Oracle-assisted static Diffie-Hellman is easier than discrete logarithms

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

Volumn 5921 LNCS, Issue , 2009, Pages 351-367

  Joux, Antoine ^a   Lercier, Reynald ^b,c   Naccache, David ^d   Thomé, Emmanuel ^e  

^a UNIVERSITY OF VERSAILLES   (France)

^b Delegation Generale pour l'Armement   (France)

^c UNIVERSITÉ DE RENNES 1   (France)

^d ECOLE NORMALE SUPÉRIEURE   (France)

^e LORIA   (France)

Author keywords

DLP; FFS; NFS; SDHP

Indexed keywords

CODES (SYMBOLS);

DIFFIE HELLMAN; DIFFIE-HELLMAN PROBLEM; DISCRETE LOGARITHMS; FINITE FIELDS; RESOLUTION METHODS; SDHP;

CRYPTOGRAPHY;

EID: 72449182104     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-10868-6_21     Document Type: Conference Paper

References (17)

1. Brown, D., Gallant, R.: The static Diffie-Hellman problem, Cryptology ePrint Archive, Report 2004/306 (2004), http://eprint.iacr.org
2. Chaum, D., van Antwerpen, H.: Undeniable signatures. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 212-216. Springer, Heidelberg (1990)
3. Dickman, K.: On the frequency of numbers containing prime factors of a certain relative magnitude. Ark. Mat. Astr. Fys. 22, 1-14 (1930)
4. El-Gamal, T.: A public-key cryptosystem and a signature scheme based on discrete logarithms. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10-18. Springer, Heidelberg (1985)
5. Ford, W., Kaliski, B.: Server-assisted generation of a strong secret from a password. In: Nineth international workshop on enabling technologies - wet ice 2000. IEEE Press, Los Alamitos (2000)
6. IEEE p1363.2/d23, Draft standard for specifications for password-based public key cryptographic techniques, p. 24 (March 2006)
7. iso 11770-4, Information technology - security techniques - key management - part 4: Mechanisms based on weak secrets, iso (November 2004)
8. 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)
9. Joux, A., Lercier, R.: The function field sieve in the medium prime case. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 254-270. Springer, Heidelberg (2006)
10. Joux, A., Lercier, R., Smart, N., Vercauteren, F.: The number field sieve in the medium prime case. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 326-344. Springer, Heidelberg (2006)
11. Joux, A., Naccache, D., Thomé, E.: When e-th Roots Become Easier Than Factoring. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 13-28. Springer, Heidelberg (2007)
12. Koblitz, N., Menezes, A.: Another look at non-standard discrete log and Diffie-Hellman problems, Cryptology ePrint Archive, Report 2007/442 (2007), eprint.iacr.org
13. Lenstra, A., Lenstra, H., Manasse, M., Pollard, J.: The number field sieve. In: Lenstra, A., Lenstra, H. (eds.) The development of the number field sieve. LNM, vol. 1554, pp. 11-42. Springer, Heidelberg (1993)
14. Panario, D., Gourdon, X., Flajolet, P.: An analytic approach to smooth polynomials over finite fields. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 226-236. Springer, Heidelberg (1998)
15. Schirokauer, O.: Discrete logarithms and local units. Philos. Trans. Roy. Soc. London Ser. a 345(1676), 409-423 (1993)
16. Schirokauer, O.: Virtual logarithms. J. Algorithms 57(2), 140-147 (2005)
17. Wiedemann, D.: Solving sparse linear equations over finite fields. IEEE Transactions on Information Theory IT-32, 54-62 (1986)