Biblio

Suppose that you have n truly random bits x=(x1,…,xn) and you wish to use them to generate m≫ n pseudorandom bits y=(y1,…, ym) using a local mapping, i.e., each yi should depend on at most d=O(1) bits of x. In the polynomial regime of m=ns, stextgreater1, the only known solution, originates from (Goldreich, ECCC 2000), is based on Random Local Functions: Compute yi by applying some fixed (public) d-ary predicate P to a random (public) tuple of distinct inputs (xi1,…,xid). Our goal in this paper is to understand, for any value of s, how the pseudorandomness of the resulting sequence depends on the choice of the underlying predicate. We derive the following results: (1) We show that pseudorandomness against F2-linear adversaries (i.e., the distribution y has low-bias) is achieved if the predicate is (a) k=Ω(s)-resilience, i.e., uncorrelated with any k-subset of its inputs, and (b) has algebraic degree of Ω(s) even after fixing Ω(s) of its inputs. We also show that these requirements are necessary, and so they form a tight characterization (up to constants) of security against linear attacks. Our positive result shows that a d-local low-bias generator can have output length of nΩ(d), answering an open question of Mossel, Shpilka and Trevisan (FOCS, 2003). Our negative result shows that a candidate for pseudorandom generator proposed by the first author (computational complexity, 2015) and by O’Donnell and Witmer (CCC 2014) is insecure. We use similar techniques to refute a conjecture of Feldman, Perkins and Vempala (STOC 2015) regarding the hardness of planted constraint satisfaction problems. (2) Motivated by the cryptanalysis literature, we consider security against algebraic attacks. We provide the first theoretical treatment of such attacks by formalizing a general notion of algebraic inversion and distinguishing attacks based on the Polynomial Calculus proof system. We show that algebraic attacks succeed if and only if there exist a degree e=O(s) non-zero polynomial Q whose roots cover the roots of P or cover the roots of P’s complement. As a corollary, we obtain the first example of a predicate P for which the generated sequence y passes all linear tests but fails to pass some polynomial-time computable test, answering an open question posed by the first author (Question 4.9, computational complexity 2015).

Motivated by applications in cryptography, we introduce and study the problem of distribution design. The goal of distribution design is to find a joint distribution on \$n\$ random variables that satisfies a given set of constraints on the marginal distributions. Each constraint can either require that two sequences of variables be identically distributed or, alternatively, that the two sequences have disjoint supports. We present several positive and negative results on the existence and efficiency of solutions for a given set of constraints. Distribution design can be seen as a strict generalization of several well-studied problems in cryptography. These include secret sharing, garbling schemes, and non-interactive protocols for secure multiparty computation. We further motivate the problem and our results by demonstrating their usefulness towards realizing non-interactive protocols for ad-hoc secure multiparty computation, in which any subset of the parties may choose to participate and the identity of the participants should remain hidden to the extent possible.

Many lattice-based cryptosystems are based on the security of the Ring learning with errors (Ring-LWE) problem. The most critical and computationally intensive operation of these Ring-LWE based cryptosystems is polynomial multiplication. In this paper, we exploit the number theoretic transform to build a high-speed polynomial multiplier for the Ring-LWE based public key cryptosystems. We present a versatile pipelined polynomial multiplication architecture to calculate the product of two \$n\$-degree polynomials in about ((nlg n)/4 + n/2) clock cycles. In addition, we introduce several optimization techniques to reduce the required ROM storage. The experimental results on a Spartan-6 FPGA show that the proposed hardware architecture can achieve a speedup of on average 2.25 than the state of the art of high-speed design. Meanwhile, our design is able to save up to 47.06% memory blocks.

We ask whether it is possible to anonymously communicate a large amount of data using only public (non-anonymous) communication together with a small anonymous channel. We think this is a central question in the theory of anonymous communication and to the best of our knowledge this is the first formal study in this direction. Towards this goal, we introduce the novel concept of anonymous steganography: think of a leaker Lea who wants to leak a large document to Joe the journalist. Using anonymous steganography Lea can embed this document in innocent looking communication on some popular website (such as cat videos on YouTube or funny memes on 9GAG). Then Lea provides Joe with a short decoding key dk which, when applied to the entire website, recovers the document while hiding the identity of Lea among the large number of users of the website. Our contributions include: Introducing and formally defining anonymous steganography, A construction showing that anonymous steganography is possible (which uses recent results in circuits obfuscation), A lower bound on the number of bits which are needed to bootstrap anonymous communication.

Since many cryptographic schemes are about performing computation on data, it is important to consider a computation model which captures the prominent features of modern system architecture. Parallel random access machine (PRAM) is such an abstraction which not only models multiprocessor platforms, but also new frameworks supporting massive parallel computation such as MapReduce. In this work, we explore the feasibility of designing cryptographic solutions for the PRAM model of computation to achieve security while leveraging the power of parallelism and random data access. We demonstrate asymptotically optimal solutions for a wide-range of cryptographic tasks based on indistinguishability obfuscation. In particular, we construct the first publicly verifiable delegation scheme with privacy in the persistent database setting, which allows a client to privately delegate both computation and data to a server with optimal efficiency. Specifically, the server can perform PRAM computation on private data with parallel efficiency preserved (up to poly-logarithmic overhead). Our results also cover succinct randomized encoding, searchable encryption, functional encryption, secure multiparty computation, and indistinguishability obfuscation for PRAM. We obtain our results in a modular way through a notion of computational-trace indistinguishability obfuscation (CiO), which may be of independent interests.

The isomorphism of polynomials with two secret (IP2S) problem is one candidate of computational assumptions for post- quantum cryptography. The only identification scheme based on IP2S is introduced in 1996 by Patarin. However, the security of the scheme has not been formally proven and we discover that the originally proposed parameters are no longer secure based on the most recent research. In this paper, we present the first formal security proof of identification scheme based on IP2S against impersonation under passive attack, sequential active attack, and concurrent active attack. We propose new secure parameters and methods to reduce the implementation cost. Using the proposed methods, we are able to cut the storage cost and average communication cost in a drastic way that the scheme is implementable even on the lightweight devices in the current market.

We introduce the Nondeterministic Strong Exponential Time Hypothesis (NSETH) as a natural extension of the Strong Exponential Time Hypothesis (SETH). We show that both refuting and proving NSETH would have interesting consequences. In particular we show that disproving NSETH would give new nontrivial circuit lower bounds. On the other hand, NSETH implies non-reducibility results, i.e. the absence of (deterministic) fine-grained reductions from SAT to a number of problems. As a consequence we conclude that unless this hypothesis fails, problems such as 3-SUM, APSP and model checking of a large class of first-order graph properties cannot be shown to be SETH-hard using deterministic or zero-error probabilistic reductions.

Physical layer security for wireless communication is broadly considered as a promising approach to protect data confidentiality against eavesdroppers. However, despite its ample theoretical foundation, the transition to practical implementations of physical-layer security still lacks success. A close inspection of proven vulnerable physical-layer security designs reveals that the flaws are usually overlooked when the scheme is only evaluated against an inferior, single-antenna eavesdropper. Meanwhile, the attacks exposing vulnerabilities often lack theoretical justification. To reduce the gap between theory and practice, we posit that a physical-layer security scheme must be studied under multiple adversarial models to fully grasp its security strength. In this regard, we evaluate a specific physical-layer security scheme, i.e. orthogonal blinding, under multiple eavesdropper settings. We further propose a practical "ciphertext-only attack" that allows eavesdroppers to recover the original message by exploiting the low entropy fields in wireless packets. By means of simulation, we are able to reduce the symbol error rate at an eavesdropper below 1% using only the eavesdropper's receiving data and a general knowledge about the format of the wireless packets.

We give attacks on Feistel-based format-preserving encryption (FPE) schemes that succeed in message recovery (not merely distinguishing scheme outputs from random) when the message space is small. For \$4\$-bit messages, the attacks fully recover the target message using \$2textasciicircum1 examples for the FF3 NIST standard and \$2textasciicircum5 examples for the FF1 NIST standard. The examples include only three messages per tweak, which is what makes the attacks non-trivial even though the total number of examples exceeds the size of the domain. The attacks are rigorously analyzed in a new definitional framework of message-recovery security. The attacks are easily put out of reach by increasing the number of Feistel rounds in the standards.