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We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design…
We consider the secret key generation problem when sources are randomly excited by the sender and there is a noiseless public discussion channel. Our setting is thus similar to recent works on channels with action-dependent states where the…
Authors of cryptographic software are well aware that their code should not leak secrets through its timing behavior, and, until 2018, they believed that following industry-standard constant-time coding guidelines was sufficient. However,…
We obfuscate words of a given length in a free monoid on two generators with a simple factorization algorithm (namely $SL_2(\mathbb{N})$) to create a public-key encryption scheme. We provide a reference implementation in Python and…
Constraint satisfaction problems (CSPs) are ubiquitous in theoretical computer science. We study the problem of StrongCSPs, i.e. instances where a large induced sub-instance has a satisfying assignment. More formally, given a CSP instance…
Several recently proposed code-based cryptosystems base their security on a slightly generalized version of the classical (syndrome) decoding problem. Namely, in the so-called restricted (syndrome) decoding problem, the error values stem…
We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of…
A finite constraint language $\mathscr{R}$ is a finite set of relations over some finite domain $A$. We show that intractability of the constraint satisfaction problem $\operatorname{CSP}(\mathscr{R})$ can, in all known cases, be replaced…
We present a novel approach to post-quantum cryptography that employs directed-graph decryption of noise-enhanced high-memory convolutional codes. The proposed construction generates random-like generator matrices that effectively conceal…
This paper considers smooth strongly convex and strongly concave (SC-SC) stochastic saddle point (SSP) problems. Suppose there is an arbitrary oracle that in expectation returns an $\epsilon$-solution in the sense of certain gaps, which can…
We propose a framework for constructing efficient code-based encryption schemes from codes that do not hide any structure in their public matrix. The framework is in the spirit of the schemes first proposed by Alekhnovich in 2003 and based…
We give an overview of the Hidden Subgroup Problem (HSP) as of July 2010, including new results discovered since the survey of arXiv:quant-ph/0411037v1. We recall how the problem provides a framework for efficient quantum algorithms and…
Recent results of Kaplan et al., building on previous work by Kuwakado and Morii, have shown that a wide variety of classically-secure symmetric-key cryptosystems can be completely broken by quantum chosen-plaintext attacks (qCPA). In such…
We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of…
A dealer aims to share a secret with participants so that only predefined subsets can reconstruct it, while others learn nothing. The dealer and participants access correlated randomness and communicate over a one-way, public, rate-limited…
We study the power of the bounded-width consistency algorithm in the context of the fixed-template Promise Constraint Satisfaction Problem (PCSP). Our main technical finding is that the template of every PCSP that is solvable in bounded…
The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting…
Shared randomness is a valuable resource in distributed computing, allowing some form of coordination between processors without explicit communication. But what happens when the shared random string can affect the inputs to the system?…
We present a unified framework on the limits of constraint satisfaction problems (CSPs) and efficient parameter testing which depends only on array exchangeability and the method of cut decomposition without recourse to the weakly regular…