Experiments on the linear algebra step in the number field sieve

Authors:
Kazumaro Aoki;Takeshi Shimoyama;Hiroki Ueda
Affiliations:
NTT, Musashino-shi, Tokyo, Japan;Fujitsu Laboratories Ltd., Kawasaki-shi, Kanagawa-ken, Japan;Nippon Telegraph and Telephone West Corporation, Musashino-shi, Tokyo, Japan
Venue:
IWSEC'07 Proceedings of the Security 2nd international conference on Advances in information and computer security
Year:
2007

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Abstract

This paper shows experimental results of the linear algebra step in the number field sieve on parallel environment with implementation techniques. We developed an efficient algorithm that shares the sum of vectors in each node, and the network structure among the nodes only requires to include a ring. We also investigated the construction of a network for the linear algebra step. The construction can be realized through switches and network interface cards, whose prices are not expensive. Moreover, we investigated the implementation of the linear algebra step using various parameters. The implementation described in this paper was used for the integer factoring of a 176 digit number by GNFS and a 274 digit number by SNFS.