Abstract
We estimate the yield of the number field sieve factoring algorithm when applied to the 1024-bit composite integer RSA-1024 and the parameters as proposed in the draft version [17] of the TWIRL hardware factoring device [18]. We present the details behind the resulting improved parameter choices from [18].
Chapter PDF
Similar content being viewed by others
References
Bach, E., Peralta, R.: Asymptotic semi-smoothness probabilities, University of Wisconsin, Technical report #1115 (October 1992)
Bernstein, D.J.: Circuits for integer factorization: a proposal (November 2001) (manuscript), available at http://cr.yp.to/papers.html#nfscircuit
Canfield, E.R., Erdös, P., Pomerance, C.: On a problem of Oppenheim concerning. Factorisatio Numerorum, J. Number Theory 17, 1–28 (1983)
Cavallar, S., Dodson, B., Lenstra, A.K., Lioen, W., Montgomery, P.L., Murphy, B., te Riele, H.J.J., et al.: Factorization of a 512-bit RSA modulus. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 1–17. Springer, Heidelberg (2000)
Coppersmith, D.: Modifications to the number field sieve. Journal of Cryptology  6, 169–180 (1993)
Crandall, R., Pomerance, C.: Prime numbers. Springer, Heidelberg (2001)
De Bruijn, N.G.: On the number of positive integers ≤ x and free of prime factors > y, II. Indag. Math. 38, 239–247 (1966)
International Technology Roadmap for Semiconductors 2002 Update (2002), http://public.itrs.net/
Lambert, R.: Computational aspects of discrete logarithms, Ph.D. thesis, University of Waterloo (1996)
Lenstra, A.K., Lenstra Jr., H.W. (eds.): The development of the number field sieve. Lecture Notes in Math., vol. 1554. Springer, Heidelberg (1993)
Lenstra, A.K., Shamir, A.: Analysis and optimization of the TWINKLE factoring device. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 35–52. Springer, Heidelberg (2000)
Lenstra, A.K., Shamir, A., Tomlinson, J., Tromer, E.: Analysis of Bernstein’s factorization circuit. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 1–26. Springer, Heidelberg (2002)
Montgomery, P.L., Murphy, B.: Improved polynomial selection for the number field sieve, extended abstract for the conference on the mathematics of public-key cryptography, The Fields institute, Toronto, Ontario, Canada, June 13-17 (1999)
Murphy, B.: Modelling the yield of the number field sieve polynomials. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 137–150. Springer, Heidelberg (1998)
Murphy, B.: Polynomial selection for the number field sieve integer factorisation algorithm, PhD thesis, The Australian National University (July 1999)
RSA Challenge Administrator, see http://www.rsasecurity.com/rsalabs/challenges/factoring/index.html
Shamir, A., Tromer, E.: Factoring large numbers with the TWIRL device (preliminary draft) (February 4, 2003), available at www.wisdom.weizmann.ac.il/~tromer/papers/twirl-20030208.ps.gz
Shamir, A., Tromer, E.: Factoring Large Numbers with the TWIRL Device. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 1–26. Springer, Heidelberg (2003)
Shamir, A.: Factoring large numbers with the TWINKLE device. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, p. 2. Springer, Heidelberg (1999)
Silverman, R.D.: Optimal parameterization of SNFS, Manuscript (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lenstra, A. et al. (2003). Factoring Estimates for a 1024-Bit RSA Modulus. In: Laih, CS. (eds) Advances in Cryptology - ASIACRYPT 2003. ASIACRYPT 2003. Lecture Notes in Computer Science, vol 2894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40061-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-40061-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20592-0
Online ISBN: 978-3-540-40061-5
eBook Packages: Springer Book Archive