By Jin-Yi Cai (auth.), Wieb Bosma (eds.)
This e-book constitutes the refereed complaints of the 4th foreign Algorithmic quantity conception Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000.
The ebook offers 36 contributed papers that have passed through an intensive around of reviewing, choice and revision. additionally incorporated are four invited survey papers. one of the subject matters addressed are gcd algorithms, primality, factoring, sieve equipment, cryptography, linear algebra, lattices, algebraic quantity fields, classification teams and fields, elliptic curves, polynomials, functionality fields, and tool sums.
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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Extra info for Algorithmic Number Theory: 4th International Symposium, ANTS-IV Leiden, The Netherlands, July 2-7, 2000. Proceedings
It is clear that for an honest prover P with unlimited computing power, since all the balls Bp (r) are disjoint, he has no diﬃculty meeting his obligation. However, suppose the prover P is dishonest, so that in fact λ1 (L) ≤ t. Then for any lattice point p picked by the veriﬁer, there is at least one nearby lattice point p with ||p − p || ≤ t. Then Bp (r) and Bp (r) would have a large intersection. This follows from the fact that the radius is almost n1/2 times the distance of their respective centers.
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. In Proc. 24th IEEE Symposium on Foundations of Computer Science, 1983, 1 – 10. 50. A. K. Lenstra, H. W. Lenstra, and L. Lov´asz. Factoring polynomials with rational coeﬃcients. Mathematische Annalen, 261:515–534, 1982. 51. H. W. Lenstra, Jr. Integer programming with a ﬁxed number of variables.
B. Vall´ee. Un probl`eme central en g´eom´etrie algorithmique des nombres: la r´eduction des r´eseaux;atour de l’algorithme LLL. Inform. Th´eor. , 345–376, 1989. English transl. by E. Kranakis, CWI Quart 3:95–120, 1990. 66. P. van Emde Boas. Another NP-complete partition problem and the complexity of computing short vectors in lattices. Technical Report 81-04, Mathematics Department, University of Amsterdam, 1981.