This paper reports on the factorization of the 512â€“bit number RSAâ€“155 by the Number Field Sieve factoring method (NFS) and discusses the implications for RSA.

On February 2, 1999, we completed the factorization of the 140â€“digit number RSAâ€“140 with the help of the Number Field Sieve factoring method (NFS). This is a new general factoring record. Theâ€¦ (More)

The purpose of this paper is to report the unexpected results that we obtained while experimenting with the multi-large prime variation of the general number field sieve integer factoring algorithmâ€¦ (More)

The Elliptic Curve Method for integer factorization (ECM) was invented by H. W. Lenstra, Jr., in 1985 [14]. In the past 20 years, many improvements of ECM were proposed on the mathematical,â€¦ (More)

We estimate the yield of the number field sieve factoring algorithm when applied to the 1024-bit composite integer RSA-1024 and the parameters as proposed in the draft version [17] of the TWIRLâ€¦ (More)

We report the factorization of a 135-digit integer by the triple-large-prime variation of the multiple polynomial quadratic sieve. Previous workers [6][10] had suggested that using more than twoâ€¦ (More)