Most Wanted Factorizations Using the Quadratic Sieve

摘要

The study of the crypto-security of the RSA algorithm at Sandia National Laboratories has focused attention on factorization of large integers, as no attack of lesser computational complexity has thus far surfaced. This report describes recent experience in the development of a state-of-the-art factorization capability. The various changes in the algorithm that have enabled factorization of 70-digit numbers in times comparable to those for 50 digits a year ago are described in some detail. (ERA citation 09:045296)