On Constant-Round Concurrent Zero-Knowledge from a Knowledge Assumption

In this work, we consider the long-standing open question of constructing constant-round concurrent zero-knowledge protocols in the plain model. Resolving this question is known to require non-black-box techniques. We consider non-black-box techniques for zero-knowledge based on knowledge assumptions, a line of thinking initiated by the work of Hada and Tanaka (CRYPTO 1998). Prior to our work, it was not known whether knowledge assumptions could be used for achieving security in the concurrent setting, due to a number of significant limitations that we discuss here. Nevertheless, we obtain the following results: 1. We obtain the first constant round concurrent zero-knowledge argument for \textbf{NP} in the plain model based on a new variant of knowledge of exponent assumption. Furthermore, our construction avoids the inefficiency inherent in previous non-black-box techniques such that those of Barak (FOCS 2001); we obtain our result through an efficient protocol compiler. 2. Unlike Hada and Tanaka, we do not require a knowledge assumption to argue the soundness of our protocol. Instead, we use a discrete log like assumption, which we call Diffie-Hellman Logarithm Assumption, to prove the soundness of our protocol. 3. We give evidence that our new variant of knowledge of exponent assumption is in fact plausible. In particular, we show that our assumption holds in the generic group model. 4. Knowledge assumptions are especially delicate assumptions whose plausibility may be hard to gauge. We give a novel framework to express knowledge assumptions in a more flexible way, which may allow for formulation of plausible assumptions and exploration of their impact and application in cryptography.Comment: 30 pages, 3 figure

Breaking the O(n)O(\sqrt n)-Bit Barrier: Byzantine Agreement with Polylog Bits Per Party

Byzantine agreement (BA), the task of $n$ parties to agree on one of their input bits in the face of malicious agents, is a powerful primitive that lies at the core of a vast range of distributed protocols. Interestingly, in protocols with the best overall communication, the demands of the parties are highly unbalanced: the amortized cost is $\tilde O(1)$ bits per party, but some parties must send $\Omega(n)$ bits. In best known balanced protocols, the overall communication is sub-optimal, with each party communicating $\tilde O(\sqrt{n})$. In this work, we ask whether asymmetry is inherent for optimizing total communication. Our contributions in this line are as follows: 1) We define a cryptographic primitive, succinctly reconstructed distributed signatures (SRDS), that suffices for constructing $\tilde O(1)$ balanced BA. We provide two constructions of SRDS from different cryptographic and Public-Key Infrastructure (PKI) assumptions. 2) The SRDS-based BA follows a paradigm of boosting from "almost-everywhere" agreement to full agreement, and does so in a single round. We prove that PKI setup and cryptographic assumptions are necessary for such protocols in which every party sends $o(n)$ messages. 3) We further explore connections between a natural approach toward attaining SRDS and average-case succinct non-interactive argument systems (SNARGs) for a particular type of NP-Complete problems (generalizing Subset-Sum and Subset-Product). Our results provide new approaches forward, as well as limitations and barriers, towards minimizing per-party communication of BA. In particular, we construct the first two BA protocols with $\tilde O(1)$ balanced communication, offering a tradeoff between setup and cryptographic assumptions, and answering an open question presented by King and Saia (DISC'09)

Toward RSA-OAEP without Random Oracles

We show new partial and full instantiation results under chosen-ciphertext security for the widely implemented and standardized RSA-OAEP encryption scheme of Bellare and Rogaway (EUROCRYPT 1994) and two variants. Prior work on such instantiations either showed negative results or settled for ``passive\u27\u27 security notions like IND-CPA. More precisely, recall that RSA-OAEP adds redundancy and randomness to a message before composing two rounds of an underlying Feistel transform, whose round functions are modeled as random oracles (ROs), with RSA. Our main results are: \begin{itemize} \item Either of the two oracles (while still modeling the other as a RO) can be instantiated in RSA-OAEP under IND-CCA2 using mild standard-model assumptions on the round functions and generalizations of algebraic properties of RSA shown by Barthe, Pointcheval, and Báguelin (CCS 2012). The algebraic properties are only shown to hold at practical parameters for small encryption exponent ($e=3$), but we argue they have value for larger $e$ as well. \item Both oracles can be instantiated simultaneously for two variants of RSA-OAEP, called ``$t$-clear\u27\u27 and ``$s$-clear\u27\u27 RSA-OAEP. For this we use extractability-style assumptions in the sense of Canetti and Dakdouk (TCC 2010) on the round functions, as well as novel yet plausible ``XOR-type\u27\u27 assumptions on RSA. While admittedly strong, such assumptions may nevertheless be necessary at this point to make positive progress. \end{itemize} In particular, our full instantiations evade impossibility results of Shoup (J.~Cryptology 2002), Kiltz and Pietrzak (EUROCRYPT 2009), and Bitansky et al. (STOC 2014). Moreover, our results for $s$-clear RSA-OAEP yield the most efficient RSA-based encryption scheme proven IND-CCA2 in the standard model (using bold assumptions on cryptographic hashing) to date

The Birth of Cryptographic Obfuscation -- A Survey

The first candidate indistinguishability obfuscator (iO) of Garg et al. (FOCS 2013) changed the previously pessimistic attitude towards general-purpose cryptographic obfuscation. The potential realizability of such a powerful tool motivated a plethora of applications, including solutions for long-standing open problems, from almost all areas of cryptography. At the same time, the question of whether iO is realizable under standard assumptions is still open. In this work, we review the rapid development of candidate constructions and organize the results of the first four years since the breakthrough. Our goal is to give a bird\u27s-eye view of the infancy of cryptographic obfuscation, providing insight into the most important ideas and techniques

Enhancing Privacy Protection:Set Membership, Range Proofs, and the Extended Access Control

Privacy has recently gained an importance beyond the field of cryptography. In that regard, the main goal behind this thesis is to enhance privacy protection. All of the necessary mathematical and cryptographic preliminaries are introduced at the start of this thesis. We then show in Part I how to improve set membership and range proofs, which are cryptographic primitives enabling better privacy protection. Part II shows how to improve the standards for Machine Readable Travel Documents (MRTDs), such as biometric passports. Regarding set membership proofs, we provide an efficient protocol based on the Boneh-Boyen signature scheme. We show that alternative signature schemes can be used and we provide a general protocol description that can be applied for any secure signature scheme. We also show that signature schemes in our design can be replaced by cryptographic accumulators. For range proofs, we provide interactive solutions where the range is divided in a base u and the u-ary digits are handled by one of our set membership proofs. A general construction is also provided for any set membership proof. We additionally explain how to handle arbitrary ranges with either two range proofs or with an improved solution based on sumset representation. These efficient solutions achieve, to date, the lowest asymptotical communication load. Furthermore, this thesis shows that the first efficient non-interactive range proof is insecure. This thesis thus provides the first efficient and secure non-interactive range proof. In the case of MRTDs, two standards exist: one produced by the International Civil Aviation Organization (ICAO) and the other by the European Union, which is called the Extended Access Control (EAC). Although this thesis focuses on the EAC, which is supposed to solve all privacy concerns, it shows that both standards fail to provide complete privacy protection. Lastly, we provide several solutions to improve them