Advances in Cryptology — CRYPTO’ 99: 19th Annual by Jean-Sébastien Coron, David Naccache, Julien P. Stern

By Jean-Sébastien Coron, David Naccache, Julien P. Stern (auth.), Michael Wiener (eds.)

Crypto ’99, the 19th Annual Crypto convention, was once subsidized through the foreign organization for Cryptologic learn (IACR), in cooperation with the IEEE desktop Society Technical Committee on defense and privateness and the pc technology division, college of California, Santa Barbara (UCSB). the final Chair, Donald Beaver, was once chargeable for neighborhood association and registration. this system Committee thought of 167 papers and chosen 38 for presentation. This year’s convention application additionally incorporated invited lectures. i used to be happy to incorporate within the software UeliM aurer’s presentation “Information Theoretic Cryptography” and Martin Hellman’s presentation “The Evolution of Public Key Cryptography.” this system additionally included the conventional Rump consultation for casual brief shows of recent effects, run by means of Stuart Haber. those complaints contain the revised types of the 38 papers authorized by means of this system Committee. those papers have been chosen from the entire submissions to the convention in line with originality, caliber, and relevance to the sphere of cryptology. Revisions weren't checked, and the authors undergo complete accountability for the contents in their papers.

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Extra resources for Advances in Cryptology — CRYPTO’ 99: 19th Annual International Cryptology Conference Santa Barbara, California, USA, August 15–19, 1999 Proceedings

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M − 1], find integers α1 , . . M − 1] such that there exist vectors x1 , . . , xn ∈ Zm with entries in {0, 1} satisfying: b = α1 x1 + α2 x2 + · · · + αn xn (mod M ) (1) Throughout this section, we will assume that (b, M ) is a correct input. That is, there exist integers α1 , . . M − 1], vectors x1 , . . , xn ∈ Zm with entries in {0, 1}, and a vector k ∈ Zm such that: b = α1 x1 + α2 x2 + · · · + αn xn + M k (2) Our attack proceeds in three steps: ¯ x , where Lx is the lattice generated by 1.

Yn−1 ) = A(x0 , . . , xn−1 ) if and i n−1 only if y = i=0 ai xq . 2 Proof: There are q (n ) n×n matrices over F and (q n )n sums of n monomials over K, and thus the number of linear mappings and the number of polynomials of this form is identical. Each polynomial represents some linear mapping, and two distinct polynomials cannot represent the same mapping since their difference would be a non zero polynomial of degree q n−1 with q n roots in a field. Consequently, each linear mapping is represented by some univariate polynomial of this type over the extension field.

0 bm x1,m x2,m . . xn,m 0 . . 0 M We note that L⊥ must contain a point of the form (−1, α1, . . , . . ), since the αj ’s satisfy the system. It follows that in any basis of L⊥ , there exists a linear combination (of the basis elements) for which the first coordinate is equal to −1. Such a combination can easily be computed from an extended gcd algorithm applied to the list formed by the first coordinate of each basis element. The element obtained is of the form (−1, β1 , . . , . . ).

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