Abstract
In this paper we show that for any one-way function f, being able to determine any single bit in ax + b mod p for a random Ω(|x|)-bit prime p and random a, b with probability only slightly better than 50% is equivalent to inverting f(x).
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References
W. Alexi, B. Chor, O. Goldreich and C. P. Schnorr: RSA and Rabin Functions: Certain Parts Are as Hard as the Whole. SIAM J. on Computing vol 17, no 2 1988, pp. 194–209.
L. Blum, M. Blum and M. Shub: A simple Unpredictable Pseudo-random Number Generator. SIAM J. on Computing vol 15, no 2 1986, pp. 364–383.
M. Blum and S. Micali: How to Generate Cryptographically Strong Sequences of Pseudo-random Bits. SIAM J. on Computing vol 13, no 4 1986 pp. 850–864.
O. Goldreich and L. A. Levin: A Hard Core Predicate for any One Way Function. STOC 1989, pp. 25–32.
S. Goldwasser and S. Micali: Probabilistic Encryption. JCSS vol 28, no 2, 1984, pp. 270–299.
J. Håstad, A. W. Schrift and A. Shamir: The Discrete Logarithm Modulo a Composite Hides O(n) Bits. JCSS 47 1993, pp. 376–403.
L. Kuipers and H. Niederreiter: Uniform Distribution of Sequences. John Wiley & Sons 1974, ISBN 0-471-51045-9.
D. L. Long and A. Wigderson: The Discrete Log hides O(logn) bits. SIAM J. on Computing vol 17, no 2 1988 pp. 413–420.
A. W. Schrift and A. Shamir: On the Universality of the Next Bit Test. Proceedings Crypto 1990, LNCS 537, pp. 394–408, Springer Verlag.
M. Näslund: Universal Hash Functions & Hard Core Bits. Proceedings Eurocrypt 1995, LNCS 921, pp. 356–366, Springer Verlag.
U. V. Vazirani and V. V. Vazirani: Efficient and Secure Pseudo-Random Number Generation. Proceedings FOCS 1984, pp. 458–463.
A. C. Yao: Theory and Applications of Trapdoor Functions. Proceedings FOCS 1982, pp. 80–91.
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© 1996 Springer-Verlag Berlin Heidelberg
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Näslund, M. (1996). All Bits in ax + b mod p are Hard. In: Koblitz, N. (eds) Advances in Cryptology — CRYPTO ’96. CRYPTO 1996. Lecture Notes in Computer Science, vol 1109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68697-5_10
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DOI: https://doi.org/10.1007/3-540-68697-5_10
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