Experiments on the linear algebra step in the number field sieve

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4752 LNCS, Issue , 2007, Pages 58-73

  Aoki, Kazumaro ^a   Shimoyama, Takeshi ^b   Ueda, Hiroki ^a,c  

^a NTT CORPORATION   (Japan)

^b FUJITSU LABORATORIES LTD   (Japan)

^c West Corporation Hiroshima Health Administration Center

Author keywords

Block lanczos; Ethernet; Integer factoring; Number field sieve; Parallel computation

Indexed keywords

ETHERNET; INTEGER PROGRAMMING; PARALLEL PROCESSING SYSTEMS;

BLOCK LANCZOS; INTEGER FACTORING; NUMBER FIELD SIEVES;

LINEAR ALGEBRA;

EID: 38149079783     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-75651-4_5     Document Type: Conference Paper

References (10)

1. Lenstra, A.K., Lenstra Jr., H.W. (eds.): The development of the number field sieve. Lecture Notes in Mathematics, vol. 1554. Springer, Heidelberg (1993)
2. Kleinjung, T.: rsa200 (2005), http://www.crypto-world.com/announcements/ rsa200.txt
3. 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
4. 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)
5. Aoki, K., Kida, Y., Shimoyama, T., Ueda, H.: GNFS176 (2005), http://www.crypto-world.com/announcements/c176.txt
6. 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)
7. Coppersmith, D.: Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm. Mathematics of Computation 62, 333-350 (2004)
8. Montgomery, P.L.: Distributed linear algebra. In: presentation slides for ECC2000 (2000) http://www.cacr.math.uwaterloo.ca/conferences/2000/ecc2000/ montgomery.p8
9. 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)
10. Aoki, K., Kida, Y., Shimoyama, T., Sonoda, Y., Ueda, H.: SNFS248 (2004), http://www.rkmath.rikkyo.ac.jp/-kida/snfs248e.htm