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, used to be subsidized via the foreign organization for Cryptologic learn (IACR), in cooperation with the IEEE desktop Society Technical Committee on safety and privateness and the pc technological know-how division, college of California, Santa Barbara (UCSB). the final Chair, Donald Beaver, was once accountable for neighborhood association and registration. this system Committee thought of 167 papers and chosen 38 for presentation. This year’s convention software additionally incorporated 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 included the normal Rump consultation for casual brief shows of recent effects, run by way of Stuart Haber. those complaints comprise the revised types of the 38 papers accredited via this system Committee. those papers have been chosen from all of the submissions to the convention in accordance with originality, caliber, and relevance to the sphere of cryptology. Revisions weren't checked, and the authors endure complete accountability for the contents in their papers.

**Read or Download Advances in Cryptology — CRYPTO’ 99: 19th Annual International Cryptology Conference Santa Barbara, California, USA, August 15–19, 1999 Proceedings PDF**

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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**

Schnorr, An Efficient Solution of the Congruence x2 + ky2 = m(mod n), IEEE Trans. Information Theory, vol. IT-33, no. 5, 1987, pp. 702-709. S93. A. 1-12. fr/~{pnguyen,stern}/ Abstract. At Eurocrypt’98, Boyko, Peinado and Venkatesan presented simple and very fast methods for generating randomly distributed pairs of the form (x, gx mod p) using precomputation. The security of these methods relied on the potential hardness of a new problem, the so-called hidden subset sum problem. Surprisingly, apart from exhaustive search, no algorithm to solve this problem was known.

The good news is that instead of a marginally defined system of n equations in n variables, we get an overdefined system of about n2 equations in about rn variables where r << n. Consider the general problem of solving e randomly generated homogeneous quadratic equations in m variables. The well known linearization technique for solving such equations is to replace any product of two variables xi xj for i ≤ j by a new variable yij . The total number of new variables is n(n + 1)/2. Each quadratic equation in the original x variables can be rewritten as a linear equation in the new y variables.

An important corollary of this proof is: Lemma 3. : Let C be any collection of n homogeneous multivariate polynomials of degree d in n variables over F. Then the only powers of x which can occur with non-zero coefficients in its univariate polynomial representation G(x) over K are sums of exactly d (not necessarily distinct) powers of q: q i1 + q i2 + . . + q id . If d is a constant, then G(x) is sparse, and its coefficients can be found in polynomial time. Proof: Mappings defined by a single variable are linear functions, and thus i can be represented as the sum of monomials of the form xq , and each monomial contains a single power of q.

### 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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