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 overseas Cryptology convention was once held in Santa Barbara, California, in August 2007. The convention drew researchers from around the globe who got here to give their findings and speak about the newest advancements within the box. This e-book constitutes the refereed lawsuits of the conference.

Thirty-three complete papers are provided besides one vital invited lecture. each has been conscientiously reviewed by way of the editor to make sure that all papers are actual, effortless to learn, and make a big contribution to the field.

The papers deal with present foundational, theoretical, and study facets of cryptology, cryptography, and cryptanalysis. moreover, readers will notice many complex and rising applications.

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

Example text

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.

Example 1 (Perfect Matching in Bipartite Graphs). Consider the problem of finding a perfect matching in a bipartite graph G = G, E . To decide whether an input edge u, v is relevant we do the following: (i) Denote by G the graph that results from deleting u, v and all the edges adjacent to them from G. (ii) Check whether there is a perfect matching in G . Evidently, u, v is relevant to G if and only if G has a perfect matching. Hence, perfect matching has an efficient canonical representative algorithm.

As a canonical representative algorithm simply perform the Gaussian elimination procedure on the system. Elementary linear algebra argument shows that if two systems have the same sets of solutions, then they have the same structure after performing the Gaussian elimination procedure. We now show a simple output sampling algorithm for the problem: Compute an arbitrary solution y0 ∈ Fm satisfying M y0 = v. Compute k = rank(M ) and compute an m × (n − k) matrix K representing the kernel of the matrix M .

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