Oded Goldreich, Leonid Levin, Noam Nisan

We show how to construct length-preserving 1-1 one-way

functions based on popular intractability assumptions (e.g., RSA, DLP).

Such 1-1 functions should not

be confused with (infinite) families of (finite) one-way permutations.

What we want and obtain is a single (infinite) 1-1 one-way function.

Oded Goldreich

We provide an exposition of three Lemmas which relate

general properties of distributions

with the exclusive-or of certain bit locations.

The first XOR-Lemma, commonly attributed to U.V. Vazirani,

relates the statistical distance of a distribution from uniform

to the maximum bias of the xor of certain bit positions.

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Oded Goldreich

We suggest a candidate one-way function using combinatorial

constructs such as expander graphs. These graphs are used to

determine a sequence of small overlapping subsets of input bits,

to which a hard-wired random predicate is applied.

Thus, the function is extremely easy to evaluate:

all that is needed ...
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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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Iftach Haitner, Danny Harnik, Omer Reingold

We consider two of the most fundamental theorems in Cryptography. The first, due to Haastad et. al. [HILL99], is that pseudorandom generators can be constructed from any one-way function. The second due to Yao [Yao82] states that the existence of weak one-way functions (i.e. functions on which every efficient algorithm ... more >>>

Minh-Huyen Nguyen, Shien Jin Ong, Salil Vadhan

We show that every language in NP has a *statistical* zero-knowledge

argument system under the (minimal) complexity assumption that

one-way functions exist. In such protocols, even a computationally

unbounded verifier cannot learn anything other than the fact that the

assertion being proven is true, whereas a polynomial-time prover

cannot convince ...
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David Xiao

Learning is a central task in computer science, and there are various

formalisms for capturing the notion. One important model studied in

computational learning theory is the PAC model of Valiant (CACM 1984).

On the other hand, in cryptography the notion of ``learning nothing''

is often modelled by the simulation ...
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Oded Goldreich

We present a candidate counterexample to the

easy cylinders conjecture, which was recently suggested

by Manindra Agrawal and Osamu Watanabe (ECCC, TR09-019).

Loosely speaking, the conjecture asserts that any 1-1 function

in $P/poly$ can be decomposed into ``cylinders'' of sub-exponential

size that can each be inverted by some polynomial-size circuit.

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Iftach Haitner, Omer Reingold, Salil Vadhan, Hoeteck Wee

We put forth a new computational notion of entropy, which measures the

(in)feasibility of sampling high entropy strings that are consistent

with a given protocol. Specifically, we say that the i'th round of a

protocol (A, B) has _accessible entropy_ at most k, if no

polynomial-time strategy A^* can generate ...
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Iftach Haitner, Eran Omri, Hila Zarosim

In the random oracle model, the parties are given oracle access to a random member of

a (typically huge) function family, and are assumed to have unbounded computational power

(though they can only make a bounded number of oracle queries). This model provides powerful

properties that allow proving the security ...
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Kfir Barhum, Thomas Holenstein

We present a new framework for proving fully black-box

separations and lower bounds. We prove a general theorem that facilitates

the proofs of fully black-box lower bounds from a one-way function (OWF).

Loosely speaking, our theorem says that in order to prove that a fully black-box

construction does ...
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Benny Applebaum

Constant parallel-time cryptography allows to perform complex cryptographic tasks at an ultimate level of parallelism, namely, by local functions that each of their output bits depend on a constant number of input bits. A natural way to obtain local cryptographic constructions is to use \emph{random local functions} in which each ... more >>>

Itay Berman, Iftach Haitner, Aris Tentes

We show that the existence of a coin-flipping protocol safe against any non-trivial constant bias (e.g., $.499$) implies the existence of one-way functions. This improves upon a recent result of Haitner and Omri [FOCS '11], who proved this implication for protocols with bias $\frac{\sqrt2 -1}2 - o(1) \approx .207$. Unlike ... more >>>

YiHsiu Chen, Mika G\"o{\"o}s, Salil Vadhan, Jiapeng Zhang

We study \emph{entropy flattening}: Given a circuit $\mathcal{C}_X$ implicitly describing an $n$-bit source $X$ (namely, $X$ is the output of $\mathcal{C}_X$ on a uniform random input), construct another circuit $\mathcal{C}_Y$ describing a source $Y$ such that (1) source $Y$ is nearly \emph{flat} (uniform on its support), and (2) the Shannon ... more >>>

Marshall Ball, Elette Boyle, Akshay Degwekar, Apoorvaa Deshpande, Alon Rosen, Vinod Vaikuntanathan, Prashant Vasudevan

Reductions between problems, the mainstay of theoretical computer science, efficiently map an instance of one problem to an instance of another in such a way that solving the latter allows solving the former. The subject of this work is ``lossy'' reductions, where the reduction loses some information about the input ... more >>>

Eric Allender, Mahdi Cheraghchi, Dimitrios Myrisiotis, Harsha Tirumala, Ilya Volkovich

One-way functions (OWFs) are central objects of study in cryptography and computational complexity theory. In a seminal work, Liu and Pass (FOCS 2020) proved that the average-case hardness of computing time-bounded Kolmogorov complexity is equivalent to the existence of OWFs. It remained an open problem to establish such an equivalence ... more >>>

Rahul Ilango, Hanlin Ren, Rahul Santhanam

We show that one-way functions exist if and only if there is some samplable distribution D such that it is hard to approximate the Kolmogorov complexity of a string sampled from D. Thus we characterize the existence of one-way functions by the average-case hardness of a natural \emph{uncomputable} problem on ... more >>>

Yanyi Liu, Rafael Pass

We show equivalence between the existence of one-way

functions and the existence of a \emph{sparse} language that is

hard-on-average w.r.t. some efficiently samplable ``high-entropy''

distribution.

In more detail, the following are equivalent:

- The existentence of a $S(\cdot)$-sparse language $L$ that is

hard-on-average with respect to some samplable ...
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Noga Amit, Guy Rothblum

We study the following question: what cryptographic assumptions are needed for obtaining constant-round computationally-sound argument systems? We focus on argument systems with almost-linear verification time for subclasses of $\mathbf{P}$, such as depth-bounded computations.

Kilian's celebrated work [STOC 1992] provides such 4-message arguments for $\mathbf{P}$ (actually, for $\mathbf{NP}$) using collision-resistant hash ...
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Zhenjian Lu, Rahul Santhanam

We develop new characterizations of Impagliazzo's worlds Algorithmica, Heuristica and Pessiland by the intractability of conditional Kolmogorov complexity $\mathrm{K}$ and conditional probabilistic time-bounded Kolmogorov complexity $\mathrm{pK}^t$.

In our first set of results, we show that $\mathrm{NP} \subseteq \mathrm{BPP}$ iff $\mathrm{pK}^t(x \mid y)$ can be computed efficiently in the worst case ... more >>>

Noga Amit, Guy Rothblum

What are the minimal cryptographic assumptions that suffice for constructing efficient argument systems, and for which tasks? Recently, Amit and Rothblum [STOC 2023] showed that one-way functions suffice for constructing constant-round arguments for bounded-depth computations. In this work we ask: what other tasks have efficient argument systems based only on ... more >>>