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Electronic Colloquium on Computational Complexity

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Reports tagged with One-Way Functions:
TR95-029 | 15th June 1995
Oded Goldreich, Leonid Levin, Noam Nisan

On Constructing 1-1 One-Way Functions

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.

more >>>

TR95-056 | 26th November 1995
Oded Goldreich

Three XOR-Lemmas -- An Exposition

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.
more >>>

TR00-090 | 3rd December 2000
Oded Goldreich

Candidate One-Way Functions Based on Expander Graphs

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 ... more >>>

TR01-096 | 21st November 2001
Jörg Rothe

Some Facets of Complexity Theory and Cryptography: A Five-Lectures Tutorial

Revisions: 1

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 ... more >>>

TR05-135 | 19th November 2005
Iftach Haitner, Danny Harnik, Omer Reingold

On the Power of the Randomized Iterate

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 >>>

TR06-075 | 19th June 2006
Minh-Huyen Nguyen, Shien Jin Ong, Salil Vadhan

Statistical Zero-Knowledge Arguments for NP from Any One-Way Function

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 ... more >>>

TR09-006 | 19th January 2009
David Xiao

On basing ZK != BPP on the hardness of PAC learning

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 ... more >>>

TR09-028 | 2nd April 2009
Oded Goldreich

A Candidate Counterexample to the Easy Cylinders Conjecture

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.
more >>>

TR09-045 | 20th May 2009
Iftach Haitner, Omer Reingold, Salil Vadhan, Hoeteck Wee

Inaccessible Entropy

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 ... more >>>

TR12-129 | 9th October 2012
Iftach Haitner, Eran Omri, Hila Zarosim

On the Power of Random Oracles

Revisions: 3

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 ... more >>>

TR12-173 | 8th December 2012
Kfir Barhum, Thomas Holenstein

A Cookbook for Black-Box Separations and a Recipe for UOWHFs

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 ... more >>>

TR15-027 | 25th February 2015
Benny Applebaum

Cryptographic Hardness of Random Local Functions -- Survey

Revisions: 1

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 >>>

TR15-106 | 22nd June 2015
Itay Berman, Iftach Haitner, Aris Tentes

Coin Flipping of Any Constant Bias Implies One-Way Functions

Revisions: 1

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 >>>

TR18-119 | 21st June 2018
YiHsiu Chen, Mika G\"o{\"o}s, Salil Vadhan, Jiapeng Zhang

A Tight Lower Bound for Entropy Flattening

Revisions: 1

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 >>>

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