The quadratic sieve factoring algorithm
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Using MPI: portable parallel programming with the message-passing interface
Using MPI: portable parallel programming with the message-passing interface
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
A design for a number theory package with an optimized trial division routine
Communications of the ACM
A block Lanczos algorithm for finding dependencies over GF(2)
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Integer factorization by a parallel GNFS algorithm for public key cryptosystems
ICESS'05 Proceedings of the Second international conference on Embedded Software and Systems
Computers & Mathematics with Applications
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Currently, RSA is a very popular, widely used and secure public key cryptosystem, but the security of the RSA cryptosystem is based on the difficulty of factoring large integers. The General Number Field Sieve (GNFS) algorithm is the best known method for factoring large integers over 110 digits. Our previous work on the parallel GNFS algorithm, which integrated the Montgomery’s block Lanczos algorithm to solve the large and sparse linear systems over GF(2), has one major disadvantage, namely the input has to be symmetric (we have to symmetrize the input for nonsymmetric case and this will shrink the rank). In this paper, we successfully implement the parallel General Number Field Sieve (GNFS) algorithm and integrate with a new algorithm called the biorthogonal block Lanczos algorithm for solving large and sparse linear systems over GF(2). This new algorithm is based on the biothorgonal technique, can find more solutions or dependencies than Montgomery’s block Lanczos method with less iterations. The detailed experimental results on a SUN cluster will be presented as well.