Oded Goldreich, Johan Håstad

We investigate the computational complexity of languages

which have interactive proof systems of bounded message complexity.

In particular, we show that

(1) If $L$ has an interactive proof in which the total

communication is bounded by $c(n)$ bits

then $L$ can be recognized a probabilitic machine

in time ...
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Oded Goldreich

We show simple constant-round interactive proof systems for

problems capturing the approximability, to within a factor of $\sqrt{n}$,

of optimization problems in integer lattices; specifically,

the closest vector problem (CVP), and the shortest vector problem (SVP).

These interactive proofs are for the ``coNP direction'';

that is, ...
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Jörg Rothe

In this tutorial, selected topics of cryptology and of

computational complexity theory are presented. We give a brief overview

of the history and the foundations of classical cryptography, and then

move on to modern public-key cryptography. Particular attention is

paid to cryptographic protocols and the problem of constructing ...
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Alan L. Selman, Samik Sengupta

It is known \cite{BHZ87} that if every language in coNP has a

constant-round interactive proof system, then the polynomial hierarchy

collapses. On the other hand, Lund {\em et al}.\ \cite{LFKN92} have shown that

#SAT, the #P-complete function that outputs the number of satisfying

assignments of a Boolean ...
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Boaz Barak, Yehuda Lindell, Salil Vadhan

We show new lower bounds and impossibility results for general (possibly <i>non-black-box</i>) zero-knowledge proofs and arguments. Our main results are that, under reasonable complexity assumptions:

<ol>

<li> There does not exist a two-round zero-knowledge <i>proof</i> system with perfect completeness for an NP-complete language. The previous impossibility result for two-round zero ...
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Abuzer Yakaryilmaz

Condon and Lipton (FOCS 1989) showed that the class of languages having a space-bounded interactive proof system (IPS) is a proper subset of decidable languages, where the verifier is a probabilistic Turing machine. In this paper, we show that if we use architecturally restricted verifiers instead of restricting the working ... more >>>

Abuzer Yakaryilmaz

We introduce a new public quantum interactive proof system, namely qAM, by augmenting the verifier with a fixed-size quantum register in Arthur-Merlin game. We focus on space-bounded verifiers, and compare our new public system with private-coin interactive proof (IP) system in the same space bounds. We show that qAM systems ... more >>>

A. C. Cem Say, Abuzer Yakaryilmaz

We give a new characterization of NL as the class of languages whose members have certificates that can be verified with small error in polynomial time by finite state machines that use a constant number of random bits, as opposed to its conventional description in terms of deterministic logarithmic-space verifiers. ... more >>>

Oded Goldreich

We present a somewhat simpler variant of the doubly-efficient interactive proof systems of Goldwasser, Kalai, and Rothblum (JACM, 2015).

Recall that these proof systems apply to log-space uniform sets in NC (or, more generally, to inputs that are acceptable by log-space uniform bounded-depth circuits, where the number of rounds in ...
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Oded Goldreich

We provide an overview of the doubly-efficient interactive proof systems of Reingold, Rothblum, and Rothblum (STOC, 2016).

Recall that by their result, any set that is decidable in polynomial-time by an algorithm of space complexity $s(n)\leq n^{0.499}$, has a constant-round interactive proof system

in which the prover runs polynomial time ...
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Oded Goldreich, Guy Rothblum

We present two main results regarding the complexity of counting the number of $t$-cliques in a graph.

\begin{enumerate}

\item{\em A worst-case to average-case reduction}:

We reduce counting $t$-cliques in any $n$-vertex graph to counting $t$-cliques in typical $n$-vertex graphs that are drawn from a simple distribution of min-entropy ${\widetilde\Omega}(n^2)$. For ...
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Shafi Goldwasser, Guy Rothblum, Jonathan Shafer, Amir Yehudayoff

We consider the following question: using a source of labeled data and interaction with an untrusted prover, what is the complexity of verifying that a given hypothesis is "approximately correct"? We study interactive proof systems for PAC verification, where a verifier that interacts with a prover is required to accept ... more >>>

Eric Allender, John Gouwar, Shuichi Hirahara, Caleb Robelle

A version of time-bounded Kolmogorov complexity, denoted KT, has received attention in the past several years, due to its close connection to circuit complexity and to the Minimum Circuit Size Problem MCSP. Essentially all results about the complexity of MCSP hold also for MKTP (the problem of computing the KT ... more >>>

Tal Herman, Guy Rothblum

Given i.i.d. samples from an unknown distribution over a large domain $[N]$, approximating several basic quantities, including the distribution's support size, its entropy, and its distance from the uniform distribution, requires $\Theta(N / \log N)$ samples [Valiant and Valiant, STOC 2011].

Suppose, however, that we can interact with a powerful ... more >>>

Lijie Chen, Roei Tell

What is the actual cost of derandomization? And can we get it for free? These questions were recently raised by Doron et. al (FOCS 2020) and have been attracting considerable interest. In this work we extend the study of these questions to the setting of *derandomizing interactive proofs systems*.

... more >>>Eric Allender, Jacob Gray, Saachi Mutreja, Harsha Tirumala, Pengxiang Wang

We show that the space-bounded Statistical Zero Knowledge classes SZK_L and NISZK_L are surprisingly robust, in that the power of the verifier and simulator can be strengthened or weakened without affecting the resulting class. Coupled with other recent characterizations of these classes, this can be viewed as lending support to ... more >>>

Benny Applebaum, Oded Nir

A major open problem in information-theoretic cryptography is to obtain a super-polynomial lower bound for the communication complexity of basic cryptographic tasks. This question is wide open even for very powerful non-interactive primitives such as private information retrieval (or locally-decodable codes), general secret sharing schemes, conditional disclosure of secrets, and ... more >>>