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

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

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

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

Example text

Clearly λn (L) ≤ g(L) ≤ bl(L). The following inequality is shown in [14] for every lattice L of dimension n, using and extending the techniques of [9]: gi (L) · λn−i+1 (L∗ ) ≤ Cn, (8) for some universal constant C, and for all i, 1 ≤ i ≤ n. We will sketch the proof for the case i = n for the generating radius g(L). The main tools of the proof are Gaussian-like measures on a lattice, and their Fourier transforms. For a given lattice L we define 2 σL ({v}) = e−π||v|| . −π||x||2 x∈L e (9) The Fourier transform of σL is e2πi σL (u) = u,x e2πi dσL = x∈Rn u,v σL ({v}), (10) v∈L where u ∈ Rn .

J-Y. Cai. Some recent progress on the complexity of lattice problems. de/eccc/. 14. J-Y. Cai. A New Transference Theorem in the Geometry of Numbers. The 5th International Computing and Combinatorics Conference, 113–122, (COCOON) 1999, Tokyo, Japan. Lecture Notes in Computer Science, 1627. 15. J-Y. Cai. Applications of a New Transference Theorem to Ajtai’s Connection Factor. In the Proceedings of the 14th Annual IEEE Conference on Computational Complexity, pp 205–214, 1999. 16. J-Y. Cai. A Relation of Primal-Dual Lattices and the Complexity of Shortest Lattice Vector Problem.

H˚ astad. Dual Vectors and Lower Bounds for the Nearest Lattice Point Problem. Combinatorica, 8:75–81, 1988. 41. C. Hermite. Extraits de lettres de M. Ch. Hermite ` a M. Jacobi sur diff´erents objets de la th´eorie des nombres. Journal f¨ ur die Reine und Angewandte Mathematik, 40:261–278, 279–290, 291–307, 308–315, 1850. 42. E. Hewitt and K. A. Ross. Abstract Harmonic Analysis, Vol II. Berlin G¨ ottingen Heidelberg: Springer 1970. 43. E. Kaltofen. Polynomial factorization 1987–1991. LATIN ’92, I.

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