Signature Schemes Based on the Strong RSA Assumption

ACM Transactions on Information and System Security

Volumn 3, Issue 3, 2000, Pages 161-185

  Cramer, Ronald ^a   Shoup, Victor ^b  

^a AARHUS UNIVERSITY   (Denmark)

^b IBM RESEARCH ZURICH   (Switzerland)

Author keywords

Algorithms; digital signatures; provable security; RSA; Security; Theory

Indexed keywords

EID: 85024261619     PISSN: 10949224     EISSN: 15577406     Source Type: Journal    
DOI: 10.1145/357830.357847     Document Type: Article

References (30)

1. Bach, E. and Shallit, J. 1996. Algorithmic number theory. MIT Press foundations of computing series, vol. 1. MIT Press, Cambridge, MA
2. Baric, N. and Pfitzmann, B. 1997. Collision-free accumulators and fail-stop signature schemes without trees. In Proceedings of the Conference on Advances in Cryptology (EUROCRYPT'97, Berlin, Germany), W. Fumy, Ed. Springer-Verlag, New York, NY, 480-494
3. Bateman, P. and Horn, R. 1962. A heuristic asymptotic formula concerning the distribution of prime numbers. Math. Comput. 16, 363-367
4. Bateman, P. and Horn, R. 1965. Primes represented by irreducible polynomials in one variable. In Proceedings of the Symposium on Pure Mathematics. 119-135
5. Bellare, M. and Rogaway, P. 1993. Random oracles are practical: a paradigm for designing efficient protocols. In Proceedings of the First ACM Conference on Computer and Communications Security (Fairfax, VA, Nov. 3-5), D. Denning, R. Pyle, R. Ganesan, R. Sandhu, and V. Ashby, Chairs. ACM Press, New York, NY, 62-73
6. Bellare, M. and Rogaway, P. 1997. Collision-resistant hashing: Towards making UOWHFs practical. In Proceedings of the 17th Annual International Conference on Advances in Cryptology (CRYPTO '97, Santa Barbara, CA, Aug.). Springer-Verlag, New York, NY
7. Bleichenbacher, D. 1996. Efficiency and security of cryptosystems based on number theory. Ph.D. Dissertation. Swiss Federal Institute of Technology, Zurich, Switzerland
8. Brillhart, J., Lehmer, D., and Selfridge, J. 1975. New primality criteria and factorizations of 2m ± 1. Math. Comput. 29, 620-647
9. Canetti, R., Goldreich, O., and Halevi, S. 1998. The random oracle methodology, revisited (preliminary version). In Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC '98, Dallas, TX, May 23-26), J. Vitter, Chair. ACM Press, New York, NY, 209-218
10. Cramer, R. and Damgaard, I. 1996. New generation of secure and practical RSA-based signatures. In Proceedings of the 16th Annual International Conference on Advances in Cryptology (CRYPTO '96, Santa Barbara, CA, Aug.), N. Koblitz, Ed. Springer-Verlag, New York, NY, 173-185
11. Damgaard, I., Landrock, P., and Pomerance, C. 1993. Average case error estimates for the strong probable prime test. Math. Comput. 61, 204 (Oct.), 177-194
12. Dwork, C. and Naor, M. 1994. An efficient existentially unforegeable signature scheme and its applications. In Proceedings of the Conference on Advances in Cryptology (CRYPTO'94, Santa Barbara, CA), Y. G. Desmedt, Ed. Springer-Verlag, New York, NY, 218-238
13. Fiat, A. and Shamir, A. 1987. How to prove yourself: practical solutions to identification and signature problems. In Proceedings of the 6th Annual International Conference on Advances in Cryptology (CRYPTO '86, Santa Barbara, CA, Aug. 11-15), A. M. Odlyzko, Ed. Springer-Verlag, Berlin, Germany, 186-194
14. Fujisaki, E. and Okamoto, T. 1997. Statistical zero knowledge protocols to prove modular polynomial relations. In Proceedings of the 17th Annual International Conference on Advances in Cryptology (CRYPTO '97, Santa Barbara, CA, Aug.). Springer-Verlag, New York, NY
15. Gennaro, R., Halevi, S., and Rabin, T. 1999. Secure hash-and-sign signatures without the random oracle. In Proceedings of the Conference on Advances in Cryptology (EUROCRYPT '99). Springer-Verlag, New York, NY, 123-139
16. Goldwasser, S., Micali, S., and Rivest, R. L. 1988. A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17, 2 (Apr.), 281-308
17. Guillou, L. C. and Quisquater, J.-J. 1988. A practical zero-knowledge protocol fitted to security microprocessor minimizing both transmission and memory. In Proceedings of the Conference on Advances in Cryptology (EUROCRYPT '88, Davos, Switzerland, May 25-27), C. G. Günther, Ed. Springer-Verlag, New York, NY, 123-128
18. Halberstam, H. and Richert, H. 1974. Sieve Methods. Academic Press, Inc., Duluth, MN
19. Impagliazzo, R. and Zuckermann, D. 1989. How to recycle random bits. In Proceedings of the 30th IEEE Symposium on Foundations of Computer Science (FOCS '89, Research Triangle Park, NC, Oct. 30-Nov. 1). IEEE Computer Society Press, Los Alamitos, CA, 248-253
20. Kilian, J. and Rogaway, P. 1996. How to protect DES against exhaustive key search. In Proceedings of the 16th Annual International Conference on Advances in Cryptology (CRYPTO '96, Santa Barbara, CA, Aug.), N. Koblitz, Ed. Springer-Verlag, New York, NY, 252-267
21. Krawczyk, H. and Rabin, T. 1998. Chameleon Hashing and Signatures
22. Lim, C. H. and Lee, P. J. 1994. More flexible exponentiation with precomputation. In Proceedings of the Conference on Advances in Cryptology (CRYPTO'94, Santa Barbara, CA), Y. G. Desmedt, Ed. Springer-Verlag, New York, NY, 95-107
23. Luby, M. 1996. Pseudorandomness and Cryptographic Applications. Princeton University Press, Princeton, NJ
24. Maurer, U. 1995. Fast generation of prime numbers and secure public-key cryptographic parameters. J. Cryptology 8, 123-155
25. Naor, M. and Yung, M. 1989. Universal one-way hash functions and their cryptographic applications. In Proceedings of the 21st Annual ACM Symposium on Theory of Computing (STOC '89, Seattle, WA, May 15-17), D. S. Johnson, Ed. ACM Press, New York, NY, 33-43
26. Pointcheval, D. and Stern, J. 1996. Provably secure blind signature schemes. In Proceedings of the 16th Annual International Conference on Advances in Cryptology (CRYPTO '96, Santa Barbara, CA, Aug.), N. Koblitz, Ed. Springer-Verlag, New York, NY, 252-265
27. Rabin, M. O. 1980. Probabilistic algorithms for testing primality. J. Number Theory 12, 128-138
28. Rosser, J. and Schoenfeld, L. 1962. Approximate formulas for some functions of prime numbers. Ill. J. Math. 6, 64-94
29. Shoup, V. 2000a. A composition theorem for universal one-way hash functions. In Proccedings of the Workshop on Advances in Cryptology (EUROCRYPT 2000). Springer-Verlag, New York, NY
30. Shoup, V. 2000b. Using hash functions as a hedge against chosen ciphertext attack. In Proccedings of the Workshop on Advances in Cryptology (EUROCRYPT 2000). Springer-Verlag, New York, NY