Blockchain Papers

David Heath, Vladimir Kolesnikov

No abstract is available for this record.

Carmit Hazay, Muthuramakrishnan Venkitasubramaniam, Mor Weiss

Zero-Knowledge PCPs (ZK-PCPs; Kilian, Petrank, and Tardos, STOC `97) are PCPs with the additional zero-knowledge guarantee that the view of any (possibly malicious) verifier making a bounded number of queries to the proof can be efficiently simulated up to a small statistical distance. Similarly, ZK-PCPs of Proximity (ZK-PCPPs; Ishai and Weiss, TCC `14) are PCPPs in which the view of an adversarial verifier can be efficiently simulated with few queries to the input. Previous ZK-PCP constructions obtained an exponential gap between the query complexity q of the honest verifier, and the bound q^* on the queries of a malicious verifier (i.e., q = poly log (q^*)), but required either exponential-time simulation, or adaptive honest verification. This should be contrasted with standard PCPs, that can be verified non-adaptively (i.e., with a single round of queries to the proof). The problem of constructing such ZK-PCPs, even when q^* = q, has remained open since they were first introduced more than 2 decades ago. This question is also open for ZK-PCPPs, for which no construction with non-adaptive honest verification is known (not even with exponential-time simulation). We resolve this question by constructing the first ZK-PCPs and ZK-PCPPs which simultaneously achieve efficient zero-knowledge simulation and non-adaptive honest verification. Our schemes have a square-root query gap, namely q^*/q = O(√n) where n is the input length. Our constructions combine the "MPC-in-the-head" technique (Ishai et al., STOC `07) with leakage-resilient secret sharing. Specifically, we use the MPC-in-the-head technique to construct a ZK-PCP variant over a large alphabet, then employ leakage-resilient secret sharing to design a new alphabet reduction for ZK-PCPs which preserves zero-knowledge.

Jing Pan, Xiaofeng Chen, Fangguo Zhang, Willy Susilo

No abstract is available for this record.

Yuyu Wang, Jiaxin Pan, Yu Chen

No abstract is available for this record.

Aarushi Goel, Matthew Green, Mathias Hall-Andersen, Gabriel Kaptchuk

No abstract is available for this record.

Thomas Attema, Ronald Cramer, Lisa Kohl

We show a lattice-based solution for commit-and-prove transparent circuit zero-knowledge (ZK) with polylog-communication, the first not depending on PCPs. We start from compressed Σ-protocol theory (CRYPTO 2020), which is built around basic Σ-protocols for opening an arbitrary linear form on a long secret vector that is compactly committed to. These protocols are first compressed using a recursive “folding-technique” adapted from Bulletproofs, at the expense of logarithmic rounds. Proving in ZK that the secret vector satisfies a given constraint – captured by a circuit – is then by (blackbox) reduction to the linear case, via arithmetic secret-sharing techniques adapted from MPC. Commit-and-prove is also facilitated, i.e., when commitment(s) to the secret vector are created ahead of any circuit-ZK proof. On several platforms (incl. DL) this leads to logarithmic communication. Non-interactive versions follow from Fiat-Shamir. This abstract modular theory strongly suggests that it should somehow be supported by a lattice platform as well. However, when going through the motions and trying to establish low communication (on an SIS-platform), a certain significant lack in current understanding of multi-round protocols is exposed. Namely, as opposed to the DL-case, the basic Σ-protocol in question typically has poly-small challenge space. Taking into account the compression-step – which yields non-constant rounds – and the necessity for parallelization to reduce error, there is no known tight result that the compound protocol admits an efficient knowledge extractor. We resolve the state of affairs here by a combination of two novel results which are fully general and of independent interest. The first gives a tight analysis of efficient knowledge extraction in case of non-constant rounds combined with poly-small challenge space, whereas the second shows that parallel repetition indeed forces rapid decrease of knowledge error. Moreover, in our present context, arithmetic secret sharing is not defined over a large finite field but over a quotient of a number ring and this forces our careful adaptation of how the linearization techniques are deployed. We develop our protocols in an abstract framework that is conceptually simple and can be flexibly instantiated. In particular, the framework applies to arbitrary rings and norms.

Alexander R. Block, Justin Holmgren, Alon Rosen, Ron D. Rothblum · 5 authors

No abstract is available for this record.

Jung Hee Cheon, Dongwoo Kim, Keewoo Lee

We propose a multi-party computation (MPC) protocol over \(\mathbb {Z}_{2^k}\) secure against actively corrupted majority from somewhat homomorphic encryption. The main technical contributions are: (i) a new efficient packing method for \(\mathbb {Z}_{2^k}\)-messages in lattice-based somewhat homomorphic encryption schemes, (ii) a simpler reshare protocol for level-dependent packings, (iii) a more efficient zero-knowledge proof of plaintext knowledge on cyclotomic rings \({\mathbb Z}[X]/\varPhi _M(X)\) with M being a prime. Integrating them, our protocol shows from 2.2x upto 4.8x improvements in amortized communication costs compared to the previous best results. Our techniques not only improve the efficiency of MPC over \(\mathbb {Z}_{2^k}\) considerably, but also provide a toolkit that can be leveraged when designing other cryptographic primitives over \(\mathbb {Z}_{2^k}\).

Amit Sahai, Brent Waters

We introduce a new technique, that we call punctured programs, to apply indistinguishability obfuscation towards cryptographic problems. We use this technique to carry out a systematic study of the applicability of indistinguishability obfuscation to a variety of cryptographic goals. Along the way, we resolve the 16-year-old open question of Deniable Encryption, posed by Canetti, Dwork, Naor, and Ostrovsky in 1997: In deniable encryption, a sender who is forced to reveal to an adversary both her message and the randomness she used for encrypting it should be able to convincingly provide “fake” randomness that can explain any alternative message that she would like to pretend that she sent. We resolve this question by giving the first construction of deniable encryption that does not require any pre-planning by the party that must later issue a denial. In addition, we show the generality of our punctured programs technique by also constructing a variety of core cryptographic objects from indistinguishability obfuscation and one-way functions (or close variants). In particular we obtain: public key encryption, short “hash-and-sign” selectively secure signatures, chosen-ciphertext secure public key encryption, non-interactive zero knowledge proofs (NIZKs), injective trapdoor functions, and oblivious transfer. These results suggest the possibility of indistinguishability obfuscation becoming a “central hub” for cryptography. Amit Sahai is supported for this research effort in part from NSF grants 1228984, 1136174, 1118096, 1065276, 0916574 and 0830803, a Xerox Faculty Research Award, a Google Faculty Research Award, an equipment grant from Intel, and an Okawa Foundation Research Grant. The views expressed are those of the author and do not reflect the official policy or position of the National Science Foundation, or the U.S. Government. Brent Waters is supported by NSF CNS-0915361 and CNS-0952692, CNS-1228599 DARPA through the U.S. Office of Naval Research under Contract N00014-11-1-0382, DARPA N11AP20006, Google Faculty Research award, the Alfred P. Sloan Fellowship, Microsoft Faculty Fellowship, and Packard Foundation Fellowship. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Department of Defense or the U.S. Government.

Anh The Ta, Thanh Xuan Khuc, Tuong Ngoc Nguyen, Huy Quoc Le · 8 authors

No abstract is available for this record.

Matteo Campanelli, Hamidreza Khoshakhlagh

No abstract is available for this record.

Vincenzo Botta, Daniele Friolo, Daniele Venturi, Ivan Visconti

In this work, we consider executions of smart contracts for implementing secure multi-party computation (MPC) protocols on forking blockchains (e.g., Ethereum), and we study security and delay issues due to forks. In this setting, the classical double-spending problem tells us that messages of the MPC protocol should be confirmed on-chain before playing the next ones, thus slowing down the entire execution. Our contributions are twofold: For the concrete case of fairly tossing multiple coins with penalties, we notice that the lottery protocol of Andrychowicz et al. (S&P ’14) becomes insecure if players do not wait for the confirmations of several transactions. In addition, we present a smart contract that instead retains security even when all honest players immediately answer to transactions appearing on-chain. We analyze the performance using Ethereum as testbed.We design a compiler that takes any “digital and universally composable” MPC protocol (with or without honest majority), and transforms it into another one (for the same task and same setup) which maintains security even if all messages are played on-chain without delays. The special requirements on the starting protocol mean that messages consist only of bits (e.g., no hardware token is sent) and security holds also in the presence of other protocols. We further show that our compiler satisfies fairness with penalties as long as honest players only wait for confirmations once. By reducing the number of confirmations, our protocols can be significantly faster than natural constructions.

M. Albrecht, Alex Davidson, Amit Deo, Nigel P. Smart

No abstract is available for this record.

Yaron Gvili, Sarah Scheffler, Mayank Varia

No abstract is available for this record.

Benny Applebaum, Eyal Golombek

We study the randomness complexity of interactive proofs and zero-knowledge proofs. In particular, we ask whether it is possible to reduce the randomness complexity, R, of the verifier to be comparable with the number of bits, C_V, that the verifier sends during the interaction. We show that such randomness sparsification is possible in several settings. Specifically, unconditional sparsification can be obtained in the non-uniform setting (where the verifier is modelled as a circuit), and in the uniform setting where the parties have access to a (reusable) common-random-string (CRS). We further show that constant-round uniform protocols can be sparsified without a CRS under a plausible worst-case complexity-theoretic assumption that was used previously in the context of derandomization. All the above sparsification results preserve statistical-zero knowledge provided that this property holds against a cheating verifier. We further show that randomness sparsification can be applied to honest-verifier statistical zero-knowledge (HVSZK) proofs at the expense of increasing the communication from the prover by R-F bits, or, in the case of honest-verifier perfect zero-knowledge (HVPZK) by slowing down the simulation by a factor of 2^{R-F}. Here F is a new measure of accessible bit complexity of an HVZK proof system that ranges from 0 to R, where a maximal grade of R is achieved when zero-knowledge holds against a "semi-malicious" verifier that maliciously selects its random tape and then plays honestly. Consequently, we show that some classical HVSZK proof systems, like the one for the complete Statistical-Distance problem (Sahai and Vadhan, JACM 2003) admit randomness sparsification with no penalty. Along the way we introduce new notions of pseudorandomness against interactive proof systems, and study their relations to existing notions of pseudorandomness.

Marc Fischlin, Felix Rohrbach

No abstract is available for this record.

Inbar Kaslasi, Ron D. Rothblum, Prashant Nalini Vasudevanr

No abstract is available for this record.

Samuel Dittmer, Yuval Ishai, Rafail Ostrovsky

We introduce and study a simple kind of proof system called line-point zero knowledge (LPZK). In an LPZK proof, the prover encodes the witness as an affine line 𝐯(t) : = at + 𝐛 in a vector space 𝔽ⁿ, and the verifier queries the line at a single random point t = α. LPZK is motivated by recent practical protocols for vector oblivious linear evaluation (VOLE), which can be used to compile LPZK proof systems into lightweight designated-verifier NIZK protocols. We construct LPZK systems for proving satisfiability of arithmetic circuits with attractive efficiency features. These give rise to designated-verifier NIZK protocols that require only 2-5 times the computation of evaluating the circuit in the clear (following an input-independent preprocessing phase), and where the prover communicates roughly 2 field elements per multiplication gate, or roughly 1 element in the random oracle model with a modestly higher computation cost. On the theoretical side, our LPZK systems give rise to the first linear interactive proofs (Bitansky et al., TCC 2013) that are zero knowledge against a malicious verifier. We then apply LPZK towards simplifying and improving recent constructions of reusable non-interactive secure computation (NISC) from VOLE (Chase et al., Crypto 2019). As an application, we give concretely efficient and reusable NISC protocols over VOLE for bounded inner product, where the sender’s input vector should have a bounded L₂-norm.

Thomas Attema, Ronald Cramer, Serge Fehr

No abstract is available for this record.

Jonathan Bootle, Vadim Lyubashevsky, Ngoc Khanh Nguyen, Gregor Seiler

No abstract is available for this record.

San Ling, Khoa Nguyen, Duong Hieu Phan, Khai Hanh Tang · 5 authors

No abstract is available for this record.

Ron D. Rothblum, Adam Sealfon, Katerina Sotiraki

No abstract is available for this record.

Daiki Miyahara, Hiromichi Haneda, Takaaki Mizuki

No abstract is available for this record.

Raimu Isuzugawa, Daiki Miyahara, Takaaki Mizuki

No abstract is available for this record.