When e-th roots become easier than factoring

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

Volumn 4833 LNCS, Issue , 2007, Pages 13-28

  Joux, Antoine ^a   Naccache, David ^b   Thomé, Emmanuel ^c  

^a UNIVERSITY OF VERSAILLES   (France)

^b ECOLE NORMALE SUPÉRIEURE   (France)

^c LORIA   (France)

Author keywords

Factoring; NFS; Roots; RSA

Indexed keywords

COMPUTATIONAL COMPLEXITY; FACTORIZATION; INVERSE PROBLEMS; PROBLEM SOLVING;

FACTORING; RSA; SUBEXPONENTIAL NUMBER;

COMPUTATIONAL METHODS;

EID: 38149117031     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-76900-2_2     Document Type: Conference Paper

References (19)

1. Aoki, K., Franke, J., Kleinjung, T., Lenstra, A., Osvik, D.: Electronic newsgroup posting announcing the factorization of the 1039-th Mersenne number by the snfs (May 21, 2007), http://www.loria.fr/zimmerma/records/21039-
2. Bellare, M., Namprempre, C., Pointcheval, D., Semanko, M.: The One-More-RSA-Inversion Problems and the Security of Chaum's Blind Signature Scheme. Journal of Cryptology 16(3), 185-215 (2003)
3. Buhler, J.P., Lenstra, A.K., Pollard, J.M.: Factoring integers with the number field sieve. In: Lenstra, A.K., Lenstra Jr., H.W. (eds.) The development of the number field sieve. LMN, vol. 1554, pp. 50-94. Springer, Heidelberg (1993)
4. Brier, É., Clavier, C., Coron, J.-S., Naccache, D.: Cryptanalysis of RSA signatures with fixed-pattern padding. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 433-439. Springer, Heidelberg (2001)
5. Commeine, A., Semaev, I.: An algorithm to solve the discrete logarithm problem with the number field sieve. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol. 3958, pp. 174-190. Springer, Heidelberg (2006)
6. Coron, J.-S., Naccache, D., Stern, J.P.: On the Security of RSA padding. In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 1-18. Springer, Heidelberg (1999)
7. De Jonge, W., Chaum, D.: Attacks on some RSA signatures. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 18-27. Springer, Heidelberg (1986)
8. Eberly, W., Giesbrecht, M., Giorgi, P., Storjohann, A., Villard, G.: Solving sparse rational linear systems. In: Trager, B.M. (ed.) ISSAC 2006, pp. 63-70. ACM Press, New York (2006)
9. Eberly, W., Giesbrecht, M., Giorgi, P., Storjohann, A., Villard, G.: Faster inversion and other black box matrix computations using efficient block projections. In: Brown, C.W. (ed.) ISSAC 2007, pp. 143-150. ACM Press, New York (2007)
10. Girault, M., Misarksy, J.-F.: Selective forgery of RSA signatures using redundancy. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 495-507. Springer, Heidelberg (1997)
11. Joux, A., Lercier, R.: Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method. Mathematics of Computation 242(72), 953-967 (2003)
12. Lenstra, A.K., Lenstra Jr., H.W., Manasse, M.S., Pollard, J.M.: The number field sieve. In: Lenstra, A.K., Lenstra Jr., H.W. (eds.) AMCP 1998. LNM, vol. 1554, pp. 11-42. Springer, Heidelberg (1993)
13. Lenstra, A.K., Shparlinski, I.: Selective forgery of RSA signatures with fixed-pattern padding. In: Proceedings of the 5-th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography. LNCS, vol. 2274, pp. 228-236. Springer, Heidelberg (2002)
14. Misarsky, J.-F.: A multiplicative attack using LLL algorithm on RSA signatures with redundancy. In: Proceedings of Crypto 1997. LNCS, vol. 1294, pp. 221-234. Springer, Heidelberg (1997)
15. Misarsky, J.-F.: How (not) to design RSA signature schemes. In: Imai, H., Zheng, Y. (eds.) PKC 1998. LNCS, vol. 1431, pp. 14-28. Springer, Heidelberg (1998)
16. Montgomery, P.L.: Square roots of products of algebraic numbers. In: W. Gautschi, Ed., Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics, vol. 48 of Proc. Sympos. Appl. Math., pp. 567-571. AMS (1994)
17. Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public key cryptosystems. CACM 21 (1978)
18. RSA Laboratories, pkcs #1 : RSA cryptography specifications, version 2.0 (September 1998)
19. Schirokauer, O.: Discrete logarithms and local units. Philos. Trans. Roy. Soc. London Ser. a 345(1676), 409-423 (1993)