde{n}$ coins of any other currencies, for any $n$ and $\tilde{n}$. We do not require any custom scripting language supported by the corresponding blockchains, besides the bare minimum ability to verify signatures on transactions. For the special case when the blockchains use ECDSA or Schnorr signatures, we design a practically efficient protocol based on adaptor signatures and time-lock puzzles. As a byproduct of our approach, atomic swaps transactions no longer include custom scripts and are identical to standard one-to-one transactions. We also show that our protocol naturally generalizes to any cycle of users, i.e., atomic swaps with more than two participants. To demonstrate the practicality of our approach, we have evaluated a prototypical implementation of our protocol for Schnorr/ECDSA signatures and observed that an atomic swap requires below one second on commodity machines. Even on blockchains with expressive smart contract support (e.g., Ethereum), our approach reduces the on-chain cost both in terms of transaction size and gas cost.
This paper focuses on isogeny representations, defined as ways to evaluate isogenies and verify membership to the language of isogenous supersingular curves (the set of triples $D,E_1,E_2$ with a cyclic isogeny of degree $D$ between $E_1$ and $E_2$). The tasks of evaluating and verifying isogenies are fundamental for isogeny-based cryptography. Our main contribution is the design of the suborder representation, a new isogeny representation targeted at the case of (big) prime degree. The core of our new method is the revelation of endomorphisms of smooth norm inside a well-chosen suborder of the codomain's endomorphism ring. This new representation appears to be opening interesting prospects for isogeny-based cryptography under the hardness of a new computational problem: the SubOrder to Ideal Problem (SOIP). As an application, we introduce pSIDH, a new NIKE based on the suborder representation. Studying new assumption appears to be particularly crucial in the light of the recent attacks against isogeny-based cryptography. In order to manipulate efficiently the suborder representation, we develop several heuristic algorithmic tools to solve norm equations inside a new family of quaternion orders. These new algorithms may be of independent interest.
When do classical zero-knowledge protocols remain secure against quantum attacks? In this work, we develop the techniques, tools, and abstractions necessary to answer this question for foundational protocols: 1) We prove that the Goldreich-Micali-Wigderson protocol for graph non-isomorphism and the Feige-Shamir protocol for NP remain zero-knowledge against quantum adversaries. At the heart of our proof is a new quantum rewinding technique that enables extracting information from multiple invocations of a quantum adversary without disturbing its state. 2) We prove that the Goldreich-Kahan protocol for NP is post-quantum zero knowledge using a simulator that can be seen as a natural quantum extension of the classical simulator. Our results achieve negligible simulation error, appearing to contradict a recent impossibility result due to Chia-Chung-Liu-Yamakawa (FOCS 2021). This brings us to our final contribution: 3) We introduce coherent-runtime expected quantum polynomial time, a simulation notion that (1) precisely captures all of our zero-knowledge simulators, (2) cannot break any polynomial hardness assumptions, (3) implies strict polynomial-time epsilon-simulation and (4) is not subject to the CCLY impossibility. In light of our positive results and the CCLY negative results, we propose coherent-runtime simulation to be the appropriate quantum analogue of classical expected polynomial-time simulation.
This paper investigates __anonymity__ of all NIST PQC Round 3 KEMs: Classic McEliece, Kyber, NTRU, Saber, BIKE, FrodoKEM, HQC, NTRU Prime (Streamlined NTRU Prime and NTRU LPRime), and SIKE. We show the following results: * NTRU is anonymous in the quantum random oracle model (QROM) if the underlying deterministic PKE is strongly disjoint-simulatable. NTRU is collision-free in the QROM. A hybrid PKE scheme constructed from NTRU as KEM and appropriate DEM is anonymous and robust. (Similar results for BIKE, FrodoKEM, HQC, NTRU LPRime, and SIKE hold except for two of three parameter sets of HQC.) * Classic McEliece is anonymous in the QROM if the underlying PKE is strongly disjoint-simulatable and a hybrid PKE scheme constructed from it as KEM and appropriate DEM is anonymous. * Grubbs, Maram, and Paterson pointed out that Kyber and Saber have a gap in the current IND-CCA security proof in the QROM (EUROCRYPT 2022). We found that Streamlined NTRU Prime has another technical obstacle for the IND-CCA security proof in the QROM. Those answer the open problem to investigate the anonymity and robustness of NIST PQC Round~3 KEMs posed by Grubbs, Maram, and Paterson (EUROCRYPT 2022). We use strong disjoint-simulatability of the underlying PKE of KEM and strong pseudorandomness and smoothness/sparseness of KEM as the main tools, which will be of independent interest.
Stake-based multiparty cryptographic primitives operate in a setting where participants are associated with their stake, security is argued against an adversary that is bounded by the total stake it possesses —as opposed to number of parties— and we are interested in scalability, i.e., the complexity of critical operations depends only logarithmically in the number of participants (who are assumed to be numerous). In this work we put forth a new stake-based primitive, stake-based threshold multisignatures (STM, or “Mithril” signatures), which allows the aggregation of individual signatures into a compact multisignature provided the stake that supports a given message exceeds a stake threshold. This is achieved by having for each message a pseudorandomly sampled subset of participants eligible to issue an individual signature; this ensures the scalability of signing, aggregation and verification. We formalize the primitive in the universal composition setting and propose efficient constructions for STMs. We also showcase that STMs are eminently useful in the cryptocurrency setting by providing two applications: (i) stakeholder decision-making for Proof of Work (PoW) blockchains, specifically, Bitcoin, and (ii) fast bootstrapping for Proof of Stake (PoS) blockchains.
In CRYPTO 2019, Gohr shows that well-trained neural networks can perform cryptanalytic distinguishing tasks superior to traditional differential distinguishers. Moreover, applying an unorthodox key guessing strategy, an 11-round key-recovery attack on a modern block cipher Speck32/64 improves upon the published state-of-the-art result. This calls into the next questions. To what extent is the advantage of machine learning (ML) over traditional methods, and whether the advantage generally exists in the cryptanalysis of modern ciphers? To answer the first question, we devised ML-based key-recovery attacks on more extended round-reduced Speck32/64. We achieved an improved 12-round and the first practical 13-round attacks. The essential for the new results is enhancing a classical component in the ML-based attacks, that is, the neutral bits. To answer the second question, we produced various neural distinguishers on round-reduced Simon32/64 and provided comparisons with their pure differential-based counterparts.
The Tower variant of the Number Field Sieve (TNFS) is known to be asymptotically the most efficient algorithm to solve the discrete logarithm problem in finite fields of medium characteristics, when the extension degree is composite. A major obstacle to an efficient implementation of TNFS is the collection of algebraic relations, as it happens in dimension greater than 2. This requires the construction of new sieving algorithms which remain efficient as the dimension grows. In this article, we overcome this difficulty by considering a lattice enumeration algorithm which we adapt to this specific context. We also consider a new sieving area, a high-dimensional sphere, whereas previous sieving algorithms for the classical NFS considered an orthotope. Our new sieving technique leads to a much smaller running time, despite the larger dimension of the search space, and even when considering a larger target, as demonstrated by a record computation we performed in a 521-bit finite field GF(p^6). The target finite field is of the same form than finite fields used in recent zero-knowledge proofs in some blockchains. This is the first reported implementation of TNFS.
Plactic key agreement is a new key agreement scheme that uses Knuth’s multiplication of semistandard tableaus from combinatorial algebra. The security of plactic key agreement relies on the difficulty of some computational problems, such as division of semistandard tableaus. Division by erosion uses backtracking to divide tableaus. Division by erosion is estimated to be infeasible against public keys of 768 or more bytes. If division by erosion is the best attack against plactic key agreement, then secure plactic key agreement could be practical. Chris Monico found a new attack on plactic key agreement, which is fast, potentially polynomial-time, and could very well make plactic key agreement insecure.
In universally composable (UC) security, a global setup is intended to capture the ideal behavior of a primitive which is accessible by multiple protocols, allowing them to share state. A representative example is the Bitcoin ledger. Indeed, since Bitcoin---and more generally blockchain ledgers---are known to be useful in various scenarios, it has become increasingly popular to capture such ledgers as global setup. Intuitively, one would expect UC to allow us to make security statements about protocols that use such a global setup, e.g., a global ledger, which can then be automatically translated into the setting where the setup is replaced by a protocol implementing it, such as Bitcoin. We show that the above reasoning is flawed and such a generic security-preserving replacement can only work under very (often unrealistic) strong conditions on the global setup and the security statement. For example, the UC security of Bitcoin for realizing a ledger proved by Badertscher et al. [CRYPTO'17] is not sufficient per se to allow us to replace the ledger by Bitcoin when used as a global setup. In particular, we cannot expect that all security statements in the global ledger-hybrid world would be preserved when using Bitcoin as a ledger. On the positive side, we provide characterizations of security statements for protocols that make use of global setups, for which the replacement is sound. Our results can be seen as a first guide on how to navigate the very tricky question of what constitutes a ``good'' global setup and how to use it in order to keep the modular protocol-design approach intact.
Non-interactive zero knowledge (NIZK) enables proving the validity of NP statement without leaking anything else. We study multi-instance NIZKs in the common reference string (CRS) model, against an adversary that adaptively corrupts parties and chooses statements to be proven. We construct the first such $\textit{triply adaptive}$ NIZK that provides full adaptive soundness, as well as adaptive zero-knowledge, assuming either LWE or else LPN and DDH (previous constructions rely on non-falsifiable knowledge assumptions). In addition, our NIZKs are universally composable (UC). Along the way, we: - Formulate an ideal functionality, $\mathcal{F}_\textsf{NICOM}$, which essentially captures $\textit{non-interactive}$ commitments, and show that it is realizable by existing protocols using standard assumptions. - Define and realize, under standard assumptions, Sigma protocols which satisfy triply adaptive security with access to $\mathcal{F}_\textsf{NICOM}$. - Use the Fiat-Shamir transform, instantiated with correlation intractable hash functions, to compile a Sigma protocol with triply adaptive security with access to $\mathcal{F}_\textsf{NICOM}$ into a triply adaptive UC-NIZK argument in the CRS model with access to $\mathcal{F}_\textsf{NICOM}$, assuming LWE (or else LPN and DDH). - Use the UC theorem to obtain UC-NIZK in the CRS model.
The Global and Externalized UC frameworks [Canetti-Dodis-Pass-Walfish, TCC 07] extend the plain UC framework to additionally handle protocols that use a ``global setup'', namely a mechanism that is also used by entities outside the protocol. These frameworks have broad applicability: Examples include public-key infrastructures, common reference strings, shared synchronization mechanisms, global blockchains, or even abstractions such as the random oracle. However, the need to work in a specialized framework has been a source of confusion, incompatibility, and an impediment to broader use. We show how security in the presence of a global setup can be captured within the plain UC framework, thus significantly simplifying the treatment. This is done as follows: - We extend UC-emulation to the case where both the emulating protocol $\pi$ and the emulated protocol $\phi$ make subroutine calls to protocol $\gamma$ that is accessible also outside $\pi$ and $\phi$. As usual, this notion considers only a single instance of $\phi$ or $\pi$ (alongside $\gamma$). - We extend the UC theorem to hold even with respect to the new notion of UC emulation. That is, we show that if $\pi$ UC-emulates $\phi$ in the presence of $\gamma$, then $\rho^{\phi\rightarrow\pi}$ UC-emulates $\rho$ for any protocol $\rho$, even when $\rho$ uses $\gamma$ directly, and in addition calls many instances of $\phi$, all of which use the same instance of $\gamma$. We prove this extension using the existing UC theorem as a black box, thus further simplifying the treatment. We also exemplify how our treatment can be used to streamline, within the plain UC model, proofs of security of systems that involve global set-up, thus providing greater simplicity and flexibility.
Subterranean 2.0 is a cipher suite that can be used for hashing, authenticated encryption, MAC computation, etc. It was designed by Daemen, Massolino, Mehrdad, and Rotella, and has been selected as a candidate in the second round of NIST's lightweight cryptography standardization process. Subterranean 2.0 is a duplex-based construction and utilizes a single-round permutation in the duplex. It is the simplicity of the round function that makes it an attractive target of cryptanalysis. In this paper, we examine the single-round permutation in various phases of Subterranean 2.0 and specify three related attack scenarios that deserve further investigation: keystream biases in the keyed squeezing phase, state collisions in the keyed absorbing phase, and one-round differential analysis in the nonce-misuse setting. To facilitate cryptanalysis in the first two scenarios, we novelly propose a set of size-reduced toy versions of Subterranean 2.0: Subterranean-m. Then we make an observation for the first time on the resemblance between the non-linear layer in the round function of Subterranean 2.0 and SIMON's round function. Inspired by the existing work on SIMON, we propose explicit formulas for computing the exact correlation of linear trails of Subterranean 2.0 and other ciphers utilizing similar non-linear operations. We then construct our models for searching trails to be used in the keystream bias evaluation and state collision attacks. Our results show that most instances of Subterranean-m are secure in the first two attack scenarios but there exist instances that are not. Further, we find a flaw in the designers' reasoning of Subterranean 2.0's linear bias but support the designers' claim that there is no linear bias measurable from at most $2^{96}$ data blocks. Due to the time-consuming search, the security of Subterranean 2.0 against the state collision attack in keyed modes still remains an open question. Finally, we observe that one-round differentials allow to recover state bits in the nonce-misuse setting. By proposing nested one-round differentials, we obtain a sufficient number of state bits, leading to a practical state recovery with only 20 repetitions of the nonce and 88 blocks of data. It is noted that our work does not threaten the security of Subterranean 2.0.
In this short paper, we provide a protocol to batch multiple non-membership proofs into a single proof of constant size with bilinear accumulators via a succinct argument of knowledge for polynomial commitments. We use similar techniques to provide a constant-sized proof that a polynomial commitment as in [KZG10] is a commitment to a separable (square-free) polynomial. In the context of the bilinear accumulator, this can be used to prove that a committed multiset is, in fact, a set. This has applications to any setting where a Verifier needs to be convinced that no element was added more than once. This protocol easily generalizes to a succinct protocol that shows that no element was inserted more than k times. We use the protocol for the derivative to link a committed polynomial to a commitment to its degree, in zero-knowledge. We have designed all of the protocols so that the Verifier needs to store just four elliptic curve points for any verification, despite the linear CRS. We also provide ways to speed up the verification of membership and non-membership proofs and to shift most of the computational burden from the Verifier to the Prover. Since all the challenges are public coin, the protocols can be made non-interactive with a Fiat-Shamir heuristic.
We present EverCrypt: a comprehensive collection of verified, high-performance cryptographic functionalities available via a carefully designed API. The API provably supports agility (choosing between multiple algorithms for the same functionality) and multiplexing (choosing between multiple implementations of the same algorithm). Through abstraction and zero-cost generic programming, we show how agility can simplify verification without sacrificing performance, and we demonstrate how C and assembly can be composed and verified against shared specifications. We substantiate the effectiveness of these techniques with new verified implementations (including hashes, Curve25519, and AES-GCM) whose performance matches or exceeds the best unverified implementations. We validate the API design with two high-performance verified case studies built atop EverCrypt, resulting in line-rate performance for a secure network protocol and a Merkle-tree library, used in a production blockchain, that supports 2.7 million insertions/sec. Altogether, EverCrypt consists of over 124K verified lines of specs, code, and proofs, and it produces over 29K lines of C and 14K lines of assembly code.
The complexity of computing the solutions of a system of multivariate polynomial equations by means of Groebner bases computations is upper bounded by a function of the solving degree. In this paper, we discuss how to rigorously estimate the solving degree of a system, focusing on systems arising within public-key cryptography. In particular, we show that it is upper bounded by, and often equal to, the Castelnuovo-Mumford regularity of the ideal generated by the homogenization of the equations of the system, or by the equations themselves in case they are homogeneous. We discuss the underlying commutative algebra and clarify under which assumptions the commonly used results hold. In particular, we discuss the assumption of being in generic coordinates (often required for bounds obtained following this type of approach) and prove that systems that contain the field equations or their fake Weil descent are in generic coordinates. We also compare the notion of solving degree with that of degree of regularity, which is commonly used in the literature. We complement the paper with some examples of bounds obtained following the strategy that we describe.
This paper surveys the landscape of security verification approaches and techniques for computer systems at various levels: from a software-application level all the way to the physical hardware level. Different existing projects are compared, based on the tools used and security aspects being examined. Since many systems require both hardware and software components to work together to provide the system's promised security protections, it is not sufficient to verify just the software levels or just the hardware levels in a mutually exclusive fashion. This survey especially highlights system levels that are verified by the different existing projects and presents to the readers the state of the art in hardware and software system security verification. Few approaches come close to providing full-system verification, and there is still much room for improvement.