The multiple polynomial quadratic sieve

Author:
Robert D. Silverman

Journal:
Math. Comp. **48** (1987), 329-339

MSC:
Primary 11Y05

DOI:
https://doi.org/10.1090/S0025-5718-1987-0866119-8

MathSciNet review:
866119

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A modification, due to Peter Montgomery, of Pomerance's Quadratic Sieve for factoring large integers is discussed along with its implementation. Using it, allows factorization with over an order of magnitude less sieving than the basic algorithm. It enables one to factor numbers in the 60-digit range in about a day, using a large minicomputer. The algorithm has features which make it well adapted to parallel implementation.

**[1]**J. Brillhart, D. H. Lehmer, J. L. Selfridge, B. Tuckerman & S. S. Wagstaff, Jr.,*Factorizations of*,*Up to High Powers*, Contemp. Math., vol. 22, Amer. Math. Soc., Providence, R. I., 1983. MR**715603 (84k:10005)****[2]**J. Davis & D. Holdridge,*Factorization Using the Quadratic Sieve*, Sandia Report #SAND 83-1346, 1983.**[3]**J. Davis & D. Holdridge, "Status report on factoring,"*Advances in Cryptology*(T. Beth, N. Cot, and I. Ingemarrson, eds.), Lecture Notes in Comput. Sci., vol. 209, Springer-Verlag, Berlin and New York, 1985, pp. 183-215.**[4]**J. Gerver, "Factoring large numbers with a quadratic sieve,"*Math. Comp.*, v. 41, 1983, pp. 287-294. MR**701639 (85c:11122)****[5]**D. Knuth,*The Art of Computer Programming*, Vol. 2,*Semi-Numerical Algorithms*, Addison-Wesley, Reading, Mass., 1969. MR**633878 (83i:68003)****[6]**P. Montgomery, personal communication.**[7]**M. Morrison & J. Brillhart, "A method of factoring and the factorization of*F*7,"*Math. Comp.*, v. 29, 1975, pp. 183-205. MR**0371800 (51:8017)****[8]**C. Pomerance, personal communication.**[9]**C. Pomerance, "The quadratic sieve factoring algorithm,"*Advances in Cryptology*(T. Beth, N. Cot, and I. Ingemarrson, eds.), Lecture Notes in Comput. Sci., vol. 209, Springer-Verlag, Berlin and New York, 1985, pp. 169-182. MR**825590 (87d:11098)****[10]**C. Pomerance, "Analysis and comparison of some integer factoring algorithms," in*Computational Methods in Number Theory*(H. Lenstra and R. Tijdeman, eds.), 1982, pp. 89-141. MR**700260 (84i:10005)****[11]**C. Pomerance & S. S. Wagstaff, Jr., "Implementation of the continued fraction integer algorithm,"*Congress. Numer.*, v. 37, 1983, pp. 99-118. MR**703581 (85c:11124)**

Retrieve articles in *Mathematics of Computation*
with MSC:
11Y05

Retrieve articles in all journals with MSC: 11Y05

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1987-0866119-8

Article copyright:
© Copyright 1987
American Mathematical Society