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Algorithmic Number Theory: 4th International Symposium, - download pdf or read online

Posted On February 24, 2018 at 4:07 am by / Comments Off on Algorithmic Number Theory: 4th International Symposium, - download pdf or read online

By Jin-Yi Cai (auth.), Wieb Bosma (eds.)

ISBN-10: 3540449949

ISBN-13: 9783540449942

ISBN-10: 3540676953

ISBN-13: 9783540676959

This e-book constitutes the refereed court cases of the 4th overseas Algorithmic quantity conception Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000.
The e-book offers 36 contributed papers that have passed through a radical around of reviewing, choice and revision. additionally incorporated are four invited survey papers. one of the themes addressed are gcd algorithms, primality, factoring, sieve equipment, cryptography, linear algebra, lattices, algebraic quantity fields, type teams and fields, elliptic curves, polynomials, functionality fields, and tool sums.

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Read Online or Download Algorithmic Number Theory: 4th International Symposium, ANTS-IV Leiden, The Netherlands, July 2-7, 2000. Proceedings PDF

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Additional info for Algorithmic Number Theory: 4th International Symposium, ANTS-IV Leiden, The Netherlands, July 2-7, 2000. Proceedings

Sample text

A. Dupr´e. Sur le nombre de divisions `a effectuer pour obtenir le plus grande commun diviseur entre deux nombres entiers. Journal de Math´ ematiques, 11:41– 74, 1846. 29. S. Even, A. L. Selman and Y. Yacobi. The Complexity of Promise Problems with Applications to Public-key Cryptography. Information and Control 61:159–173, 1984. 30. U. Feige and C. Lund. On the hardness of computing permanent of random matrices. In Proc. 14th ACM Symposium on Theory of Computing, 1982, 643–654. 31. P. Gemmell and M.

3. If L(n−i+1) is the orthogonal projection of L to (lsp{b1 , . . , bi−1 })⊥ then ||bi || = λ1 (L(n−i+1) ). Essentially, a Korkin-Zolotarev basis is one which is weakly reduced, and the orthogonal projection of bi is a vector of minimum length in the orthogonal proasz’s algorithm, jection of L in the complement of {b1 , . . , bi−1}. In terms of Lov´ if instead of comparing bi (i) and bi+1 (i), we searched for a vector of minimum The Complexity of Some Lattice Problems 21 length in lsp{bi (i), .

Theorem 6 (Lagarias, Lenstra, Schnorr). If NP = coNP, then the problem of approximating λ1 (L) within a factor n is not NP-hard. The interplay between the primal and dual lattices and the related transference theorems play important roles in Ajtai’s worst-case to average-case connection as well. We will discuss this topic in more detail in the next section. Here we present the following rather pretty result due to Goldreich and√Goldwasser which improved the approximation factor for non-NP-hardness to n.

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Algorithmic Number Theory: 4th International Symposium, ANTS-IV Leiden, The Netherlands, July 2-7, 2000. Proceedings by Jin-Yi Cai (auth.), Wieb Bosma (eds.)


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