Prime Numbers and Factoring
This page is a collection of links related to prime numbers and
factoring of very large numbers.
- The Prime
Page Chris K. Caldwell's page on primes, especially large ones,
with lots of links to related information and software.
- The Great Internet Mersenne
Prime Search (GIMPS) A group dedicated to using the resources
of the net to find Mersenne primes and to solve other
computationally intensive problems in number theory. Mersenne
Primes, Golomb rulers, RC5 hacking, etc.
Multiple Precision Arithmetic Library Documentation for a
portable collection of routines for manipulating large numbers.
Very fast routines for a variety of platforms.
- RSA Challenges
- DES Challenge
Coordinated Effort page This is another group that participated
in the DES challenge, but didn't win.
- [Bre89] D.M. Bressoud. Factorization and Primality Testing.
- [Knu81] D.E. Knuth. The Art of Computer Programming, volume 2,
Seminumerical Algorithms. Addison-Wesley, 2nd edition, 1981.
- [Kob94] N. Koblitz. A Course in Number Theory and Cryptography.
- [Len87] H.W. Lenstra Jr. Factoring integers with elliptic
curves. Annuals of Mathematics., 126: 649-673, 1987.
- [LL90] A.K. Lenstra and H.W. Lenstra Jr. Algorithms in number
theory. In J. van Leeuwen, editor, Handbook of Theoretical Computer
Science, volume A, pages 673-715, MIT Press/Elsevier, Amsterdam,
- [Pol74] J. Pollard. Theorems of factorization and primality
testing. Proceedings of Cambridge Philosophical Society, 76:
- [Pol75] J. Pollard. Monte Carlo method for factorization. BIT,
15: 331-334, 1975.
- [BLP94] J.P. Buhler, H.W. Lenstra, and C. Pomerance. The
development of the number field sieve. Volume 1554 of Lecture Notes
in Computer Science, Springer-Verlag, 1994.
- [BLZ94] J. Buchmann, J. Loho, and J. Zayer. An implementation
of the general number field sieve. In Advances in Cryptology -
Crypto '93, pages 159-166, Springer-Verlag, 1994.
- [Sil87] R.D. Silverman. The multiple polynomial quadratic
sieve. Mathematics of Computation, 48: 329-339, 1987.
- [DL95] B. Dodson and A.K. Lenstra. NFS with four large primes:
An explosive experiment. In Advances in Cryptology Crypto '95,
pages 372-385, Springer-Verlag, 1995.
- [LLM93] A.K. Lenstra, H.W. Lenstra Jr., M.S. Manasse, and J.M.
Pollard. The factorization of the ninth Fermat number. Mathematics
of Computation, 61(203): 319-349, 1993.
- [BLS88] J. Brillhart, D.H. Lehmer, J.L. Selfridge, B.
Tuckerman, and S.S. Wagstaff Jr. Factorizations of bn ± 1, b
= 2,3,5,6,7,10,11,12 up to High Powers. Volume 22 of Contemporary
Mathematics, American Mathematical Society, 2nd edition, 1988.
- [BBC88] P. Beauchemin, G. Brassard, C. Crepeau, C. Goutier, and
C. Pomerance. The generation of random numbers that are probably
prime. Journal of Cryptology, 1: 53-64, 1988.
- [Riv91a] R.L. Rivest. Finding four million random primes. In
Advances in Cryptology - Crypto '90, pages 625-626,
- [BD93b] J. Brandt and I. Damgard. On generation of probable
primes by incremental search. In Advances in Cryptology - Crypto
'92, pages 358-370, Springer-Verlag, 1993.
This page is maintained by Ray Ontko.
Please send additions, corrections and comments to email@example.com.