论文信息 - Factoring with the quadratic sieve on large vector computers

Factoring with the quadratic sieve on large vector computers

Abstract The results are presented of experiments with the multiple polynomial version of the quadratic sieve factorization method on a CYBER 205 and on a NEC SX-2 vector computer. Various numbers in the 50–92 decimal digits range have been factorized, as a contribution to (i) the Cunningham project, (ii) Brent's table of factors of Mersenne numbers, and (iii) a proof by Brent and G. Cohen of the non-existence of odd perfect numbers below 10 200 . The factorized 92-decimal digits number is a record for general purpose factorization methods.

[1] James A. Davis,et al. Status Report on Factoring (At the Sandia National Laboratories) , 1984, EUROCRYPT.

[2] Robert D. Silverman. The multiple polynomial quadratic sieve , 1987 .

[3] Jeffrey W. Smith,et al. A Pipeline Architecture for Factoring Large Integers with the Quadratic Sieve Algorithm , 1988, SIAM J. Comput..

[4] A. K. Lenstra,et al. Implementation of a New Primality Test , 1985 .

[5] Robert D. Silverman,et al. A Distributed Batching System for Parallel Processing , 1989, Softw. Pract. Exp..

[6] H. W. Lenstra,et al. Factoring integers with elliptic curves , 1987 .

[7] H. Riesel. Prime numbers and computer methods for factorization , 1985 .

[8] J. L. Selfridge,et al. Factorizations of b[n]±1, b=2, 3, 5, 6, 7, 10, 11, 12 up to high powers , 1985 .

[9] Adi Shamir,et al. A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[10] P. L. Montgomery. Speeding the Pollard and elliptic curve methods of factorization , 1987 .

[11] Marvin C. Wunderlich,et al. A compact algorithm for Gaussian elimination over GF(2) implemented on highly parallel computers , 1984, Parallel Comput..

[12] Robert D. Silverman,et al. Tables of Fibonacci and Lucas factorizations , 1988 .

[13] W D Blair,et al. Factoring large numbers on a pocket calculator , 1986 .