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 foreign convention overlaying all facets of conception and alertness of cryptology and data protection, is being held at Beijing Friendship inn from October 18 to 22. this can be the fourth of the Asiacrypt meetings. ASIACRYPT’98 is subsidized by way of the kingdom Key Laboratory of knowledge protection (SKLOIS), college of technological know-how and know-how of China (USTC), and the Asiacrypt steerage Committee (ASC), in cooperation with the overseas organization for Cryptology examine (IACR). The 16-member software Committee prepared the clinical application and thought of 118 submissions. of those, 32 have been approved for presentation. The authors’ affiliations of the 118 submissions and the 32 permitted papers diversity over 18 and thirteen international locations or areas, respectively. The submitted model of every paper was once despatched to all participants of this system Committee and used to be largely tested via no less than 3 committee contributors and/or open air specialists. The overview procedure was once conscientiously blinded and the anonymity of every submission are maintained until eventually the choice was once accomplished. We the normal coverage that every member of this system Committee will be an writer of at such a lot one authorised paper. those court cases comprise the revised models of the 32 contributed talks in addition to a brief be aware written by way of one invited speaker. reviews from this system Committee have been taken into consideration within the revisions. even if, the authors (not the committee) endure 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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Therefore, the question of the security of HM remains open... 14 Conclusion Among cryptologists that have studied the problem, two main opinions arise as concerns public key schemes built with multivariate polynomials. Some of them think that most of these schemes should be vulnerable to attacks based on general principles, still to be found. According to others, the status of those many schemes can be compared to the one of most secret key algorithms: no relative proof of security is known, but the great flexibility for the choice among the possible variants of the schemes, together with the relative easiness for building efficient schemes that avoid known attacks, may support a certain confidence in the security of the schemes, at least – a priori – for those which do not seem too close to known cryptanalytic techniques.

One may wonder whether a similar partial key exposure attack is possible using the most significant bits of d. The answer is no. The reason is that low public exponent rsa leaks half the most significant bits of d. In other words, the adversary may obtain half the most significant bits of d from e and N alone. Consequently, revealing the most significant bits of d does not help the adversary in exposing the rest of d. This is stated more precisely in the following fact. Fact 5. 2, suppose there exists an algorithm A that given the n/2 msb bits of d discovers all of d in time t(n).

For our purposes, “small” implies that exhaustive search on all values less than e is feasible. In particular, since k ≤ e holds, our attack algorithm can try all possible values of k (recall that k is the unique integer satisfying de − kφ(N ) = 1). We can now prove Theorem 1. Theorem 4. 2, given the bits of d, we can factor N in polynomial time in n and e. n 4 least significant An Attack on RSA Given a Small Fraction of the Private Key Bits Proof. Suppose we are given the least-significant know d0 = d mod 2n/4 .

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