Read e-book online Advances in Cryptology — ASIACRYPT 2000: 6th International PDF

By Alex Biryukov, Adi Shamir (auth.), Tatsuaki Okamoto (eds.)

ISBN-10: 3540414045

ISBN-13: 9783540414049

ASIACRYPT 2000 used to be the 6th annual ASIACRYPT convention. It was once sp- sored by way of the foreign organization for Cryptologic learn (IACR) in - operation with the Institute of Electronics, info, and communique Engineers (IEICE). The ?rst convention with the identify ASIACRYPT came about in 1991, and the sequence of ASIACRYPT meetings have been held in 1994, 1996, 1998, and 1999, in cooperation with IACR. ASIACRYPT 2000 used to be the ?rst convention within the sequence to be subsidized by way of IACR. The convention bought one hundred forty submissions (1 submission was once withdrawn by means of the authors later), and this system committee chosen forty five of those for presen- tion. prolonged abstracts of the revised types of those papers are incorporated in those complaints. this system additionally integrated invited lectures via Thomas Berson (Cryptography in every single place: IACR special Lecture) and Hideki Imai (CRYPTREC undertaking – Cryptographic assessment venture for the japanese digital Government). Abstracts of those talks are incorporated in those proce- ings. The convention application additionally integrated its conventional “rump consultation” of brief, casual or impromptu displays, kindly chaired by way of Moti Yung. these p- sentations aren't re?ected in those complaints. the choice of this system used to be a not easy job as many top of the range submissions have been got. this system committee labored very demanding to guage the papers with admire to caliber, originality, and relevance to cryptography. i'm tremendous thankful to this system committee contributors for his or her en- mous funding of time and e?ort within the di?cult and mild technique of overview and selection.

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North-Holland, 1987. 7. N. Howgrave-Graham. Finding small roots of univariate modular equations revisited. In Cryptography and Coding, volume 1355 of LNCS, pages 131–142. SpringerVerlag, 1997. 8. C. S. Jutla. On finding small solutions of modular multivariate polynomial equations. In Proc. of Eurocrypt ’98, volume 1403 of LNCS, pages 158–170. IACR, Springer-Verlag, 1998. 9. A. K. Lenstra, H. W. , and L. Lov´ asz. Factoring polynomials with rational coefficients. , 261:513–534, 1982. 10. Waterloo Maple.

A choice of parameters suggested by the authors is: p is a 256-bit prime, q is a 768-bit prime, e is an 880-bit number, and d is a 256-bit number. 4 The Attack Algorithm In this section we demonstrate how to launch an attack on Schemes (I) and (III). The approach used here closely follows that taken by Boneh and Durfee [3], but differs in several crucial ways to allow it to work when the factors p and q of the public modulus N are unbalanced. Interestingly, our attack gets better (works for larger and larger d) the more unbalanced the factors of the modulus become.

Example of the lattice formed by the vectors gk,i,b (xX, yY, zZ) and hk,j (xX, yY, zZ) when m = 2, t = 1, and a = 1. The matrix is lower triangular. Entries marked with “–” indicate off-diagonal quantities whose values do not affect the determinant calculation. The polynomials used are listed on the left, and the monomials they introduce are listed across the top. The double line break occurs between the gk,i,b and the hk,j , while the single line breaks occur between increments of k. The last single line break separates the helper polynomials (top) from the two primary polynomials (bottom).

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Advances in Cryptology — ASIACRYPT 2000: 6th International Conference on the Theory and Application of Cryptology and Information Security Kyoto, Japan, December 3–7, 2000 Proceedings by Alex Biryukov, Adi Shamir (auth.), Tatsuaki Okamoto (eds.)


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