By Craig Gentry, Jakob Jonsson, Jacques Stern, Michael Szydlo (auth.), Colin Boyd (eds.)

The origins of the Asiacrypt sequence of meetings should be traced again to 1990, while the ?rst Auscrypt convention used to be held, even supposing the identify Asiacrypt was once ?rst used for the 1991 convention in Japan. beginning with Asiacrypt 2000, the convention is now one in every of 3 annual meetings geared up by means of the Inter- tional organization for Cryptologic study (IACR). the continued good fortune of Asiacrypt is in no small half end result of the e?orts of the Asiacrypt guidance C- mittee (ASC) and the powerful aid of the IACR Board of administrators. there have been 153 papers submitted to Asiacrypt 2001 and 33 of those have been approved for inclusion in those complaints. The authors of each paper, no matter if approved or no longer, made a valued contribution to the good fortune of the convention. Sending out rejection noti?cations to such a lot of challenging operating authors is likely one of the such a lot disagreeable initiatives of this system Chair. The evaluation strategy lasted a few 10 weeks and consisted of an preliminary refe- eing section by way of an in depth dialogue interval. My heartfelt thank you visit all individuals of this system Committee who installed severe quantities of time to offer their specialist research and critiques at the submissions. All papers have been reviewed through not less than 3 committee contributors; in lots of circumstances, relatively for these papers submitted via committee contributors, extra reports have been obt- ned. professional stories have been supplied via a military of exterior reviewers with no whom our judgements may were even more di?cult.

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**Extra info for Advances in Cryptology — ASIACRYPT 2001: 7th International Conference on the Theory and Application of Cryptology and Information Security Gold Coast, Australia, December 9–13, 2001 Proceedings**

**Example text**

Dm−1 ∈ [ϕ(N )] arbitrarily, we obtain a congruence of the form fm dm ≡ D (mod ϕ(N )) which has at most gcd(fm , ϕ(N )) ≤ fm < 2 solutions dm ∈ [ϕ(N )]. Finally, for any of ϕ(N )m−2 possible choices of dm+1 , . . , d2m−2 ∈ m−2 the equation (7) gives at most one value for dm−1 and then the second [ϕ(N )] congruence in (4) gives us at most gcd(f2m , ϕ(N )) ≤ f2m < 2 possible values for d2m . So the total number of solutions for such u is at most 22 ϕ(N )2m−3 . The total number of such vectors is at most U 2m .

One point worth mentioning is the re-keying of the generator from the previous output. It is well known, see [3], that it is secure to do this, if the underlying generator is itself secure. , xn once at the start of the whole procedure, and then use just the msbk (1/(a + xi )) part of the output to re-key a and form the output bits of the PRNG. The Modular Inversion Hidden Number Problem 47 Parameters and performance. The parameters m (the size of the prime p) and k (the number of bits to output from each 1/(a + xi )) must be chosen such that solving the MIHNP with k output bits modulo a prime of size |p| = m is infeasible.

L. Blum, M. Blum, M. Shub, “A simple unpredictable pseudo-random number generator”, SIAM J. Comput. 15, 2 (1986) 364–383. 3. M. Blum and S. Micali. How to Generate Cryptographically Strong Sequences of Pseudo-Random Bits. Computing, 13(4):850–864, November 1984. 4. D. , “Hardness of Computing the Most Signiﬁcant Bits of Secret Keys in Diﬃe-Hellman and Related Schemes”, Proc. of Crypto, 1996, pp. 129–142, 1996. 5. D. Boneh, I. Shparlinksi, “On the unpredictability of bits of the elliptic curve Diﬃe–Hellman scheme”, In Advances in Cryptology – CRYPTO 2001, volume 2139 of Lecture Notes in Computer Science, pp.