A. K. Lenstra, "Massively parallel computing and factoring," Proceedings Latin Amer. Symp. on Theor. Inform. '92, Lecture Notes in Comput. Sci. 583 (1992), pp. 344-355.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....37 A better method, known as structured Gaussian elimination, was presented in [18] 22] Structured Gauss takes the large sparse matrix and reduces it to a smaller, dense matrix in an intelligent way. The smaller matrix, typically about one fourth or one third the size of the original matrix [11] [12], can then be processed by regular Gaussian elimination. Arjen Lenstra has used this method quite a bit, and has programmed it on a full size MasPar MP 1 massively parallel computer [12] This implementation was used to solve the RSA 129 matrix [2] The 524,339 Theta569,466 matrix of density 47 ....

....way. The smaller matrix, typically about one fourth or one third the size of the original matrix [11] 12] can then be processed by regular Gaussian elimination. Arjen Lenstra has used this method quite a bit, and has programmed it on a full size MasPar MP 1 massively parallel computer [12]. This implementation was used to solve the RSA 129 matrix [2] The 524,339 Theta569,466 matrix of density 47 was reduced to a 188,614 Theta188,160 dense matrix which required over 4 gigabytes to store on disk. The dense matrix was solved in 45 hours. Clearly structured Gauss requires too much ....

A. K. Lenstra, "Massively parallel computing and factoring," Proceedings Latin Amer. Symp. on Theor. Inform. '92, Lecture Notes in Comput. Sci. 583 (1992), pp. 344-355.

....1GB disk storage capacity. Approaching 100 digits, the needs for memory and disk capacity become substantial. However, it was still not yet necessary to use the possible improvements we could imagine of until now. 4 The Real Parallelisation The parallel MPQS implementations described in [3] and [6] were not applicable on our machine. Following Silverman s approach who implemented MPQS in a cluster of independent workstations, every processor would have to work on its own hypercube. But the need to keep (l 3)R integers per hypercube does not leave enough memory for the sieve array with ....

.... 3)R integers per hypercube does not leave enough memory for the sieve array with growing R, e.g. with R = 80:000; l = 10 this sums up to 4,16 MB. Additionally, every message sent spawns threads on the way taken by itself to the destination processor. The implementation of Lenstra described in [6] was done on a Single Instruction Multiple Data parallel computer. We were glad not to face the difficulties resulting from a single instruction machine. Moreover, a forced synchronisation of all processors in our machine did not seem reasonable to us. 1 available from ftp.nosc.mil in the ....

A. K. Lenstra, "Massively Parallel Computing and Factoring", Proceedings Latin '92, Lecture Notes in Computer Science 583 (1992), pp.344 - 355.

....at our university s Zentrum fur Paralleles Rechnen is a MIMD parallel computer and consists of 1024 Inmos T805 transputers. Every processor has only 4 MByte RAM, 350 kByte of which are occupied by the operating system. Therefore both parallel MPQS implementations described in [CaSi88] and [Lens92] were not applicable on our machine. We just mention the development of two parallel approaches particularly suited for MIMD parallel computers (a full description of both implementations including the communication aspects will be given in [Wamb94] While the first one is presently used, the ....

A. K. Lenstra, "Massively Parallel Computing and Factoring", Proceeding Latin '92, Lecture Notes in Computer Science 583 (1992), pp.344 - 355.

....12 CPU hours on a Sparc 10 workstation, 97 of which was spent building the 4 436 201 280 byte dense matrix, in 268 separate files of about 16 MBytes each. To find a dependency among the rows of the dense matrix, we used the incremental version from [1] of the MasPar dense matrix eliminator from [11]. The dense matrix was processed in 5 blocks. With a core size of 1GByte, 41 595 rows could be processed per block. Each new block was first eliminated with the pivots found in the previous blocks, then with the new pivots in the block itself, after which the result was written to disk. Each of ....

A. K. Lenstra, Massively parallel computing and factoring, Proceedings Latin'92, Lecture Notes in Comput. Sci. 583 (1992) 344--355.

.... Theta 245810 bit matrix. To find dependencies modulo two among its rows the third author used the technique described in [9] with the extension from [1] structured Gaussian elimination (cf. 5; 13] followed by the incremental version from [1] of the MasPar dense matrix eliminator described in [6]. Structured Gauss managed to reduce the size of the matrix to 89304 Theta 89088. This took 15 hours on a Sparc10 workstation, 10 of which were needed to build the 994489344 byte dense matrix, in 47 separate files of more than 21MB each. This dense matrix was smaller than expected (and smaller ....

Lenstra, A.K.: Massively parallel computing and factoring. Proceedings Latin'92, Lecture Notes in Comput. Sci. 583 (1992) 344--355

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