Almost uniform density of power residues and the provable security of ESIGN

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

Volumn 2894, Issue , 2003, Pages 287-301

  Okamoto, Tatsuaki ^a   Stern, Jacques ^b  

^a NTT CORPORATION   (Japan)

^b ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

NUMBER THEORY; SECURITY OF DATA;

DIRICHLET CHARACTERS; PARAMETER CHOICE; PROVABLE SECURITY; RANDOM ORACLE MODEL; RESTRICTED MODELS; SECURITY PROOFS; SIGNATURE SCHEME; TWO-DIMENSIONAL LATTICES;

CRYPTOGRAPHY;

EID: 0345058963     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-40061-5_17     Document Type: Article

References (24)

1. M. Bellare and P. Rogaway. Random Oracles Are Practical: a Paradigm for Designing Efficient Protocols. In Proc. of the 1st CCS, pages 62-73, ACM Press, New York, 1993.
2. M. Bellare and P. Rogaway. The Exact Security of Digital Signatures - How to Sign with RSA and Rabin. In Eurocrypt '96, LNCS 1070, pages 399-416, Springer-Verlag, Berlin, 1996.
3. E. Brickell and J. M. DeLaurentis. An Attack on a Signature Scheme proposed by Okamoto and Shiraishi. In Crypto '85, LNCS 218, pages 28-32, Springer-Verlag, Berlin, 1986.
4. D.A. Burgess. On character sums and primitive roots, Proc. London Math. Soc., 12 (1962), 179-192.
5. H. Davenport. Multiplicative Number theory, Graduate Texts in Mathematics, Vol 74, Springer Verlag, (1980).
6. W. J. Ellison and M. Mendes France. Les nombres premiers, Hermann, Paris (1975).
7. M. Girault, P. Toffin and B. Vallée. Computation of Approximate L-th Roots Modulo n and Application to Cryptography. In Crypto '88, LNCS 403, pages 100-118, Springer-Verlag, Berlin, 1989.
8. S. Goldwasser, S. Micali, and R. Rivest. A Digital Signature Scheme Secure Against Adaptative Chosen-Message Attacks. SIAM Journal of Computing, 17(2):281-308, April 1988.
9. L. Granboulan. How to repair ESIGN, NESSIE internal document, may 2002. See http://www.cryptonessie.org, Docuemnyt NES/DOC/ENS/WP5/019.
10. IEEE Standard 1363-2000. Standard Specifications for Public Key Cryptography. IEEE. Available from http://grouper.ieee.org/groups/1363, August 2000.
11. IEEE P1363a Draft Version 9. Standard Specifications for Public Key Cryptography:Additional Techniques.
12. J. Jonsson. Security Proofs for RSA-PSS and Its Variants. Cryptology ePrint Archive 2001/053. June 2001. Available from http://eprint.iacr.org/.
13. A. K. Lenstra, H. W. Lenstra and L. Lovász, Factoring polynomials with rational coefficients, Mathematische Ann., 261, (1982), 513-534.
14. T. Okamoto. A Fast Signature Scheme Based on Congruential Polynomial Operations. IEEE Transactions on Information Theory, IT-36 (1), pages 47-53, 1990.
15. T. Okamoto, E. Fujisaki and H. Morita. TSH-ESIGN: Efficient Digital Signature Scheme Using Trisection Size Hash, Submission to P1363a, 1998.
16. T. Okamoto and A. Shiraishi. A Fast Signature Scheme Based on Quadratic Inequalities. Proc. of the ACM Symp. Security and Privacy, ACM Press, pages 123-132, 1985.
17. G. Pólya. Über die Verteilung des quadratischen Reste und Nichtreste, Göttinger Nachtrichten (1918), 21-26.
18. R. Rivest, A. Shamir, and L. Adleman. A Method for Obtaining Digital Signatures and Public Key Cryptosystems. Communications of the ACM, 21(2):120-126, February 1978.
19. V. Shoup. OAEP Reconsidered. In Crypto '2001, LNCS 2139, pages 239-259. Springer-Verlag, Berlin, 2001.
20. Also appeared in the Cryptology ePrint Archive 2000/060. November 2000. Available from http://eprint.iacr.org/.
21. J. Stern, D. Pointcheval, J. Malone-Lee, and N. Smart. Flaws in Applying Proof Methodologies to Signature Schemes. In Crypto '02, LNCS 2442, pages 93-110.
22. B. Vallée, M. Girault, and P. Toffin. How to break Okamoto's Cryptosystem by Reducing Lattice Bases. In Eurocrypt '88, LNCS 330, pages 281-292, Springer-Verlag, Berlin, 1988.
23. B. Vallée, M. Girault and P. Toffin. How to Guess ℓth Roots Modulo n by Reducing Lattice Bases. In AAECC-6, LNCS 357, pages 427-442, Springer-Verlag, Berlin, 1988.
24. I.M. Vinogradov. Sur la distributions des résidus et des non-résidus des puissances, J. Phys.-Math. Soc. Perm. 1 (1918), 94-96.