Advances in Cryptology — ASIACRYPT 2001: 7th International by Craig Gentry, Jakob Jonsson, Jacques Stern, Michael Szydlo

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

The origins of the Asiacrypt sequence of meetings will be traced again to 1990, while the ?rst Auscrypt convention used to be held, even if the identify Asiacrypt was once ?rst used for the 1991 convention in Japan. beginning with Asiacrypt 2000, the convention is now considered one of 3 annual meetings prepared through the Inter- tional organization for Cryptologic examine (IACR). the ongoing luck of Asiacrypt is in no small half because 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 authorized or no longer, made a valued contribution to the good fortune of the convention. Sending out rejection noti?cations to such a lot of tough operating authors is without doubt one of the such a lot disagreeable initiatives of this system Chair. The assessment approach lasted a few 10 weeks and consisted of an preliminary refe- eing section via an intensive dialogue interval. My heartfelt thank you visit all individuals of this system Committee who installed severe quantities of time to offer their professional research and reviews at the submissions. All papers have been reviewed through no less than 3 committee contributors; in lots of instances, relatively for these papers submitted through committee contributors, extra reports have been obt- ned. professional stories have been supplied through a military of exterior reviewers with out whom our judgements might were even more di?cult.

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Extra resources 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

Sample text

Halevi, and N. Howgrave-Graham at most nd (d + 1)r · d. ) Recall that the determinant of our lattice is roughly 2m·weight(relations)−(m−k)·weight(terms) . To get the determinant above 1, we therefore must have m· n n (d + 1)r d > (m − k) · (d + 1)r d(1 + r/2) d d which means that m > (m − k)(1 + r/2), or k/m > r/(r + 2). 4 Cryptographic Applications The apparent intractability of MIHNP, suggests that it may be useful as the basis for cryptographic applications. Indeed, we show below how to use the decisionMIHNP assumption and the computational-MIHNP assumptions, respectively, to get an efficient pseudorandom generator and a MAC.

N+r . , id , the terms that we get are exactly all the terms in the expression ( i1 · i2 ··· id ) · (1 + n+1 + ··· + d n+1 ) · · · (1 + n+r + ··· + d n+r ) This means that for this choice of ij ’s, we have (d + 1)r terms, and the weight of these terms vary between d and d + rd. The total weight of all these terms is d d d ... k1 =0 k2 =0 (d + k1 + k2 + . . kr ) = (d + 1)r · (d + rd/2) kr =0 Therefore, we have nd (d + 1)r terms, of total weight nd (d + 1)r · d(1 + r/2). On the other hand, we cannot have more relations than terms, and the weight of a relation cannot be more than d, so the total weight of the relations is 2 Clearly, this is not the only way to eliminate the unbounded variables.

Xn , r1 , . . , rn are chosen uniformly at random in Zp . The δDMIHNP assumption states that no polynomial time algorithm can distinguish these two ensembles with non-negligible advantage whenever k < δm. As before, we cannot reduce this problem to either of the previous problems, but we know of no algorithms for D-MIHNP, other than first finding the hidden element α. In a sense, it seems that the tools that we have for designing algorithms for these problems are too crude to distinguish between these variants.

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