By Craig Gentry, Jakob Jonsson, Jacques Stern, Michael Szydlo (auth.), Colin Boyd (eds.)
The origins of the Asiacrypt sequence of meetings could be traced again to 1990, while the ?rst Auscrypt convention was once held, even supposing the identify Asiacrypt was once ?rst used for the 1991 convention in Japan. beginning with Asiacrypt 2000, the convention is now certainly one of 3 annual meetings prepared through the Inter- tional organization for Cryptologic learn (IACR). the ongoing good fortune of Asiacrypt is in no small half end result of the e?orts of the Asiacrypt guidance C- mittee (ASC) and the robust help of the IACR Board of administrators. there have been 153 papers submitted to Asiacrypt 2001 and 33 of those have been permitted for inclusion in those court cases. The authors of each paper, even if accredited or now not, 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 without doubt one of the such a lot disagreeable initiatives of this system Chair. The overview technique lasted a few 10 weeks and consisted of an preliminary refe- eing part by means of an in depth dialogue interval. My heartfelt thank you visit all participants of this system Committee who installed severe quantities of time to offer their professional research and critiques at the submissions. All papers have been reviewed by means of not less than 3 committee participants; in lots of instances, quite for these papers submitted via committee participants, extra reports have been obt- ned. professional stories have been supplied by means of a military of exterior reviewers with out whom our judgements could were even more di?cult.
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Asiacrypt’99 used to be held in Singapore on 14-18 November 1999. Asiacrypt is among the significant occasions within the cryptology examine group. Asiacrypt’99, the ? fth annual Asiacrypt convention, was once backed by means of the Asiacrypt guidance Comm- tee and the Centre for structures defense of the nationwide college of Singapore, and in cooperation with the overseas organization for Cryptology learn.
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Additional 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
1592, SpringerVerlag, Berlin, 1999, 1–11. 4. E. M. S. McCurley, and D. Wilson, ‘Fast exponentiation with precomputation’, Proc. Eurocrypt ’92, Lect. Notes in Comp. , Vol. 658, Springer-Verlag, Berlin, 1993, 200–207. 5. J. Coster, A. A. M. -P. Schnorr, and J. Stern, ‘Improved low-density subset sum algorithms’, Comput. Complexity, 2 (1992), 111–128. 6. D. M. Gordon, ‘A survey of fast exponentiation methods’, J. of Algorithms, 27 (1998), 129–146. 7. A. K. Lenstra, H. W. Lenstra and L. Lov´ asz, ‘Factoring polynomials with rational coeﬃcients’, Mathematische Annalen, 261 (1982), 515–534.
Suppose there is an algorithm A that solves the Basic-MIHNP problem with probability , where the probability is taken over the choice of the xi ’s and also over the choice of α. We show that this implies an algorithm B for solving Basic-MIHNP that works for any ﬁxed α with probability , where this time the probability is over the choice of the xi ’s only. Given an instance of Basic-MIHNP, xi , yi , i = 1, . . , n, algorithm B picks a random r ∈ Zp , and runs algorithm A on the Basic-MIHNP problem deﬁned by the tuples xi + r, yi , i = 1, .
First for f1 , f2 ∈ Bk, ,m we estimate the size of the set E (f1 , f2 ) of pairs of m 2m vectors d1 , d2 ∈ [ϕ(N )] such that for some u = (u1 , u2 ) ∈ [U ]± which is not similar to (f1 , f2 ) we have the equation m 2m ui di = i=1 ui di . (6) i=m+1 2m Let us ﬁx a nonzero vector u = (u1 , u2 ) ∈ [U ]± and a vector (f1 , f2 ) ∈ Bk, ,m which are not similar. Without loss of generality we may assume that u2 = 0 and is not parallel to f2 and that f2m = 0. Then excluding d2m from (6) using (3), we obtain an equation m 2m−1 ci di = i=1 ci di (7) i=m+1 with ci = ui − fi u2m /f2m , i = 1, .
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 by Craig Gentry, Jakob Jonsson, Jacques Stern, Michael Szydlo (auth.), Colin Boyd (eds.)