Efficient primitives from exponentiation in ℤp

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

Volumn 4058 LNCS, Issue , 2006, Pages 259-270

  Jiang, Shaoquan ^a  

^a UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SCIENCE; COMPUTER SYSTEMS; FUNCTIONS; SECURITY OF DATA;

COLLISION RESISTANT HASH FAMILY (CRHF); DISCRETE LOGARITHM; MODULAR MULTIPLICATION; PSEUDORANDOM GENERATOR;

SECURITY SYSTEMS;

EID: 33746371747     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11780656_22     Document Type: Conference Paper

References (42)

1. L. M. Adleman, A Subexponential Algorithm for the Discrete Logarithm Problem with Applications to Cryptography (Abstract), FOCS 1979, pp. 55-60, 1979.
2. W. Alexi, B. Chor, O. Goldreich, and C. Schnorr, RSA/Rabin Bits are 1/2 + 1/poly(log N) Secure, FOCS 1984: 449-457.
3. M. Bellare and S. Goldwasser, Verifiable Partial Key Escrow, ACM CCS'97, pp. 78-91, 1997.
4. M. Bellare, D. Micciancio, A New Paradigm for Collision-Free Hashing: Incrementality at Reduced Cost, Advances in Cryptology-EUROCRYPT 1997, pp. 163-192, 1997.
5. L. Blum, M, Blum, M. Shub, A Simple Unpredictable Pseudo-Random Number Generator, SIAM J, Comput. 15(2): 364-383 (1986).
6. M. Blum, S. Micali, How to Generate Cryptographically Strong Sequences of Pseudo Random Bits, FOCS 1982: 112-117.
7. D. Coppersmith, A. M, Odlyzko, and R. Schroeppel, Discrete Logarithms in GF(p), Algorithmica 1(1): 1-15 (1986)
8. R. Canetti and H. Krawczyk, analysis of key-exchange protocols and their use for building secure channels, Advances in Cryptology-EUROCRYPT 2001, B. Pfitzmann (Ed.), LNCS 2045, Springer-Verlag, pp. 453-474, 2001.
9. of key exchange and secure channels, Advances in Cryptology-EUROCRYPT 2002, L. R. Knudsen (Ed.), LNCS 2332, Springer-Verlag, pp. 337-351, 2002.
10. signature-based key-exchange protocol, Advances in Cryptology-CRYPTO 2002, M. Yurig (Ed.), LNCS 2442, Springer-Verlag, pp. 143-161, 2002.
11. S. Contini and A.K. Lenstra and R. Steinfeld, VSH: an Efficient and Provable Collision Resistant Hash Function, NIST Cryptographic Hash Workshop 2005, Maryland, USA, 2005.
12. R. Cramer and V. Shoup, a practical public-key cryptosystem provably secure against adaptive chosen ciphertext attack, Advances in Cryptology-CRYPTO 1998, H. Krawczyk (Ed.), LNCS 1462, Springer-Verlag, pp. 13-25, 1998.
13. I. Damgard, Collision Free Hash Functions and Public Key Signature Schemes, EUROCRYPT 1987: 203-216.
14. W. Diffie and M. E. Hellman, New Directions in Cryptography, IEEE Transactions on Information Theory, vol, IT-22, Nov. 1976, pp: 644-654.
15. N. Dedic, L. Reyzin and S. Vaclhan, An Improved Pseudorandom Generator Based on Hardness of Factoring, Security in Communication Networks 2002, S. Cimato et al. (Eds.), LNCS 2576, Springer-Verlag, pp. 55-73, 2003.
16. T. El Garnal, a public-key cryptosystem and a signature scheme based on discrete logarithms, IEEE Transactions on Information Theory, Vol. 31, No. 4, pp. 469-472, 1985.
17. R. Gennaro, An Improved Pseudo-random Generator Based on the Discrete Logarithm Problem , Journal of Cryptology, 18(2), pp.91-110, Spring 2005. Early version appeared in CRYPTO'2000.
18. S. Goldwasser, S. Micali and P. Tong, Why and how to establish a private code on a public network, FOCS'82, pp. 134-144.
19. S. Goldwasser, S. Micali, and R. L. Rivest, A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks, SIAM J. Comput., 17(2): 281-308 (1988).
20. O. Goldreich, Foundations of Cryptography: Basic Tools, Cambridge University Press, 2001.
21. O. Goldreich, S. Goldwasser amd S. Micali, How to Construct Random Functions, Journal of the ACM, Vol 33, No. 4, pp. 792-807, 1986.
22. O. Goldreich, V. Rosen, On the Security of Modular Exponentiation with Application to the Construction of Pseudorandom Generators, J. Cryptology, 16(2): 71-93 (2003).
23. J. Hast ad, R. Impagliazzo, L. A. Levin, Michael Lu by, A Pseudorandom Generator from any One-way Function, SIAM J. Comput. 28(4): 1364-1396 (1999). Early verision is in STOC'89.
24. J. Hastad, A. Schrift and A. Shamir, The Discrete Logarithm Modulo a Composite Hides O(n) Bits, JCSS, 47: 376-404, 1993.
25. L. Hua, Introduction to Number Theory, Berlin: Springer-verlag, 1982.
26. J. Katz, R. Ostrovsky and M. Yung, efficient password-authenticated key exchange using human-memorable passwords, Advances in Cryptology-EUROCRYPT 2001, B. Pfitzmann (Ed.), LNCS 2045, Springer-Verlag, pp. 475-494, 2001.
27. A. K. Lenstra and H. W. Lenstra, Jr. (Eds.), the Developement of the Number Field Sieve, LNM 1554, Springer-Verlag, 1993.
28. C. Lim, P. Lee, More Flexible Exponentiation with Precomputation, Advances in Cryptology-CRYPTO 1994, Y. Desmedt (Ed.), LNCS 839, Springer-Verlag, pp. 95-107, 1994.
29. D. L. Long, A. Wigderson, How Discreet is the Discrete Log, STOC 1983, pp. 413-420, 1983.
30. A. M. Odlyzko, Discrete Logarithms: The Past and the Future, Des. Codes Cryptography 19(2/3): 129-145 (2000).
31. S. Patel and G. S. Sundaram, An Efficient Discrete Log Pseudo Random Generator, Advances in Cryptology-CRYPTO 1998, H. Krawczyk (Ed.), LNCS 1462, Springer-Verlag, pp. 304-317, 1998.
32. C. Peikert and A. Rosen, Efficient Collision-Resistant Hashing From Worst-Case Assumptions on Cyclic Lattices, TCC 2006.
33. D. Pointcheval, The Composite Discrete Logarithm and Secure Authentication, Public Key Cryptography 2000, H. Imai and Y. Zheng (Eds.), LNCS 1751, Springer-Verlag, pp. 113-128, 2000.
34. R. Rivest, A. Shamir and L. Adleman, A Method for Obtaining Digital Signatures and Public-key Cryptosystems, Communications of ACM, Vol. 2, pp. 120-126, February 1978.
35. A. Shamir and Y. Tauman, Improved Online/Offline Signature Schemes, Advances in Cryptology-CRYPTO 2001, J. Kilian (Ed.), LNCS 2139, Springer-Verlag, pp. 355-367, 2001.
36. O. Schirokauer, Discrete Logarithm and Local Units, Philosophical Transactions: Physical Science and Engineering, Vol. 345, No. 1676, pp. 409-423, 1993.
37. Victor Shoup: Lower Bounds for Discrete Logarithms and Related Problems, Advances in Cryptology-EUROCRYPT 1997, W. Fumy (Ed.), LNCS 1233, Springer-Verlag, pp. 256-266, 1997.
38. U. Vazirani and V. Vazirani, Efficient and Secure Pseudo-random number generation, FOCS'84, pp. 458-463.
39. X. Wang, X. Lai, D. Feng, H. Chen and X. Yu, Cryptanalysis of the Hash Functions MD4 and RIPEMD, Advances in Cryptology-EUROCRYPT 2005, R. Cramer (Ed.), LNCS 3494, Springer-Verlag, pp. 1-18, 2005.
40. X. Wang and H. Yu, How to Break MD5 and Other Hash Functions, Advances in Cryptology-EUROCRYPT 2005, R. Cramer (Ed.), LNCS 3494, Springer-Verlag, pp. 19-35, 2005.
41. X. Wang, Y. L. Yin and H. Yu, Finding Collisions in Full SHA-1, Advances in Cryptology-CRYPTO 2005, V. Shoup (Ed.), LNCS 3621, Springer-Verlag, pp. 17-36, 2005.
42. A. Yao, Theory-and Applications of Trapdoor Functions (Extended Abstract), FOCS 1982: 80-91.