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Fork-Free Hybrid Consensus with Flexible Proof-of-Activity

Mon, 09/25/2017 - 10:31
Bitcoin and its underlying blockchain mechanism have been attracting much attention. One of their core innovations, Proof-of-Work (PoW), is notoriously inefficient which potentially motivates a centralization of computing power, defeating the original goal of decentralization. Proof-of-Stake (PoS) is later proposed to replace PoW. However, both PoW and PoS have different inherent advantages and disadvantages, so does Proof-of-Activity (PoA) of Bentov et al. (SIGMETRICS 2014) which only offers limited combinations of two mechanisms. On the other hand, the hybrid consensus protocol of Pass and Shi (ePrint 16/917) aims to improve the efficiency by dynamically maintaining a rotating committee. Yet, there are unsatisfactory issues including chain forks and fair committee election. In this paper, we firstly devise a generalized variant of PoW. After that, we leverage our newly proposed generalized PoW to construct a fork-free hybrid consensus protocol, which addresses issues faced by the existing hybrid consensus mechanism. We further combine our fork-free hybrid consensus mechanism with PoS for a flexible version of PoA, which offers a flexible combination of PoW and PoS. Compared with Bentov et al.’s PoA, our “flexible PoA” improves the efficiency and provides more flexible combinations of PoW and PoS, resulting in a more powerful and applicable consensus protocol.

0-RTT Key Exchange with Full Forward Secrecy

Mon, 09/25/2017 - 08:42
Reducing latency overhead while maintaining critical security guarantees like forward secrecy has become a major design goal for key exchange (KE) protocols, both in academia and industry. Of particular interest in this regard are 0-RTT protocols, a class of KE protocols which allow a client to send cryptographically protected payload in zero round-trip time (0-RTT) along with the very first KE protocol message, thereby minimizing latency. Prominent examples are Google's QUIC protocol and the upcoming TLS protocol version 1.3. Intrinsically, the main challenge in a 0-RTT key exchange is to achieve forward secrecy and security against replay attacks for the very first payload message sent in the protocol. According to cryptographic folklore, it is impossible to achieve forward secrecy for this message, because the session key used to protect it must depend on a non-ephemeral secret of the receiver. If this secret is later leaked to an attacker, it should intuitively be possible for the attacker to compute the session key by performing the same computations as the receiver in the actual session. In this paper we show that this belief is actually false. We construct the first 0-RTT key exchange protocol which provides full forward secrecy for all transmitted payload messages and is automatically resilient to replay attacks. In our construction we leverage a puncturable key encapsulation scheme which permits each ciphertext to only be decrypted once. Fundamentally, this is achieved by evolving the secret key after each decryption operation, but without modifying the corresponding public key or relying on shared state. Our construction can be seen as an application of the puncturable encryption idea of Green and Miers (S&P 2015). We provide a new generic and standard-model construction of this tool that can be instantiated with any selectively secure hierarchical identity-based key encapsulation scheme.

Why Attackers Lose: Design and Security Analysis of Arbitrarily Large XOR Arbiter PUFs

Mon, 09/25/2017 - 08:26
In a novel analysis, we formally prove that arbitrarily many Arbiter PUFs can be combined into a stable XOR Arbiter PUF. To the best of our knowledge, this design cannot be modeled by any known oracle access attack in polynomial time. Using majority vote of arbiter chain responses, our analysis shows that with a polynomial number of votes, the XOR Arbiter PUF stability of almost all challenges can be boosted exponentially close to 1; that is, the stability gain through majority voting can exceed the stability loss introduced by large XORs for a feasible number of votes. Considering state-of-the-art modeling attacks by Becker and Rührmair et al., our proposal enables the designer to increase the attacker's effort exponentially while still maintaining polynomial design effort. This is the first result that relates PUF design to this traditional cryptographic design principle.

Delayed-Input Non-Malleable Zero Knowledge and Multi-Party Coin Tossing in Four Rounds

Mon, 09/25/2017 - 08:26
In this work we start from the following two results in the state-of-the art: 1)4-round non-malleable zero knowledge (NMZK): Goyal et al. in FOCS 2014 showed the first 4-round one-one NMZK argument from one-way functions (OWFs). Their construction requires the prover to know the instance and the witness already at the 2nd round. 2) 4-round multi-party coin tossing (MPCT): Garg et al. in Eurocrypt 2016 showed the first 4-round protocol for MPCT. Their result crucially relies on 3-round 3-robust parallel non-malleable commitments. So far there is no candidate construction for such a commitment scheme under standard polynomial-time hardness assumptions. We improve the state-of-the art on NMZK and MPCT by presenting the following two results: 1) a delayed-input 4-round one-many NMZK argument $\Pi_{NMZK}$ from OWFs; moreover $\Pi_{NMZK}$ is also a delayed-input many-many synchronous NMZK argument. 2) a 4-round MPCT protocol $\Pi_{MPCT}$ from one-to-one OWFs; $\Pi_{MPCT}$ uses $\Pi_{NMZK}$ as subprotocol and exploits the special properties (e.g., delayed input, many-many synchronous) of $\Pi_{NMZK}$. Both $\Pi_{NMZK}$ and $\Pi_{MPCT}$ make use of a special proof of knowledge that offers additional security guarantees when played in parallel with other protocols. The new technique behind such a proof of knowledge is an additional contribution of this work and is of independent interest.

Four-state Non-malleable Codes with Explicit Constant Rate

Mon, 09/25/2017 - 08:25
Non-malleable codes (NMCs), introduced by Dziembowski, Pietrzak and Wichs (ITCS 2010), generalize the classical notion of error correcting codes by providing a powerful guarantee even in scenarios where error correcting codes cannot provide any guarantee: a decoded message is either the same or completely independent of the underlying message, regardless of the number of errors introduced into the codeword. Informally, NMCs are defined with respect to a family of tampering functions $F$ and guarantee that any tampered codeword either decodes to the same message or to an independent message, so long as it is tampered using a function $f \in F$. Nearly all known constructions of NMCs are for the $t$-split-state family, where the adversary tampers each of the $t$ blocks (also known as states), of a codeword, arbitrarily but independently. Cheraghchi and Guruswami (TCC 2014) obtain a Rate-1 non-malleable code for the case where $t = O(n)$ with $n$ being the codeword length and, in (ITCS 2014), show an upper bound of $1-1/t$ on the best achievable rate for any $t-$split state NMC. For $t=10$, Chattopadhyay and Zuckerman (FOCS 2014) achieve a constant rate construction where the constant is unknown. In summary, there is no known construction of an NMC with an explicit constant rate for any $t= o(n)$, let alone one that comes close to matching Cheraghchi and Guruswami's lowerbound! In this work, we construct an efficient non-malleable code in the $t$-split-state model, for $t=4$, that achieves a constant rate of $\frac{1}{3+\zeta}$, for any constant $\zeta > 0$, and error $2^{-\Omega(\ell / log^{c+1} \ell)}$, where $\ell$ is the length of the message and $c > 0$ is a constant.

A Concrete Treatment of Fiat-Shamir Signatures in the Quantum Random-Oracle Model

Mon, 09/25/2017 - 07:03
The Fiat-Shamir transform is a technique for combining a hash function and an identification scheme to produce a digital signature scheme. The resulting scheme is known to be secure in the random oracle model (ROM), which does not, however, imply security in the scenario where the adversary also has quantum access to the oracle. Due to the announced eventual change-over to cryptographic schemes that should resist attacks by quantum adversaries, the problem of constructing secure Fiat-Shamir signature schemes in the quantum random oracle model (QROM) has received increased interest. There have been recent results that proved the security of specific schemes (e.g., Alkim et al.~PQC 2017) constructed via the Fiat-Shamir transform, as well as those that gave more general constructions (e.g., Unruh, ASIACRYPT 2017), but only with asymptotic security proofs. The goal of this current paper is to create a generic framework for constructing tight reductions in the QROM from underlying hard problems to Fiat-Shamir signatures. Our generic reduction is composed of two results whose proofs, we believe, are simple and natural. We first consider a security notion (UF-NMA) in which the adversary obtains the public key and attempts to create a valid signature without accessing a signing oracle. We give a tight reduction showing that deterministic signatures (i.e., ones in which the randomness is derived from the message and the secret key) that are UF-NMA secure are also secure under the standard chosen message attack (UF-CMA) security definition. Our second result is showing that if the identification scheme is ``lossy'', as defined in (Abdalla et al.~Eurocrypt 2012), then the security of the UF-NMA scheme is tightly based on the hardness of distinguishing regular and lossy public keys of the identification scheme. This latter distinguishing problem is normally exactly the definition of some presumably-hard mathematical problem. The combination of these components gives our main result. As a concrete instantiation of our framework, we modify the recent lattice-based Dilithium digital signature scheme (Ducas et al., EPRINT 2017) so that its underlying identification scheme admits lossy public keys. The original Dilithium scheme, which is proven secure in the classical ROM based on standard lattice assumptions, has $1.5$KB public keys and $2.7$KB signatures. The new scheme, which is tightly based on the hardness of the Module-LWE problem in the QROM using our generic reductions, has $7.7$KB public keys and $5.7$KB signatures for the same security level. Furthermore, due to our proof of equivalence between the UF-NMA and UF-CMA security notions of deterministic signature schemes, we can formulate a new non-interactive assumption under which the original Dilithium signature scheme is also tightly secure in the QROM.

Kaleidoscope: An Efficient Poker Protocol with Payment Distribution and Penalty Enforcement

Mon, 09/25/2017 - 04:46
The research on secure poker protocols without trusted intermediaries has a long history that dates back to modern cryptography's infancy. Two main challenges towards bringing it into real-life are enforcing the distribution of the rewards, and penalizing misbehaving/aborting parties. Using recent advances on cryptocurrencies and blockchain technologies, Andrychowicz et al. (IEEE S\&P 2014 and FC 2014 BITCOIN Workshop) were able to address those problems. Improving on these results, Kumaresan et al. (CCS 2015) and Bentov et al. (ASIACRYPT 2017) proposed specific purpose poker protocols that made significant progress towards meeting the real-world deployment requirements. However, their protocols still lack either efficiency or a formal security proof in a strong model. Specifically, the work of Kumaresan et al. relies on Bitcoin and simple contracts, but is not very efficient as it needs numerous interactions with the cryptocurrency network as well as a lot of collateral. Bentov et al. achieve further improvements by using stateful contracts and off-chain execution: they show a solution based on general multiparty computation that has a security proof in a strong model, but is also not very efficient. Alternatively, it proposes to use tailor-made poker protocols as a building block to improve the efficiency. However, a security proof is unfortunately still missing for the latter case: the security properties the tailor-made protocol would need to meet were not even specified, let alone proven to be met by a given protocol. Our solution closes this undesirable gap as it concurrently: (1) enforces the rewards' distribution; (2) enforces penalties on misbehaving parties; (3) has efficiency comparable to the tailor-made protocols; (4) has a security proof in a simulation-based model of security. Combining techniques from the above works, from tailor-made poker protocols and from efficient zero-knowledge proofs for shuffles, and performing optimizations, we obtain a solution that satisfies all four desired criteria and does not incur a big burden on the blockchain.

"Oops, I did it again" -- Security of One-Time Signatures under Two-Message Attacks

Mon, 09/25/2017 - 04:25
One-time signatures (OTS) are called one-time, because the accompanying reductions only guarantee security under single-message attacks. However, this does not imply that efficient attacks are possible under two-message attacks. Especially in the context of hash-based OTS (which are basic building blocks of recent standardization proposals) this leads to the question if accidental reuse of a one-time key pair leads to immediate loss of security or to graceful degradation. In this work we analyze the security of the most prominent hash-based OTS, Lamport's scheme, its optimized variant, and WOTS, under different kinds of two-message attacks. Interestingly, it turns out that the schemes are still secure under two message attacks, asymptotically. However, this does not imply anything for typical parameters. Our results show that for Lamport's scheme, security only slowly degrades in the relevant attack scenarios and typical parameters are still somewhat secure, even in case of a two-message attack. As we move on to optimized Lamport and its generalization WOTS, security degrades faster and faster, and typical parameters do not provide any reasonable level of security under two-message attacks.

Variable-Length Bit Mapping and Error-Correcting Codes for Higher-Order Alphabet PUFs

Mon, 09/25/2017 - 04:11
Device-specific physical characteristics provide the foundation for PUFs, a hardware primitive for secure storage of cryptographic keys. So far, they have been implemented by either directly evaluating a binary output or by mapping outputs from a higher-order alphabet to a fixed-length bit sequence. However, the latter causes a significant bias in the derived key when combined with an equidistant quantization. To overcome this limitation, we propose a variable-length bit mapping that reflects the properties of a Gray code in a different metric, namely the Levenshtein metric instead of the classical Hamming metric. Subsequent error-correction is therefore based on a custom insertion/deletion correcting code. This new approach effectively counteracts the bias in the derived key already at the input side. We present the concept for our scheme and demonstrate its feasibility based on an empirical PUF distribution. As a result, we increase the effective output bit length of the secret by over 40% compared to state-of-the-art approaches while at the same time obtaining additional advantages, e.g., an improved tamper-sensitivity. This opens up a new direction of Error-Correcting Codes (ECCs) for PUFs that output responses with symbols of higher-order output alphabets.

Clarifying the subset-resilience problem

Mon, 09/25/2017 - 02:29
We investigate the subset-resilience problem, defined in 2002 by Reyzin and Reyzin to analyze their HORS signature scheme. We show that textbook HORS is insecure against adaptive attacks, and present a practical attack based on a greedy algorithm. We also describe weak messages for HORS, that map to smaller subsets than expected, and are thus easier to cover. This leads to an improved attack against HORS and to an improved classical attack against the signature scheme SPHINCS, of complexity $2^{270}$ instead of $2^{277}$. We propose the PRNG to obtain a random subset construction (PORS), which avoids weak messages, for a tiny computational overhead. We adapt PORS to SPHINCS to also deterministically select the HORST instance that is used to sign the input message. This new construction reduces the attack surface and increases the security level, improving the security of SPHINCS by 67 bits against classical attacks and 33 bits against quantum attacks. A version of SPHINCS using our PORS construction can work with smaller parameters that reduce the signature size by 4616 bytes and speed up signature and verification, for the same 128-bit post-quantum security as the original SPHINCS.

How to Securely Compute with Noisy Leakage in Quasilinear Complexity

Sun, 09/24/2017 - 22:46
Since their introduction in the late 90's, side-channel attacks have been considered as a major threat against cryptographic implementations. This threat has raised the need for formal leakage models in which the security of implementations can be proved. At Eurocrypt 2013, Prouff and Rivain introduced the noisy leakage model which has been argued to soundly capture the physical reality of power and electromagnetic leakages. In their work, they also provide the first formal security proof for a masking scheme in the noisy leakage model. However their work has two important limitations: (i) the security proof relies on the existence of a leak-free component, (ii) the tolerated amount of information in the leakage (aka leakage rate) is of $O(1/n)$ where $n$ is the number of shares in the underlying masking scheme. The first limitation was nicely tackled by Duc, Dziembowski and Faust one year later (Eurocrypt 2014). Their main contribution was to show a security reduction from the noisy leakage model to the conceptually simpler random-probing model. They were then able to prove the security of the well-known Ishai-Sahai-Wagner scheme (Crypto 2003) in the noisy leakage model. The second limitation was addressed last year in a paper by Andrychowicz, Dziembowski and Faust (Eurocrypt 2016). The proposed construction achieves security in the strong adaptive probing model with a leakage rate of $O(1/\log n)$ at the cost of a $O(n^2 \log n)$ complexity. The authors argue that their result can be translated into the noisy leakage model with a leakage rate of $O(1)$ by using secret sharing based on algebraic geometric codes. They further argue that the efficiency of their construction can be improved by a linear factor using packed secret sharing but no details are provided. In this paper, we show how to compute in the presence of noisy leakage with a leakage rate up to $\tilde{O}(1)$ in complexity $\tilde{O}(n)$. We use a polynomial encoding allowing quasilinear multiplication based on the fast Number Theoretic Transform (NTT). We first show that our scheme is secure in the random-probing model with leakage rate $O(1/\log n)$. Using the reduction by Duc et al. this result can be translated in the noisy leakage model with a $O(1/|\mathbb{F}|^2 \log n)$ leakage rate. However, as in the work of Andrychowicz et al., our construction also requires $|\mathbb{F}| = O(n)$. In order to bypass this issue, we refine the granularity of our computation by considering the noisy leakage model on logical instructions} that work on constant-size machine words. We provide a generic security reduction from the noisy leakage model at the logical-instruction level to the random-probing model at the arithmetic level. This reduction allows us to prove the security of our construction in the noisy leakage model with leakage rate $\tilde{O}(1)$.

Stadium: A Distributed Metadata-Private Messaging System

Sun, 09/24/2017 - 22:35
Private communication over the Internet remains a challenging problem. Even if messages are encrypted, it is hard to deliver them without revealing metadata about which pairs of users are communicating. Scalable anonymity systems, such as Tor, are susceptible to traffic analysis attacks that leak metadata. In contrast, the largest-scale systems with metadata privacy require passing all messages through a small number of providers, requiring a high operational cost for each provider and limiting their deployability in practice. This paper presents Stadium, a point-to-point messaging system that provides metadata and data privacy while scaling its work efficiently across hundreds of low-cost providers operated by different organizations. Much like Vuvuzela, the current largest-scale metadata-private system, Stadium achieves its provable guarantees through differential privacy and the addition of noisy cover traffic. The key challenge in Stadium is limiting the information revealed from the many observable traffic links of a highly distributed system, without requiring an overwhelming amount of noise. To solve this challenge, Stadium introduces techniques for distributed noise generation and differentially private routing as well as a verifiable parallel mixnet design where the servers collaboratively check that others follow the protocol. We show that Stadium can scale to support 4X more users than Vuvuzela using servers that cost an order of magnitude less to operate than Vuvuzela nodes.

Environmental Authentication in Malware

Sun, 09/24/2017 - 21:25
Malware needs to execute on a target machine while simultaneously keeping its payload confidential from a malware analyst. Standard encryption can be used to ensure the confidentiality, but it does not address the problem of hiding the key. Any analyst can find the decryption key if it is stored in the malware or derived in plain view. One approach is to derive the key from a part of the environment which changes when the analyst is present. Such malware derives a key from the environment and encrypts its true functionality under this key. In this paper, we present a formal framework for environmental authentication. We formalize the interaction between malware and analyst in three settings: 1) blind: in which the analyst does not have access to the target environment, 2) basic: where the analyst can load a single analysis toolkit on an effected target, and 3) resettable: where the analyst can create multiple copies of an infected environment. We show necessary and sufficient conditions for malware security in the blind and basic games and show that even under mild conditions, the analyst can always win in the resettable scenario.

How to Construct a Leakage-Resilient (Stateless) Trusted Party

Sun, 09/24/2017 - 20:59
Trusted parties and devices are commonly used in the real world to securely perform computations on secret inputs. However, their security can often be compromised by side-channel attacks in which the adversary obtains partial leakage on intermediate computation values. This gives rise to the following natural question: To what extent can one protect the trusted party against leakage? Our goal is to design a hardware device $T$ that allows $m\ge 1$ parties to securely evaluate a function $f(x_1,\ldots,x_m)$ of their inputs by feeding $T$ with encoded inputs that are obtained using local secret randomness. Security should hold even in the presence of an active adversary that can corrupt a subset of parties and obtain restricted leakage on the internal computations in $T$. We design hardware devices $T$ in this setting both for zero-knowledge proofs and for general multi-party computations. Our constructions can unconditionally resist either $AC^0$ leakage or a strong form of ``only computation leaks'' (OCL) leakage that captures realistic side-channel attacks, providing different tradeoffs between efficiency and security.

Resettably-Sound Resettable Zero Knowledge in Constant Rounds

Sun, 09/24/2017 - 19:56
In FOCS 2001 Barak et al. conjectured the existence of zero-knowledge arguments that remain secure against resetting provers and resetting verifiers. The conjecture was proven true by Deng et al. in FOCS 2009 under various complexity assumptions and requiring a polynomial number of rounds. Later on in FOCS 2013 Chung et al. improved the assumptions requiring one-way functions only but still with a polynomial number of rounds. In this work we show a constant-round resettably-sound resettable zero-knowledge argument system, therefore improving the round complexity from polynomial to constant. We obtain this result through the following steps. 1. We show an explicit transform from any $\ell$-round concurrent zero-knowledge argument system into an $O(\ell)$-round resettable zero-knowledge argument system. The transform is based on techniques proposed by Barak et al. in FOCS 2001 and by Deng et al. in FOCS 2009. Then, we make use of a recent breakthrough presented by Chung et al. in CRYPTO 2015 that solved the longstanding open question of constructing a constant-round concurrent zero-knowledge argument system from plausible polynomial-time hardness assumptions. Starting with their construction $\Gamma$ we obtain a constant-round resettable zero-knowledge argument system $\Lambda$. 2. We then show that by carefully embedding $\Lambda$ inside $\Gamma$ (i.e., essentially by playing a modification of the construction of Chung et al. against the construction of Chung et al.) we obtain the first constant-round resettably-sound concurrent zero-knowledge argument system $\Delta$. 3. Finally, we apply a transformation due to Deng et al. to $\Delta$ obtaining a resettably-sound resettable zero-knowledge argument system $\Pi$, the main result of this work. While our round-preserving transform for resettable zero knowledge requires one-way functions only, both $\Lambda, \Delta$ and $\Pi$ extend the work of Chung et al. and as such they rely on the same assumptions (i.e., families of collision-resistant hash functions, one-way permutations and indistinguishability obfuscation for P/poly, with slightly super-polynomial security).

Batched Multi-hop Multi-key FHE from ring-LWE with Compact Ciphertext Extension

Sun, 09/24/2017 - 19:43
Traditional fully homomorphic encryption (FHE) schemes support computation on data encrypted under a single key. In STOC 2012, L\'opez-Alt et al. introduced the notion of multi-key FHE (MKFHE), which allows homomorphic computation on ciphertexts encrypted under different keys. In this work, we focus on MKFHE constructions from standard assumptions and propose a new construction of ring-LWE-based multi-hop MKFHE scheme. Our work is based on Brakerski-Gentry-Vaikuntanathan (BGV) FHE scheme where, in contrast, all the previous works on multi-key FHE with standard assumptions were based on Gentry-Sahai-Waters (GSW) FHE scheme. Therefore, our construction can encrypt ring elements rather than a single bit and naturally inherits the advantages in aspects of the ciphertext/plaintext ratio and the complexity of homomorphic operations. Moveover, the proposed MKFHE scheme supports the Chinese Remainder Theorem (CRT)-based ciphertexts packing technique, achieves $poly\left(k,L,\log n\right)$ computation overhead for $k$ users, circuits with depth at most $L$ and an $n$ dimensional lattice, and gives the first batched MKFHE scheme based on standard assumptions to our knowledge. Furthermore, the ciphertext extension algorithms of previous schemes need to perform complex computation on each ciphertext, while our extension algorithm just needs to generate evaluation keys for the extended scheme. So the complexity of ciphertext extension is only dependent on the number of associated parities but not on the number of ciphertexts. Besides, our scheme also admits a threshold decryption protocol from which a generalized two-round MPC protocol can be similarly obtained as prior works.

On the impossibility of entropy reversal, and its application to zero-knowledge proofs

Sun, 09/24/2017 - 19:42
Zero knowledge proof systems have been widely studied in cryptography. In the statistical setting, two classes of proof systems studied are Statistical Zero Knowledge (SZK) and Non-Interactive Statistical Zero Knowledge (NISZK), where the difference is that in NISZK only very limited communication is allowed between the verifier and the prover. It is an open problem whether these two classes are in fact equal. In this paper, we rule out efficient black box reductions between SZK and NISZK. We achieve this by studying algorithms which can reverse the entropy of a function. The problem of estimating the entropy of a circuit is complete for NISZK. Hence, reversing the entropy of a function is equivalent to a black box reduction of NISZK to its complement, which is known to be equivalent to a black box reduction of SZK to NISZK [Goldreich et al, CRYPTO 1999]. We show that any such black box algorithm incurs an exponential loss of parameters, and hence cannot be implemented efficiently.

RingCT 2.0: A Compact Accumulator-Based (Linkable Ring Signature) Protocol for Blockchain Cryptocurrency Monero

Sun, 09/24/2017 - 19:35
In this work, we initially study the necessary properties and security requirements of Ring Confidential Transaction (RingCT) protocol deployed in the popular anonymous cryptocurrency Monero. Firstly, we formalize the syntax of RingCT protocol and present several formal security definitions according to its application in Monero. Based on our observations on the underlying (linkable) ring signature and commitment schemes, we then put forward a new efficient RingCT protocol (RingCT 2.0), which is built upon the well-known Pedersen commitment, accumulator with one-way domain and signature of knowledge (which altogether perform the functions of a linkable ring signature). Besides, we show that it satisfies the security requirements if the underlying building blocks are secure in the random oracle model. In comparison with the original RingCT protocol, our RingCT 2.0 protocol presents a significant space saving, namely, the transaction size is independent of the number of groups of input accounts included in the generalized ring while the original RingCT suffers a linear growth with the number of groups, which would allow each block to process more transactions.

Round-Optimal Secure Two-Party Computation from Trapdoor Permutations

Sun, 09/24/2017 - 19:32
In this work we continue the study on the round complexity of secure two-party computation with black-box simulation. Katz and Ostrovsky in CRYPTO 2004 showed a 5 (optimal) round construction assuming trapdoor permutations for the general case where both players receive the output. They also proved that their result is round optimal. This lower bound has been recently revisited by Garg et al. in Eurocrypt 2016 where a 4 (optimal) round protocol is showed assuming a simultaneous message exchange channel. Unfortunately there is no instantiation of the protocol of Garg et al. under standard polynomial-time hardness assumptions. In this work we close the above gap by showing a 4 (optimal) round construction for secure two-party computation in the simultaneous message channel model with black-box simulation, assuming trapdoor permutations against polynomial-time adversaries. Our construction for secure two-party computation relies on a special 4-round protocol for oblivious transfer that nicely composes with other protocols in parallel. We define and construct such special oblivious transfer protocol from trapdoor permutations. This building block is clearly interesting on its own. Our construction also makes use of a recent advance on non-malleability: a delayed-input 4-round non-malleable zero knowledge argument.

Improving the Linear Programming Technique in the Search for Lower Bounds in Secret Sharing

Sun, 09/24/2017 - 19:20
We present a new improvement in the Linear Programming technique to derive bounds on information theoretic problems. In our case, we deal with the search for lower bounds on the information ratio of secret sharing schemes. We obtain non-Shannon-type bounds without using information inequalities explicitly. Our new techniques makes it possible to determine the optimal information ratio of linear secret sharing schemes for all access structures on $5$ participants. New lower bounds are presented also for graph-based access structures on six participants and for some small matroidal access structures. In particular, we determine the optimal information ratio of the linear secret sharing schemes for the ports of the Vamos matroid.

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