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Improved Factoring Attacks on Multi-Prime RSA with Small Prime Difference

Sun, 03/18/2018 - 10:09
In this paper, we study the security of multi-prime RSA with small prime difference and propose two improved factoring attacks. The modulus involved in this variant is the product of r distinct prime factors of the same bit-size. Zhang and Takagi (ACISP 2013) showed a Fermat-like factoring attack on multi-prime RSA. In order to improve the previous result, we gather more information about the prime factors to derive r simultaneous modular equations. The first attack is to combine all the equations and solve one multivariate equation by generic lattice approaches. Since the equation form is similar to multi-prime Phi-hiding problem, we propose the second attack by applying the optimal linearization technique. We also show that our attacks can achieve better bounds in the experiments.

Practical Secure Aggregation for Privacy Preserving Machine Learning

Fri, 03/16/2018 - 13:35
We design a novel, communication-efficient, failure-robust protocol for secure aggregation of high-dimensional data. Our protocol allows a server to compute the sum of large, user-held data vectors from mobile devices in a secure manner (i.e. without learning each user's individual contribution), and can be used, for example, in a federated learning setting, to aggregate user-provided model updates for a deep neural network. We prove the security of our protocol in the honest-but-curious and malicious settings, and show that security is maintained even if an arbitrarily chosen subset of users drop out at any time. We evaluate the efficiency of our protocol and show, by complexity analysis and a concrete implementation, that its runtime and communication overhead remain low even on large data sets and client pools. For 16-bit input values, our protocol offers $1.73\times$ communication expansion for $2^{10}$ users and $2^{20}$-dimensional vectors, and $1.98\times$ expansion for $2^{14}$ users and $2^{24}$-dimensional vectors over sending data in the clear.

Highly-Efficient Fully-Anonymous Dynamic Group Signatures

Fri, 03/16/2018 - 10:08
Group signatures are a central tool in privacy-enhancing cryptography, which allow members of a group to anonymously produce signatures on behalf of the group. Consequently, they are an attractive means to implement privacy-friendly authentication mechanisms. Ideally, group signatures are dynamic and thus allow to dynamically and concurrently enroll new members to a group. For such schemes, Bellare et al. (CT-RSA'05) proposed the currently strongest security model (BSZ model). This model, in particular, ensures desirable anonymity guarantees. Given the prevalence of the resource asymmetry in current computing scenarios, i.e., a multitude of (highly) resource-constrained devices are communicating with powerful (cloud-powered) services, it is of utmost importance to have group signatures that are highly-efficient and can be deployed in such scenarios. Satisfying these requirements in particular means that the signing (client) operations are lightweight. We propose a novel, generic approach to construct dynamic group signature schemes, being provably secure in the BSZ model and particularly suitable for resource-constrained devices. Our results are interesting for various reasons: We can prove our construction secure without requiring random oracles. Moreover, when opting for an instantiation in the random oracle model (ROM) the so obtained scheme is extremely efficient and outperforms the fastest constructions providing anonymity in the BSZ model - which also rely on the ROM - known to date. Regarding constructions providing a weaker anonymity notion than BSZ, we surprisingly outperform the popular short BBS group signature scheme (CRYPTO'04; also proven secure in the ROM) and thereby even obtain shorter signatures. We provide a rigorous comparison with existing schemes that highlights the benefits of our scheme. On a more theoretical side, we provide the first construction following the "without encryption" paradigm introduced by Bichsel et al. (SCN'10) in the strong BSZ model.

CrowdBC: A Blockchain-based Decentralized Framework for Crowdsourcing

Thu, 03/15/2018 - 06:07
Crowdsourcing systems which utilize the human intelligence to solve complex tasks have gained considerable interest and adoption in recent years. However, the majority of existing crowdsourcing systems rely on central servers, which are subject to the weaknesses of traditional trust-based model, such as single point of failure. They are also vulnerable to distributed denial of service (DDoS) and Sybil attacks due to malicious users involvement. In addition, high service fees from the crowdsourcing platform may hinder the development of crowdsourcing. How to address these potential issues has both research and substantial value. In this paper, we conceptualize a blockchain-based decentralized framework for crowdsourcing named CrowdBC, in which a requester's task can be solved by a crowd of workers without relying on any third trusted institution, users' privacy can be guaranteed and only low transaction fees are required. In particular, we introduce the architecture of our proposed framework, based on which we give a concrete scheme. We further implement a software prototype on Ethereum with real-world dataset. Experiment results show the validity and effectiveness of our proposed crowdsourcing system.

On the Limitations of Computational Fuzzy Extractors

Thu, 03/15/2018 - 03:29
We present a negative result of fuzzy extractors with computational security. Specifically, we show that, under a certain computational condition, the existence of a computational fuzzy extractor implies the existence of an information-theoretic fuzzy extractor with slightly weaker parameters. The condition is that the generation procedure of the fuzzy extractor is efficiently invertible by an injective function. Our result implies that to circumvent the limitations of information-theoretic fuzzy extractors, we need to employ computational fuzzy extractors that are not invertible by injective functions.

MathCoin: A Blockchain Proposal that Helps Verify Mathematical Theorems In Public

Wed, 03/14/2018 - 17:06
A public blockchain is proposed in an attempt to enable the coin holders to participate in verifying mathematical theorems for public access. Incentives are designed to encourage any party to contribute their knowledge by buying tokens of mathematical propositions that they believe are true. The proposed blockchain is a platform for people to exchange their belief in mathematical propositions. An implementation of this blockchain proposal, once established, will provide the general public an easy and instant access to reliable knowledge without having to read difficult proofs or having to blindly trust a small number of experts. Conversely, experts from various fields may find it be much easier for making their work appreciated by more people, leading to a better impact. According to the incentive inherently provided by the blockchain, they can even earn significantly if they do prove some theorems that were not previously known by the blockchain. Foundations who are interested in the validity of a particular proposition not yet explicitly recorded on the blockchain can donate a fund, which will distribute to experts who contribute positive efforts toward solving the specified problems. Only the people who erroneously create or buy tokens of a proposition that is eventually proven false will lose money. A reference design of the proposed blockchain that attempts to achieve the above-mentioned goal is described and reasoned.

A Brief Retrospective Look at the Cayley-Purser Public-key Cryptosystem, 19 Years Later

Wed, 03/14/2018 - 17:06
The purpose of this paper is to describe and analyze the Cayley-Purser algorithm, which is a public-key cryptosystem proposed by Flannery in 1999. I will present two attacks on it, one of which is apparently new. I will also examine a variant of the Cayley-Purser algorithm that was patented by Slavin in 2008, and show that it is also insecure.

Vault: Fast Bootstrapping for Cryptocurrencies

Tue, 03/13/2018 - 15:53
Decentralized cryptocurrencies rely on participants to keep track of the state of the system in order to verify new transactions. As the number of users and transactions grows, this requirement places a significant burden on the users, as they need to download, verify, and store a large amount of data in order to participate. Vault is a new cryptocurrency designed to minimize these storage and bootstrapping costs for participants. Vault builds on Algorand’s proof-of-stake consensus protocol and uses several techniques to achieve its goals. First, Vault decouples the storage of recent transactions from the storage of account balances, which enables Vault to delete old account state. Second, Vault allows sharding state across participants in a way that preserves strong security guarantees. Finally, Vault introduces the notion of stamping certificates that allow a new client to catch up securely and efficiently in a proof-of-stake system without having to verify every single block. Experiments with a prototype implementation of Vault’s data structures shows that Vault reduces the bandwidth cost of joining the network as a full client by 99.7% compared to Bitcoin and 90.5% compared to Ethereum when downloading a ledger containing 500 million transactions.

Oblivious RAM with Small Storage Overhead

Tue, 03/13/2018 - 15:52
In this work, we present a new approach to constructing Oblivious RAM (ORAM). Somewhat surprisingly, and despite the large amount of research interest that ORAM has received, all existing ORAM constructions are based on a handful of conceptually different approaches. We believe it is of theoretical and practical interest to explore new ways to construct this primitive. Our first construction is conceptually extremely simple and has a worst-case bandwidth overhead of $\mathcal{O}\left(\sqrt{N} \frac{\log{N}}{\log{\log{N}}}\right)$, where N is the number of data blocks. Our main construction, Lookahead ORAM, has a worst-case bandwidth overhead of $\mathcal{O}\left(\sqrt{N}\right)$ and an additive storage overhead of $\sqrt{2N}$, which is the smallest concrete storage overhead among all existing ORAM constructions with sublinear worst-case bandwidth overhead. A small storage overhead is particularly beneficial in outsourced storage settings, where data owners have to pay their storage provider for the amount of storage they consume. In addition to having a small storage overhead, Lookahead ORAM has perfect correctness, i.e. every operation on the ORAM data structure succeeds with probability 1 and, assuming the client stores some small stash of data locally, an online bandwidth overhead of $\mathcal{O}\left(1\right)$ without server-side computation. In comparison with prior work that has sublinear worst-case bandwidth overhead, Lookahead ORAM is asymptotically the most efficient ORAM with perfect correctness.

Authenticated key exchange for SIDH

Tue, 03/13/2018 - 15:02
We survey authenticated key exchange (AKE) in the context of supersingular isogeny Diffie-Hellman key exchange (SIDH). We discuss different approaches to achieve authenticated key exchange, and survey the literature. We explain some challenges that arise in the SIDH setting if one wants to do a ``Diffie-Hellman-like'' AKE, and present several candidate authenticated key exchange protocols suitable for SIDH. We also discuss some open problems.

Compact, Scalable, and Efficient Discrete Gaussian Samplers for Lattice-Based Cryptography

Tue, 03/13/2018 - 15:01
Lattice-based cryptography, one of the leading candidates for post-quantum security, relies heavily on discrete Gaussian samplers to provide necessary uncertainty, obfuscating computations on secret information. For reconfigurable hardware, the cumulative distribution table (CDT) scheme has previously been shown to achieve the highest throughput and the smallest resource utilisation, easily outperforming other existing samplers. However, the CDT sampler does not scale well. In fact, for large parameters, the lookup tables required are far too large to be practically implemented. This research proposes a hierarchy of multiple smaller samplers, extending the Gaussian convolution lemma to compute optimal parameters, where the individual samplers require much smaller lookup tables. A large range of parameter sets, covering encryption, signatures, and key exchange are evaluated. Hardware-optimised parameters are formulated and a practical implementation on Xilinx Artix- 7 FPGA device is realised. The proposed sampling designs demonstrate promising performance on reconfigurable hardware, even for large parameters, that were otherwise thought infeasible.

Identification Protocols and Signature Schemes Based on Supersingular Isogeny Problems

Tue, 03/13/2018 - 15:01
We present signature schemes whose security relies on computational assumptions relating to isogeny graphs of supersingular elliptic curves. We give two schemes, both of them based on interactive identification protocols. The first identification protocol is due to De Feo, Jao and Pl{\^{u}}t. The second one, and the main contribution of the paper, makes novel use of an algorithm of Kohel-Lauter-Petit-Tignol for the quaternion version of the $\ell$-isogeny problem, for which we provide a more complete description and analysis, and is based on a more standard and potentially stronger computational problem. Both identification protocols lead to signatures that are existentially unforgeable under chosen message attacks in the random oracle model using the well-known Fiat-Shamir transform, and in the quantum random oracle model using another transform due to Unruh. A version of the first signature scheme was indepdendently published by Yoo, Azarderakhsh, Jalali, Jao and Soukharev. This is the full version of a paper published at ASIACRYPT 2017.

Bulletproofs: Short Proofs for Confidential Transactions and More

Tue, 03/13/2018 - 03:36
We propose Bulletproofs, a new non-interactive zero-knowledge proof protocol with very short proofs and without a trusted setup; the proof size is only logarithmic in the witness size. Bulletproofs are especially well suited for efficient range proofs on committed values: they enable proving that a committed value is in a range using only $2\log_2(n)+9$ group and field elements, where $n$ is the bit length of the range. Proof generation and verification times are linear in $n$. Bulletproofs greatly improve on the linear (in $n$) sized range proofs in existing proposals for confidential transactions in Bitcoin and other cryptocurrencies. Moreover, Bulletproofs supports aggregation of range proofs, so that a party can prove that $m$ commitments lie in a given range by providing only an additive $O(\log(m))$ group elements over the length of a single proof. To aggregate proofs from multiple parties, we enable the parties to generate a single proof without revealing their inputs to each other via a simple multi-party computation (MPC) protocol for constructing Bulletproofs. This MPC protocol uses either a constant number of rounds and linear communication, or a logarithmic number of rounds and logarithmic communication. We show that verification time, while asymptotically linear, is very efficient in practice. Moreover, the verification of multiple Bulletproofs can be batched for further speed-up. Concretely, the marginal time to verify an aggregation of 16 range proofs is about the same as the time to verify 16 ECDSA signatures. Bulletproofs build on the techniques of Bootle et al. (EUROCRYPT 2016). Beyond range proofs, Bulletproofs provide short zero-knowledge proofs for general arithmetic circuits while only relying on the discrete logarithm assumption and without requiring a trusted setup. We discuss many applications that would benefit from Bulletproofs, primarily in the area of cryptocurrencies. The efficiency of Bulletproofs is particularly well suited for the distributed and trustless nature of blockchains.

Detecting General Algebraic Manipulation Attacks

Tue, 03/13/2018 - 01:46
Algebraic manipulation detection codes are a class of error detecting codes which have found numerous applications in cryptography. In this paper we extend these codes to defeat general algebraic attacks - we call such codes general algebraic manipulation detection (GAMD) codes. Positive results are shown for the existence of GAMDs for the families of tampering functions corresponding to point additions and polynomial functions over a finite field. Compared to non-malleable codes, we demonstrate both positive and negative results regarding the existence of GAMDs for arbitrary families of tampering functions.

Security proof for Quantum Key Recycling with noise

Mon, 03/12/2018 - 09:01
Quantum Key Recycling aims to re-use the keys employed in quantum encryption and quantum authentication schemes. We consider QKR protocols where classical information is embedded in qubit states. A partial security analysis for such protocols was done in [LS2018]. In the current paper we introduce a number of small protocol modifications and provide a security proof. Our proof is based on a computation of the statistical distance between the real quantum state of the system and a state in which the keys are completely secure. This is a non-asymptotic result. It also determines how much privacy amplification is needed as a function of the bit error rate. It turns out that less privacy amplification is needed than suggested by the min-entropy analysis in [LS2018].

An Efficient and Secure Attribute-Based Signcryption Scheme for Smart Grid Applications

Mon, 03/12/2018 - 09:00
With regards to the development of modern power systems, Smart Grid (SG) as an intelligent generation of electricity networks has been faced with a tremendous attention. Fine-grained data sharing in SG plays a vital role in efficiently managing data flow in the SG. As these data commonly contain sensitive information, design of the secure and efficient privacy-preserving schemes for such networks with plenty of resource constrained devices is one of the most controversial issues. In this paper, we propose a secure Ciphertext-Policy Attribute-Based SignCryption (CP-ABSC) scheme which simultaneously provides the authenticity and privacy of the users by enforcing an arbitrary access control policy on encrypted data. Since the number of required pairings in the signcryption and designcryption algorithms are independent to the number of the involved attributes, the computational overhead is reduced in comparison with the existing schemes in the literature. In addition, we formally prove that the unforgeability and indistinguishability of the proposed scheme are reducible to the well-known hardness assumption of the q-Bilinear Diffie-Hellman Exponent (q-BDHE) problem. Moreover, we show that embedding a Physical Unclonable Function (PUF) in each smart meter will significantly reduce the storage overhead of the protocol and secure it against non-volatile memory attackers.

Chimeric Ledgers: Translating and Unifying UTXO-based and Account-based Cryptocurrencies

Mon, 03/12/2018 - 08:58
Cryptocurrencies are historically divided in two broad groups with respect to the style of transactions that they accept. In the account-based style, each address is seen as an account with a balance, and transactions are transfers of value from one account to another. In the UTXO-based style, transactions inductively spend outputs generated by previous trans- actions and create new unspent outputs, and there is no intrinsic notion of account associated with an address. Each style has advantages and disadvantages. This paper formally defines: the two styles; translations that allow to simulate one style by the other; new transaction types that allow both styles of transactions to co-exist on the same ledger; and a new transaction type that combines features from both styles.

Indifferentiability of 8-Round Feistel Networks

Mon, 03/12/2018 - 02:25
We prove that a balanced 8-round Feistel network is indifferentiable from a random permutation. This result comes on the heels of (and is part of the same body of work as) a 10-round indifferentiability result for Feistel network recently announced by the same team of authors. The current 8-round simulator achieves similar security, query complexity and runtime as the 10-round simulator and is not significantly more involved. The security of our simulator is also slightly better than the security of the 14-round simulator of Holenstein et al. for essentially the same runtime and query complexity.

Post-Quantum Group Signatures from Symmetric Primitives

Sun, 03/11/2018 - 21:02
Group signatures are used extensively for privacy in anonymous credentials schemes and in real-world systems for hardware enclave attestation. As such, there is a strong interest in making these schemes post-quantum secure. In this paper we initiate the study of group signature schemes built only from symmetric primitives, such as hash functions and PRFs, widely regarded as the safest primitives for post-quantum security. We present two constructions in the random oracle model. The first is a group signature scheme satisfying the EPID group signature syntax and security definitions needed for private hardware attestation used in Intel’s SGX. The second achieves significantly shorter signatures for many applications, including the use case of remote hardware attestation. While our group signatures for attestation are longer than standard (nongroup) post-quantum signatures, they are short enough for applications where the data being signed is large, such as analytics on large private data sets, or streaming media to a trusted display. We evaluate several instantiations of our schemes so that the costs and benefits of these constructions are clear. Along the way we also give improvements to the zero-knowledge Merkle inclusion proofs of Derler et al. (2017).

Deterministic Public-Key Encryption for Adaptively Chosen Plaintext Distributions

Sun, 03/11/2018 - 03:46
Bellare, Boldyreva, and O'Neill (CRYPTO '07) initiated the study of deterministic public-key encryption as an alternative in scenarios where randomized encryption has inherent drawbacks. The resulting line of research has so far guaranteed security only for adversarially-chosen plaintext distributions that are independent of the public key used by the scheme. In most scenarios, however, it is typically not realistic to assume that adversaries do not take the public key into account when attacking a scheme. We show that it is possible to guarantee meaningful security even for plaintext distributions that depend on the public key. We extend the previously proposed notions of security, allowing adversaries to adaptively choose plaintext distributions {\em after} seeing the public key, in an interactive manner. The only restrictions we make are that: (1) plaintext distributions are unpredictable (as is essential in deterministic public-key encryption), and (2) the number of plaintext distributions from which each adversary is allowed to adaptively choose is upper bounded by $2^{p}$, where $p$ can be any predetermined polynomial in the security parameter and plaintext length. For example, with $p = 0$ we capture plaintext distributions that are independent of the public key, and with $p = O(s \log s)$ we capture, in particular, all plaintext distributions that are samplable by circuits of size $s$. Within our framework we present both constructions in the random-oracle model based on any public-key encryption scheme, and constructions in the standard model based on lossy trapdoor functions (thus, based on a variety of number-theoretic assumptions). Previously known constructions heavily relied on the independence between the plaintext distributions and the public key for the purposes of randomness extraction. In our setting, however, randomness extraction becomes significantly more challenging once the plaintext distributions and the public key are no longer independent. Our approach is inspired by research on randomness extraction from seed-dependent distributions. Underlying our approach is a new generalization of a method for such randomness extraction, originally introduced by Trevisan and Vadhan (FOCS '00) and Dodis (PhD Thesis, MIT, '00).

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