- 1.W. B. Alexi, B. Chor, O. Goldreich and C. P. Schnorr, RSA and Rabin functions: certain parts are as hard as the whole, SIAM J. Comput., vol. 17(2), 1988, pp. 194- 209. Google ScholarDigital Library
- 2.D. Angluin, D. Lichtenstein, Provable security of cryptosystems:A survey. Tech. Rep. 288, Dept. of Computer Science, yale Univ. new Haven, Conn., 1983.Google Scholar
- 3.E. Biham, D. Boneh and O. Reingold, Breaking generalized Diffie-Hellman modulo a composite is no easier than factoring, Information Processing Letters, vol. 70, 1999, pp. 83-87. Google ScholarDigital Library
- 4.D. Boneh, The decision Diflie-Hellman problem, Proceedings of the Third Algorithmic Number Theory Symposium, Lecture Notes in Computer Science, Vol. 1423, Springer-Verlag, 1998, pp. 48-63. Google ScholarDigital Library
- 5.L. Blum, M. Blum and M. Shub, A Simple Secure Unpredictable Pseudo-Random Number Generator, SiAM J. Comput., voi. 15, 1984, pp. 364-383. Google ScholarDigital Library
- 6.M. Blum and S. Goldwasser, An Efficient Probabilistic Public-key Encryption Scheme Which Hides All Partial Information, Advances in Cryptology- CRYPTO'SJ, Lecture Notes in Computer Science, vol. 196, Springer- Verlag, 1985, pp. 289-302. Google ScholarDigital Library
- 7.M. Blum and S. Micali, How to generate cryptographically strong sequence of pseudo-random bits, SIAM J. Comput., vol. 13, 1984, pp. 850-864. Google ScholarDigital Library
- 8.G. Brassard, On computationally secure authentication tags requiring short secret shared keys, Advances of Cryptology: Proceedings of Crypto-82, D. Chaum, R.L. Rivest and A.T. Sherman, Eds. Plenum Press, New- York, 1983, pp. 79-86.Google ScholarCross Ref
- 9.R. Fischlin - Private communication.Google Scholar
- 10.R. Fischlin and C. P. Schnorr, Stronger security proofs for RSA and Rabin bits, Advances in Cryptology- EU- ROCRYPT '97, Lecture Notes in Computer Science, vol. 1233, Springer-Verlag, 1997, pp. 267-279. Google ScholarDigital Library
- 11.O. Goldreich, Foundations of Cryptography Fragments of a Book, 1995. Electronic publication: http:///www, eccc. uni-trier, de/eccc//info//ECCC- Books//eccc-books.html (Electronic Colloquium on Computational Complexity).Google Scholar
- 12.O. Goldreich, Modern cryptography, probabilistic proofs and pseudo-randomness. Algorithms and Combinatorics, vol. 17, Springer-Verlag, 1998. Google ScholarDigital Library
- 13.O. Goldreich, S. Goldwasser and S. Micali, How to construct random functions, J. of the A CM., vol. 33, 1986, pp. 792-807. Google ScholarDigital Library
- 14.O. Goldreich and L. Levin, A hard-core predicate for all one-way functions, Proc. 21st Ann. A CM Syrnp. on Theory of Computing, 1989, pp. 25-32. Google ScholarDigital Library
- 15.J. Hastad, R. Impagliazzo, L. A. Levin and M. Luby, Construction of a pseudo-random generator from any one-way function, To appear in SIAM J. Comput. Preliminary versions by Impagliazzo et. al. in ~1st STOC, 1989 and Hastad in 22nd STOC, 1990. Google ScholarDigital Library
- 16.M. Luby, Pseudo-randomness and applications, Princeton University Press, 1996. Google ScholarDigital Library
- 17.R. Motwani and P. Raghavan, Randomzied Algorithms, Cambridge Univ. Press, 1995. Google ScholarDigital Library
- 18.M. Naor and O. Reingold, Synthesizers and their application to the parallel construction of pseudo-random functions, J. of Computer and Systems Sciences, vol. 58 (2), April 1999, pp. 336-375. Google ScholarDigital Library
- 19.M. Naor and O. Reingold, Number-Theoretic constructions of efficient pseudo-random functions, Proc. 38th IEEE Syrup. on Foundations of Computer Science, 1997, pp. 458-467. Google ScholarDigital Library
- 20.M. Naor and O. Reingold, From unpredictability to indistinguishability: A simple construction of pseudorandom functions from MAC's, Advances in Cryptology . CRYPTO '98, Lecture Notes in Computer Science, vol. 1462, Springer-Verlag, 1998, pp. 267-282. Google ScholarDigital Library
- 21.A. M. Odlyzko, The ~uture of integerfactorization, RSA CyptoBytes, 2(1), 1995, pp. 5-12.Google Scholar
- 22.M. O. Rabin, Digitalized signatures and public-key functions as intractable as factorization, Technical Report, TR-212, MIT Laboratory for Computer Science, 1979. Google ScholarDigital Library
- 23.O. Reingold, Pseudo-Random Synthesizers, Functions and Permutations, PhD Thesis, Weizmann Institute of Science, 1998.Google Scholar
- 24.U.V. Vazirani and V.V. Vazirani, Efficient and Secure Pseudo-Random Number Generation, Proc. ~5th IEEE Syrup. on Foundations of CornputerScience, 1984, pp. 458-463.Google ScholarDigital Library
- 25.A. C. Yao, Theory and applications of trapdoor functions, Proc. ~3rd IEEE Syrnp. on Foundations of Computer Science, 1982, pp. 80-91.Google ScholarCross Ref
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- Pseudo-random functions and factoring (extended abstract)
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