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.
- Gnu
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.
Some references:
- [Bre89] D.M. Bressoud. Factorization and Primality Testing.
Springer-Verlag, 1989.
- [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.
Springer-Verlag, 1994.
- [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,
1990.
- [Pol74] J. Pollard. Theorems of factorization and primality
testing. Proceedings of Cambridge Philosophical Society, 76:
521-528, 1974.
- [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,
Springer-Verlag, 1991.
- [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 rayo@ontko.com.