Download e-book for iPad: Algorithmic Number Theory: 4th International Symposium, by Jin-Yi Cai (auth.), Wieb Bosma (eds.)

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

ISBN-10: 3540449949

ISBN-13: 9783540449942

ISBN-10: 3540676953

ISBN-13: 9783540676959

This publication constitutes the refereed complaints of the 4th overseas Algorithmic quantity thought Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000.
The publication provides 36 contributed papers that have undergone a radical around of reviewing, choice and revision. additionally integrated are four invited survey papers. one of the subject matters addressed are gcd algorithms, primality, factoring, sieve tools, cryptography, linear algebra, lattices, algebraic quantity fields, type teams and fields, elliptic curves, polynomials, functionality fields, and gear sums.

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

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Zolotarev. Sur les formes quadratiques positives quaternaires. Mathematische Annalen, 5:581–583, 1872. 47. J. C. Lagarias. The computational complexity of simultaneous diophantine approximation problems. SIAM Journal of Computing, 14:196–209, 1985. 48. J. C. Lagarias, H. W. Lenstra, and C. P. Schnorr. Korkin-Zolotarev Bases and Successive Minima of a Lattice and its Reciprocal Lattice. Combinatorica, 10(4):333348, 1990. 49. J. C. Lagarias and A. M. Odlyzko. Solving low-density subset sum problems.

Submitted to Information Processing Letters. 23. J-Y. Cai. A Worst-Case to Average-Case Connection for CVP. Manuscript. To appear. 24. J. W. S. Cassels. An Introduction to the Geometry of Numbers. Berlin G¨ ottingen Heidelberg: Springer 1959. 25. D. Coppersmith. Small solutions to polynomial equations, and low exponent RSA vulnerabilities. Journal of Cryptology, 10:233-260, 1997. 26. I. Dinur, G. Kindler and S. Safra. Approximating CVP to within almost-polynomial factors is NP-hard. In Proc. 39th IEEE Symposium on Foundations of Computer Science, 1998, 99–109.

For any L and any u ∈ Rn \L, we can compare d(u, L), to the distance from u to the closest parallel translation of some {v}⊥ = lsp(L ) which intersects L, over all such L . Let dZ ( u, v ) = | u, v − u, v | be the fractional part of u, v rounded to the nearest integer, then we consider δ= sup v∈L∗ , u,v ∈Z dZ ( u, v ) , ||v|| which measures the distance from u to the closest parallel translation, maximized among all directions v ∈ L∗ . Now the following quantity is defined ζ = sup sup L u∈Rn \L d(u, L) .

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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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