Download Advances in Cryptology — ASIACRYPT 2000: 6th International by Alex Biryukov, Adi Shamir (auth.), Tatsuaki Okamoto (eds.) PDF

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

ASIACRYPT 2000 was once the 6th annual ASIACRYPT convention. It used to be sp- sored through the overseas organization for Cryptologic study (IACR) in - operation with the Institute of Electronics, info, and conversation 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 through IACR. The convention got one hundred forty submissions (1 submission used to be withdrawn by way of the authors later), and this system committee chosen forty five of those for presen- tion.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 incorporated invited lectures by way of Thomas Berson (Cryptography all over: IACR unusual Lecture) and Hideki Imai (CRYPTREC undertaking – Cryptographic overview venture for the japanese digital Government). Abstracts of those talks are integrated in those proce- ings. The convention application additionally integrated its conventional “rump consultation” of brief, casual or impromptu shows, kindly chaired via Moti Yung. these p- sentations usually are not re?ected in those court cases. the choice of this system used to be a not easy job as many prime quality submissions have been bought. this system committee labored very difficult to guage the papers with appreciate to caliber, originality, and relevance to cryptography. i'm super thankful to this system committee participants for his or her en- mous funding of time and e?ort within the di?cult and gentle means of overview and selection.

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Read or Download 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 PDF

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Additional resources for 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

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K p − d + 1. log N − 2. 4α(2β +α−1) 3(1−β −α)2 , where α = log N2 + k −p d and β = log N +k k − d . 2 2 3. k must withstand an exhaustive search and k + p > 13 log2 N . 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.

For illustration purposes, when m = 64 we obtain the following results: – For any RSA public key N, e , given C = M e mod N it is possible to recover M in the time it takes to compute 2 · 2m/2 modular exponentiations. The attack succeeds with probability 18% (the probability is over the choice of M ∈ {0, 1, . . , 2m − 1}). The algorithm requires 2m/2 m bits of memory. – Let p, g, y be an ElGamal public key. When the order of g is at most p/2m , it is possible to recover M from any ElGamal ciphertext of M in the time it takes to compute 2 · 2m/2 modular exponentiations.

One then sees that the bivariate approach constrains the choice of primary and helper polynomials in a suboptimal way, resulting in worse bounds on d. 5 Implementation We implemented this attack using Victor Shoup’s Number Theory Library [16] and the Maple Analytical Computation System [10]. The attack runs very efficiently, and in all instances of Schemes (I) and (III) we tested, it produced 26 Glenn Durfee and Phong Q. Nguyen algebraically independent polynomials H1 (x, y) and H2 (x, y). These yielded a resultant H(y) = (y − p)H0 (y), where H0 (y) is irreducible, exposing the factor p of N in every instance.

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