Advances in Cryptology — ASIACRYPT’98: International by Arjen K. Lenstra (auth.), Kazuo Ohta, Dingyi Pei (eds.)

By Arjen K. Lenstra (auth.), Kazuo Ohta, Dingyi Pei (eds.)

ASIACRYPT’98, the overseas convention masking all facets of thought and alertness of cryptology and data safeguard, is being held at Beijing Friendship resort from October 18 to 22. this is often the fourth of the Asiacrypt meetings. ASIACRYPT’98 is subsidized by means of the country Key Laboratory of knowledge protection (SKLOIS), college of technological know-how and know-how of China (USTC), and the Asiacrypt guidance Committee (ASC), in cooperation with the overseas organization for Cryptology learn (IACR). The 16-member software Committee prepared the clinical software and regarded 118 submissions. of those, 32 have been authorised for presentation. The authors’ affiliations of the 118 submissions and the 32 approved papers diversity over 18 and thirteen nations or areas, respectively. The submitted model of every paper used to be despatched to all contributors of this system Committee and was once commonly tested by way of not less than 3 committee individuals and/or open air specialists. The evaluate strategy was once carefully blinded and the anonymity of every submission are maintained until eventually the choice was once accomplished. We the conventional coverage that every member of this system Committee should be an writer of at such a lot one permitted paper. those lawsuits include the revised types of the 32 contributed talks in addition to a brief be aware written via one invited speaker. reviews from this system Committee have been taken into consideration within the revisions. although, the authors (not the committee) undergo complete accountability for the contents in their papers.

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Extra info for Advances in Cryptology — ASIACRYPT’98: International Conference on the Theory and Application of Cryptology and Information Security Beijing, China, October 18–22, 1998 Proceedings

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Notice, however, that the greatest common divisor of the coefficients of the polynomial f (x, y) is r, so to use Theorem 3, we must divide through by r to get a new polynomial g(x, y) = f (x, y)/r. Now notice that the largest coefficient of g˜(x, y) = g(Xx, Y y) is at least 2n+2 /r. So, to use Theorem 3 we require XY = r−2 2n+2 < (2n+2 /r)2/3 , which is satisfied whenever r > 2(n+2)/4 . By doing exhaustive search on the first two bits of x0 and y0 this can be reduced to r ≥ 2n/4 . 3 Partial Key Exposure Attack on Low-exponent RSA In this section we consider attacks on the RSA cryptosystem with a “small” exponent e.

To solve the equation A2 = B when B ∈ Mn (K), two methods can be used: The first one is based on the Jordan reduction of matrices, and provides a polynomial time algorithm to compute the square roots of a given matrix. For details, see [3] (chapter VIII, p. 231). The second one is based on the Cayley-Hamilton theorem. Let us denote by χM (λ) = λn + αn−1 (M )λn−1 + ... + α1 (M )λ + α0 (M ) the characteristic polynomial of a matrix M ∈ Mn (K). Since K is a field of 2 characteristic 2, it is easy to prove that αi (M 2 ) = αi (M ) (0 ≤ i ≤ n − 1).

2t+1 ] with 0 ≤ t ≤ n2 . The factorization of e is unknown. The following result establishes that we can still find all of d, given some of its msb’s. Our attack works as long as k is not significantly smaller than e. At the end of the section we note that the attack heuristically works for almost all e in the range [2t , 2t+1 ]. Theorem 8. 2, let t be an integer in the range [0 . . n/2]. Suppose e is in the range [2t . . 2t+1 ]. Further suppose k > · e for some > 0. Then there is an algorithm that given the n − t most significant bits of d finds all of d.

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