Prime numbers and computer methods for factorization
Prime numbers and computer methods for factorization
A pipeline architecture for factoring large integers with the quadratic sieve algorithm
SIAM Journal on Computing - Special issue on cryptography
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A high performance factoring machine
ISCA '84 Proceedings of the 11th annual international symposium on Computer architecture
Supercomputing out of recycled garbage: preliminary experience with Piranha
ICS '92 Proceedings of the 6th international conference on Supercomputing
Time-optimal message-efficient work performance in the presence of faults
PODC '94 Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing
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Over the last 15 years the increased availability of computers and the introduction of the RSA cryptosystem has led to a number of new and remarkable algorithms for finding the prime factors of large integers. Factoring numbers is an arithmetic problem so simple to understand that school children are asked to do it. While multiplying or adding two very large numbers is simple and can be done quite quickly, the age-old problem of trying to find a number that divides another number still has no simple solution. Computer science has reached a point where it is starting to custom tailor the design of computers toward solving specific problems. This pracnique will discuss some of the more recent algorithms for factoring large numbers and how networks of computers can be used to run these algorithms quickly. Since this is a general exposition, we do not give detailed mathematical descriptions of the algorithms. We also allow ourselves to be somewhat casual with mathematical notation in places and hope that the mathematically sophisticated will forgive the looseness.