An improved pseudo-random generator based on discrete log

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

Volumn 1880, Issue , 2000, Pages 469-481

  Gennaro, Rosario ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

NUMBER THEORY;

BIT NUMBERS; DISCRETE LOGARITHM PROBLEMS; EXPONENTIATIONS; MODULAR MULTIPLICATION; PRE-COMPUTATION; PSEUDO RANDOM; PSEUDO RANDOM BIT GENERATORS; PSEUDORANDOM GENERATORS;

CRYPTOGRAPHY;

EID: 84974622962     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44598-6_29     Document Type: Conference Paper

References (20)

1. L. Adleman. A Subexponential Algorithm for the Discrete Logarithm Problem with Applications to Cryptography. IEEE FOCS, pp.55-60, 1979.
2. W. Alexi, B. Chor, O. Goldreich and C. Schnorr. RSA and Rabin Functions: Certain Parts are as Hard as the Whole. SIAM J. Computing, 17(2):194-209, April 1988.
3. L. Blum, M. Blum and M. Shub. A Simple Unpredictable Pseudo-Random Number Generator. SIAM J.Computing, 15(2):364-383, May 1986.
4. M. Blum and S. Micali. How to Generate Cryptographically Strong Sequences of Pseudo-Random Bits. SIAM J.Computing, 13(4):850-864, November 1984.
5. W. Diffie and M. Hellman. New Directions in Cryptography. IEEE Trans. Inf. Theory, IT-22:644-654, November 1976.
6. R. Fischlin and C. Schnorr. Stronger Security Proofs for RSA and Rabin Bits. J.Crypt., 13(2):221-244, Spring 2000.
7. S. Goldwasser and S. Micali. Probabilistic Encryption. JCSS, 28:270-299, 1988.
8. J. Håstad, R. Impagliazzo, L. Levin and M. Luby. A Pseudo-Random Generator from any One-Way Function. SIAM J.Computing, 28(4):1364-1396, 1999.
9. J. Håstad and M. Näslund. The Security of Individual RSA Bits. IEEE FOCS, pp.510-519, 1998.
10. J. Håstad, A. Schrift and A. Shamir. The Discrete Logarithm Modulo a Composite Hides O(n) Bits. JCSS, 47:376-404, 1993.
11. R. Impagliazzo and M. Naor. Efficient Cryptographic Schemes Provably as Secure as Subset Sum. J.Crypt., 9(4):199-216, 1996.
12. D. Knuth. The Art of Computer Programming (vol.3): Sorting and Searching. Addison-Wesley, 1973.
13. C.H. Lim and P.J. Lee. More Flexible Exponentiation with Precomputation. CRYPTO’94, LNCS 839, pp.95-107.
14. D. Long and A. Wigderson. The Discrete Log Hides O(log n) Bits. SIAM J.Computing, 17:363-372, 1988.
15. M. Naor and O. Reingold. Number-Theoretic Constructions of Efficient Pseudo-Random Functions. IEEE FOCS, pp.458-467, 1997.
16. S. Patel and G. Sundaram. An Efficient Discrete Log Pseudo Random Generator. CRYPTO’98, LNCS 1462, pp.304-317, 1998.
17. R. Peralta. Simultaneous Security of Bits in the Discrete Log. EUROCRYPT’85, LNCS 219, pp.62-72, 1986.
18. J. Pollard. Monte-Carlo Methods for Index Computation (mod p). Mathematics of Computation, 32(143):918-924, 1978.
19. C. Schnorr Security of Allmost ALL Discrete Log Bits. Electronic Colloquium on Computational Complexity. Report TR98-033. Available at http://www.eccc.uni-trier.de/eccc/.
20. A. Yao. Theory and Applications of Trapdoor Functions. IEEE FOCS, 1982.