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.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Lenstra, A.K., Lenstra Jr., H.W. (eds.): AMCP 1998. Lecture Notes in Mathematics, vol. 1554. Springer, Heidelberg (1993)
Kleinjung, T.: rsa200 (2005), http://www.crypto-world.com/announcements/rsa200.txt
Silverman, R.D.: A cost-based security analysis of symmetric and asymmetric key lengths. RSA Laboratories’ Bulletin, (revised 2001) (2000), http://www.rsasecurity.com/rsalabs/node.asp?id=2088
Leyland, P., Lenstra, A., Dodson, B., Muffett, A., Wagstaff, S.: MPQS with three large primes. In: Fieker, C., Kohel, D.R. (eds.) ANTS-V. LNCS, vol. 2369, pp. 446–460. Springer, Heidelberg (2002)
Aoki, K., Kida, Y., Shimoyama, T., Ueda, H.: GNFS176 (2005), http://www.crypto-world.com/announcements/c176.txt
Montgomery, P.L.: A block Lanczos algorithm for finding dependencies over GF(2). In: Guillou, L.C., Quisquater, J.J. (eds.) EUROCRYPT 1995. LNCS, vol. 921, pp. 106–120. Springer, Heidelberg (1995)
Coppersmith, D.: Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm. Mathematics of Computation 62, 333–350 (2004)
Montgomery, P.L.: Distributed linear algebra. In: presentation slides for ECC2000 (2000), http://www.cacr.math.uwaterloo.ca/conferences/2000/ecc2000/montgomery.ps
Golliver, R.A., Lenstra, A.K., McCurley, K.S.: Lattice sieving and trial division. In: Huang, M-D.A., Adleman, L.M. (eds.) ANTS-I. LNCS, vol. 877, pp. 18–27. Springer, Heidelberg (1994)
Aoki, K., Kida, Y., Shimoyama, T., Sonoda, Y., Ueda, H.: SNFS248 (2004), http://www.rkmath.rikkyo.ac.jp/~kida/snfs248e.htm
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aoki, K., Shimoyama, T., Ueda, H. (2007). Experiments on the Linear Algebra Step in the Number Field Sieve . In: Miyaji, A., Kikuchi, H., Rannenberg, K. (eds) Advances in Information and Computer Security. IWSEC 2007. Lecture Notes in Computer Science, vol 4752. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75651-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-75651-4_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75650-7
Online ISBN: 978-3-540-75651-4
eBook Packages: Computer ScienceComputer Science (R0)