Matrix analysis
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Factorization of RSA-140 Using the Number Field Sieve
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Fast broadcast by the divide-and-conquer algorithm
CLUSTER '04 Proceedings of the 2004 IEEE International Conference on Cluster Computing
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
Factorization of a 512-bit RSA modulus
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Parallelization of the Lanczos algorithm on multi-core platforms
ICDCN'10 Proceedings of the 11th international conference on Distributed computing and networking
Iterative sparse Matrix-Vector multiplication for integer factorization on GPUs
Euro-Par'11 Proceedings of the 17th international conference on Parallel processing - Volume Part II
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Researchers use NFS (Number Field Sieve) method with Lanczos algorithm to analyze big-sized RSA keys. NFS method includes the integer factorization process and nullspace computation of huge sparse matrices. Parallel processing is indispensible since sequential computation requires weeks (even months) of CPU time with supercomputers even for 150-digit RSA keys. This paper presents details of improved block Lanczos algorithm based on previous implementation[4,10]. It includes a new load balancing scheme by partitioning the matrix such that the numbers of nonzero components in the submatrices become equal. Experimentally, a speedup up to 6 and the maximum of efficiency of 0.74 have been achieved using an 8-node cluster with Myrinet interconnection.