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

ISBN-10: 3540484051

ISBN-13: 9783540484059

ISBN-10: 3540663479

ISBN-13: 9783540663478

Crypto ’99, the 19th Annual Crypto convention, was once subsidized by means of the overseas organization for Cryptologic examine (IACR), in cooperation with the IEEE laptop Society Technical Committee on safety and privateness and the pc technological know-how division, collage of California, Santa Barbara (UCSB). the final Chair, Donald Beaver, used to be answerable for neighborhood association and registration. this system Committee thought of 167 papers and chosen 38 for presentation. This year’s convention software additionally integrated invited lectures. i used to be happy to incorporate within the application UeliM aurer’s presentation “Information Theoretic Cryptography” and Martin Hellman’s presentation “The Evolution of Public Key Cryptography.” this system additionally integrated the normal Rump consultation for casual brief shows of recent effects, run through Stuart Haber. those court cases comprise the revised types of the 38 papers authorised by way of this system Committee. those papers have been chosen from the entire submissions to the convention according to originality, caliber, and relevance to the sector of cryptology. Revisions weren't checked, and the authors endure complete accountability for the contents in their papers.

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

**Sample text**

N ∈ ZM such that each bi is some subset sum modulo M of α1 , . . , αn . The problem borrows its name from the classical subset sum problem: given a positive integer M and b, α1, . . , αn ∈ ZM , find S ⊂ {1, . . , n} such that b ≡ j∈S αj (mod M ). The most powerful known attack [5] against the subset sum problem reduces it to a shortest vector problem in a lattice built from b, α1, . . , αn, M . 94. However, this method can hardly be applied to hidden subset sums: one cannot even build the lattice since the αj ’s are hidden.

Nguyen, J. Stern Only b, c and M are known. The attack can be adapted as follows. Clearly, lemma 3 remains correct if we take for u a vector orthogonal to b and c. Step 1 thus becomes: 1. Compute a reduced basis (u1 , u2, . . , um−2 ) of the orthogonal lattice (b, c)⊥ . ¯x. 2. Compute a basis of the orthogonal lattice (u1 , . . , um−(n+1))⊥ to obtain L The difference with the hidden subset problem is that, this time, the vector k can be much bigger, due to the presence of s. More precisely, we have s ≈ M/2 and c ≈ M m/3, so that k ≈ M m/12.

An−1 in K such that for any two n tuples over n−1 F, (x0 , . . , xn−1 ) (which represents x = i=0 xi ωi in K) and (y0 , . . , yn−1 ) n−1 (which represents y = i=0 yi ωi in K), (y0 , . . , 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.

### Advances in Cryptology — CRYPTO’ 99: 19th Annual International Cryptology Conference Santa Barbara, California, USA, August 15–19, 1999 Proceedings by Jean-Sébastien Coron, David Naccache, Julien P. Stern (auth.), Michael Wiener (eds.)

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