Advances in Cryptology - CRYPTO 2007: 27th Annual by Vivien Dubois, Pierre-Alain Fouque, Adi Shamir, Jacques

By Vivien Dubois, Pierre-Alain Fouque, Adi Shamir, Jacques Stern (auth.), Alfred Menezes (eds.)

The twenty seventh Annual foreign Cryptology convention was once held in Santa Barbara, California, in August 2007. The convention drew researchers from worldwide who got here to give their findings and speak about the most recent advancements within the box. This e-book constitutes the refereed complaints of the conference.

Thirty-three complete papers are provided in addition to one very important invited lecture. each has been rigorously reviewed by way of the editor to make sure that all papers are actual, effortless to learn, and make a huge contribution to the field.

The papers deal with present foundational, theoretical, and learn points of cryptology, cryptography, and cryptanalysis. moreover, readers will notice many complicated and rising applications.

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Extra resources for Advances in Cryptology - CRYPTO 2007: 27th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19-23, 2007. Proceedings

Example text

An algorithm A(·, ·) is resemblance preserving with respect to P if: 1. For every polynomial-time algorithm D and every polynomial p(·) there exists some n0 ∈ N such that for every x ∈ {0, 1}∗ satisfying |x| > n0 Pr[D(x, A(sn , x)) = 1] − Pr[D(x, Unif(Pn (x))) = 1] ≤ 1 . p(|x|) The probability is taken over the random choice of the seed sn and the randomness of D. Informally, taking the probability over the seed, the outputs of AP on x is indistinguishable from the uniform distribution on Pn (x).

However, here the choices for non-equivalent instances are highly correlated such that pairs of instances that have close output sets are answered identically with high probability. In Section 4 we present a generic construction of resemblance preserving algorithms, for any search problem whose output space admits a pairwise independent family of permutations, where the minimum of a permuted solution set can be computed efficiently. Examples of such search problems include finding roots or non-roots of a polynomial, solving a system of linear equations over a finite field, finding a point in a union of rectangles in a fixed dimensional space, and finding a satisfying assignment for a DNF formula.

That is, if x and y are equivalent then A always returns the same output on x and on y. If c = 1 in the above Requirement 2, then A(·, ·) is perfect resemblance preserving with respect to P. Unlike Definition 9, in the definition of resemblance preserving algorithms we do not know how to formulate this privacy using an “ideal world”. This difference implies, in particular, that in designing resemblance preserving algorithms we do not need cryptographic assumptions. In our constructions, for example, we only use pairwise independent permutations.

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