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

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

This booklet constitutes the refereed court cases of the 4th overseas Algorithmic quantity concept Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000.
The booklet provides 36 contributed papers that have passed through a radical around of reviewing, choice and revision. additionally integrated are four invited survey papers. one of the themes 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 tool sums.

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

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22. J-Y. Cai and A. Nerurkar. A note on the non-NP-hardness of approximate lattice problems under general Cook reductions. 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.

Halevi. Public-key cryptosystems from lattice reduction problems. In Advances in Cryptology – CRYPTO ’97, Burton S. Kaliski Jr. ), Lecture Notes in Computer Science, 1294:112-131, Springer-Verlag, 1997. 35. O. Goldreich, S. Goldwasser, and S. Halevi. Eliminating decryption errors in the Ajtai-Dwork cryptosystem. In Advances in Cryptology – CRYPTO ’97, Burton S. Kaliski Jr. ), Lecture Notes in Computer Science, 1294:105-111, SpringerVerlag, 1997. The Complexity of Some Lattice Problems 31 36. O.

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. It follows that there is a significant probability that a dishonest prover will be caught, since in case a point z ∈ Bp (r)∩Bp (r) is chosen, the verifier could equally have chosen p or p .

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