Implementing the elliptic curve method of factoring in reconfigurable hardware

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

Volumn 4249 LNCS, Issue , 2006, Pages 119-133

  Gaj, Kris ^a   Kwon, Soonhak ^b   Baier, Patrick ^a   Kohlbrenner, Paul ^a   Le, Hoang ^a   Khaleeluddin, Mohammed ^a   Bachimanchi, Ramakrishna ^a  

^a Krasnow Institute for Advanced Study   (United States)

^b Sungkyunkwan University   (South Korea)

Author keywords

Cipher breaking; ECM; Factoring; FPGA

Indexed keywords

COMPUTER SOFTWARE; FIELD PROGRAMMABLE GATE ARRAYS; MICROPROCESSOR CHIPS; MILITARY ELECTRONIC COUNTERMEASURES; OPTIMIZATION;

CIPHER-BREAKING; ELLIPTIC CURVE METHOD; FACTORING; NUMBER FIELD SIEVE;

COMPUTER HARDWARE;

EID: 33750699935     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11894063_10     Document Type: Conference Paper

References (19)

1. J.M. Pollard, "Factoring with cubic integers", Lecture Notes in Mathematics 1554, pp. 4-10, Springer, 1993.
2. A.K. Lenstra and H.W. Lenstra, The Development of the Number Field Sieve, Lecture Notes in Mathematics 1554, Springer, 1993.
3. Factorization of RSA-200, F. Bahr, M. Boehm, J. Franke, T. Kleinjung, http:crypto-world.com/announcements/rsa200.txt.
4. P. Zimmermann, "20 years of ECM," preprint, 2005, http://www.loria.fr/~ zimmerma/papers/ecm-submitted.pdf.
5. J. Fougeron, L. Fousse, A. Kruppa, D. Newman, and P. Zimmermann, "GMP-ECM", http://www.komite.net/laurent/soft/ecm/ecm-6.0.1.html, 2005.
6. M. Šimka, J. Pelzl, T. Kleinjung, J. Franke, C. Priplata, C. Stahlke, M. Drutarovsky, V. Fischer, and C. Paar, "Hardware factorization based elliptic curve method", IEEE Symposium on Field-Programmable Custom Computing Machines - FCCM'05, Napa, CA, USA, 2005.
7. J. Pelzl, M. Šimka, T. Kleinjung, J. Franke, C. Priplata, C. Stahlke, M. Drutarovsky, V. Fischer, and C. Paar, "Area-time efficient hardware architecture for factoring integers with the elliptic curve method", IEE Proceedings on Information Security, vol. 152, no. 1, pp. 67-78, 2005.
8. D. Hankerson, A.J. Menezes, and S.A. Vanstone, Guide to Elliptic Curve Cryptography, Springer-Verlag, 2004.
9. H.W. Lenstra, "Factoring integers with elliptic curves", Annals of Mathematics, vol. 126, pp. 649-673, 1987.
10. R.P. Brent, "Some integer factorization algorithms using elliptic curves", Australian Computer Science Communications, vol. 8, pp. 149-163, 1986.
11. P.L. Montgomery, "Speeding the Pollard and elliptic curve methods of factorization", Mathematics of Computation, vol. 48, pp. 243-264, 1987.
12. P.L. Montgomery, "An FFT extension of the elliptic curve method of factorization", Ph.D. Thesis, UCLA, 1992.
13. P.L. Montgomery, "Modular multiplication without trivial division", Mathematics of Computation, vol. 44, pp. 519-521, 1985.
14. C. McIvor, M. McLoone, J. McCanny, A. Daly, and W. Marnane, "Fast Montgomery modular multiplication and RSA cryptographic processor architectures", Proc, 37th IEEE Computer Society Asilomar Conference on Signals, Systems and Computers, Monterey, USA, pp. 379-384, Nov. 2003.
15. S. Kumar, C. Paar, J. Pelzl, G. Pfeiffer, A. Rupp, M. Schimmler, "How to break DES for 8,980 Euro", 2nd Workshop on Special-purpose Hardware for Attacking Cryptographic Systems - SHARCS 2006, Cologne, Germany, April 3-4, 2006.
16. J. Franke, T. Kleinjung, C. Paar, J. Pelzl, C. Priplata, and C. Stahlke, "SHARK: A realizable special hardware sieving device for factoring 1024-bit integers", Cryptographic Hardware and Embedded Systems - CHES 05, LNCS 3659, pp. 119-130, Springer-Verlag, 2005.
17. W. Geiselmann, F Januszewski, H Koepfer, J. Pelzl, and R. Steinwandt, "A simpler sieving device: Combining ECM and TWIRL", Cryptology ePrint Archive, http://eprint.iacr.org/2006/109.
18. SRC Computers, Inc., http://www.srccomp.com.
19. R.D. Silverman and S.S. Wagstaff,"A practical analysis of the elliptic curve factoring algorithm", Mathematics of Computation, vol. 61, no. 203, pp. 465-462, 1993.