How to construct random functions

Journal of the ACM (JACM)

Volumn 33, Issue 4, 1986, Pages 792-807

  Goldreich, Oded ^a   Goldwasser, Shafi ^a   Micali, Silvio ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER METATHEORY; COMPUTER PROGRAMMING - ALGORITHMS; CRYPTOGRAPHY;

COMPUTATIONAL COMPLEXITY; PSEUDORANDOM FUNCTION GENERATOR; RANDOM FUNCTIONS;

PROBABILITY;

EID: 0022793132     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/6490.6503     Document Type: Article

References (43)

1. ADELMAN, L. Time, Space and Randomness. Tech. Memo 131, Laboratory for Computer Science MIT, Cambridge, Mass., 1979.]
2. ALEXI, W., CHOR, B., GOLDREICH, O., AND SCHNORR, C. P. RSA and Rabin functions: Certain parts are as hard as the whole. SIAM J. Comput., to appear. (An earlier version appeared in Proceedings of the 25th IEEE Symposium on Foundations of Computer Science. IEEE, New York, 1984, pp. 449-457.)]
3. ANGLUIN, O., AND LICHTENSTEIN, D. Provable security of cryptosystems: A survey. Tech. Rep. 288, Dept. of Computer Science, Yale Univ. New Haven, Conn., 1983.]
4. BENNETT, C. H., AND GILL, J. Relative to a random oracle, A, P^ ~ NP^ ~ co-NP^ with probability I. SIAM J. Comput. I 0 ( 198 l), 96-113.]
5. BEN-OR, M., CnOR, B., AND SHAMIR, A. On the cryptographic security of single RSA bits. In Proceedings of the 15th ACM Symposium on Theory of Computing (Boston, Mass., Apr. 25-27). ACM, New~'ork, 1983, pp. 421-430.]
6. BEN-OR, M., GOLDREICH, O., MICALI, S., RIVEST, R.L. A fair protocol for signing contracts. In Automata, Languages and Programmingnd Programming, 12th Colloquium, W. Brauer, Ed. Lecture Notes in Computer Science, Vol. 194. Springer-Vedag, New York, 1985, pp. 43-52.]
7. BLUM, L., BLUM, M., and SHUB, M. A simpl~ unpredictable pseudo-random number generator. SIAM J. Comput. 15 (May 1986), 364-383.]
8. BLUM, M., AND MICALI, S. How to generate cryptographically strong sequences of pseudo-random bits. SIAM J. Comput. 13 (Nov. I984), 850-864.]
9. BRASSARD, G. On computationally secure authentication tags requiring short secret shared keys. In Advances in Cryptology: Proceedings of Crypto-82, D. Chaum, R. L. Rivest and A. T. Sherman, Eds. Plenum Press, New York, 1983, pp. 79-86.]
10. CnAITIN, G.J. On the length of programs for computing finite binary sequences. J. ACM 13, 4 (Oct. 1966), 547-570.]
11. DIFFIE, W., AND HELLMAN, M. E. New directions in cryptography. IEEE Trans. Inf. Theory IT-22 (Nov. 1976), 644-654.]
12. FREIZE, A. M., KANNAN, R., AND LAGARIAS, J.C. Linear congruential generators do not produce random sequences. In Proceedings of the 25th Symposium on Foundations of Computer Science. IEEE, New York, 1984, pp. 480-484’.]
13. GACS, P. On the symmetry of algorithmic information. Soy. Math. Dokl. 15 (1974), 1477.]
14. GOLDREICH, O., GOLDWASSER, S., AND MICALI, S. How to construct random functions. Tech. Memo 244, Laboratory for Computer Science, MIT, Cambridge, Mass., Nov. 1983.]
15. GOLDREICH, O., GOLDWASSER, S., AND MICALI, S. On the cryptographic applications of random functions. In Advances in Cryptology: Proceedings of Crypto-84. B. Blakely, Ed. Lecture Notes in Computer Science, Vol. 196. Springer-Vedag, New York, 1985, pp. 276-288.]
16. GOLDWASSER, S. Probabilistic encryption: Theory and applications. Ph.D. dissertation, Dept. of Computer Science, Univ. of California, Berkeley, Calif., 1984.]
17. GOLDWASSER, S., MICALI, S., AND RIVEST, R.L. A “paradoxical” signature scheme. In Proceedings of the 25th IEEE Symposium on Foundations of Computer Science. IEEE, New York, 1984, pp. 441-448.]
18. GOLDWASSER, A., MICALI, S., and RIVEST, R. L. A digital signature scheme secure against adaptive chosen method attack. SIAM J. Comput. to appear.]
19. GOLDWASSER, S., MICALI, S., AND TONG, P. Why and how to establish a private code on a public network. In Proceedings of the 23rd IEEE Symposium on Foundations of Computer Science. IEEE, New York, 1982, pp. 134-144.]
20. HARTMANIS, J. Generalized Kolmogorov complexity and the structure of feasible computations. In Proceedings of the 24th IEEE Symposium on Foundations of Computer Science. IEEE, New York, 1983, pp. 439-445.]
21. HASTAD, J., AND SHAMIR, A. The cryptographic security of truncated linearly related variables. In Proceedings of the 17th ACM Symposium on Theory of Computing (Providence, R.I., May 6-8). ACM, New York, 1985, pp. 356-362.]
22. KNUTn, D. The Art of Computer Programming: Seminumerical Algorithms, Vol. 2. 2nd ed. Addison-Wesley, Reading, Mass. 1981.]
23. KOLMOGOROV, A. Three approaches to the concept of “The amount of information”, Prob. Inf. Transm. I, l (1965
24. LAGARIAS, J., AND REEDS, J. Extrapolation of nonlinear recurrences. Submitted for publication.]
25. LEVIN, L.A. On the notion of a random sequence. Soy. Math. Dokl. 14, 5 (1973), 1413.]
26. LEVlN, L. A. Various measures of complexity for finite objects (axiomatic descriptions). Soy. Math. Dokl. 17, 2 (1976), 522-526.]
27. LEVIN, L.A. Randomness conservation inequalities, information and independence in mathematical theories. Inf. Control 61 (1984), 15-37.]
28. LEVIN, L.A. One-way function and pseudorandom generators. In Proceedings of the 17th ACM Symposium on Theory of Computing (Providence, R.I., May 6-8). ACM, New York, 1985, pp. 363-365.]
29. LONG, D. L., AND WIGDERSON, A. How discreet is discrete log? In preparation. A preliminary version appeared in Proceedings of the 15th ACM Symposium on Theory of Computing (Boston, Mass., Apr. 25-27). ACM, New York, 1983, pp. 413-420.]
30. Luav, M., AND RACKOFF, C. Pseudo random permutation generators and cryptographic composition. In Proceedings of the 18th ACM Symposium on Theory of Computing (Berkeley, Calif., May 28-30). ACM, New York, 1986, pp. 356-363.]
31. MARTIN-LOF, P. The definition of random sequences. Inf. Control 9 (1966), 602-619.]
32. PLUMSTEAD, J. Inferring a sequence generated by a linear congruence. In Proceedings of the 23rd IEEE Symposium on Foundations of Computer Science. IEEE, New York, 1982, pp. 153-159.]
33. RABIN, M.O. Digitalized signatures and public key functions as intractable as factoring. Tech. Rep. 212, Laboratory for Computer Science, Cambridge, Mass., 1979.]
34. RIVEST, R., SHAMIR, A., and ADLEMAN, L. A method for obtaining digital signatures and public key cryptosystems. Commun. ACM, 21, 2 (Feb. 1978), 120-126.]
35. SCHNORR, C.P. Zufaelligkeit und Wahrscheinlichkeit. Lecture Notes in Mathematics, Vol. 218. Springer-Verlag, New York, 197 i.]
36. SHAMIR, A. On the generation of cryptographically strong pseudorandom sequences. ACM Trans. Comput. Syst. 1, l (Feb. 1983), 38-44.]
37. SIr'SER, M. A complexity theoretic approach to randomness, in Proceedings of the 15th ACM Symposium on Theory of Computing (Boston, Mass., Apr. 25-27). ACM, New York, 1983, 330-335.]
38. SOLOMONOFF, R.J. A formal theory of inductive inference. Inf. Control, 7, l (1964), 1-22.]
39. WILBER, R.E. Randomness and the density of hard problems. In Proceedings of 24th IEEE Symposium on Foundations of Computer Science. IEEE, New York, 1983, pp. 335-342.]
40. VAZIRANI, U. V., and VAZIRANI, V.V. RSA bits are.732 + ~ secure, tn Advances in Cryptology: Proceedings ofCrypto-83, D. Chaum, Ed. Plenum Press, New York, 1984, pp. 369-375.]
41. VAZIRANI, U. V., AND VAZIRANI, V.V. Efficient and secure pseudo-random number generation. In Proceedings of the 25th IEEE Symposium on Foundations of Computer Science. IEEE, New York, 1984, pp. 458-463.]
42. YAO, A.C. Theory and applications of trapdoor functions. In Proceedings of the 23rd IEEE Symposium on Foundations of Computer Science. IEEE, New York, 1982, pp 80-9 I.]
43. ZVONKIN, A. K., AND LEVIN, L.A. The complexity of finite objects and the algorithmic concepts of randomness and information. UMN (Russian Math. Surveys), 25, 6 (1970), 83-124.]