By Pascal Paillier, Damien Vergnaud (auth.), Bimal Roy (eds.)
This ebook constitutes the refereed court cases of the eleventh overseas convention at the conception and alertness of Cryptology and knowledge defense, ASIACRYPT 2005, held in Chennai, India in December 2005.
The 37 revised complete papers awarded have been rigorously reviewed and chosen from 237 submissions. The papers are geared up in topical sections on algebra and quantity thought, multiparty computation, 0 wisdom and mystery sharing, info and quantum conception, privateness and anonymity, cryptanalytic options, move cipher cryptanalysis, block ciphers and hash capabilities, bilinear maps, key contract, provable safeguard, and electronic signatures.
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Additional info for Advances in Cryptology - ASIACRYPT 2005: 11th International Conference on the Theory and Application of Cryptology and Information Security, Chennai, India, December 4-8, 2005. Proceedings
Pointcheval, and M. Semanko, The One-MoreRSA-Inversion Problems and the security of Chaum’s Blind Signature Scheme. J. Cryptology 16 (2003), no. 3, 185–215. 20 P. Paillier and D. Vergnaud 4. M. Bellare and A. Palacio, GQ and Schnorr Identiﬁcation Schemes: Proofs of Security against Impersonation under Active and Concurrent Attacks. Advances in Cryptology - Crypto 2002, LNCS vol. 2442, Springer, 2002, pp. 162–177. 5. D. Boneh and R. Venkatesan, Breaking RSA may not be equivalent to factoring. Advances in Cryptology - Eurocrypt 1998, LNCS vol.
There are only ﬁnitely many levels for q less than any given bound, so it suﬃces to prove the theorem for q large and p(x) = x2+δ , where δ > 0 is ﬁxed. 4). Recall that |D| ≤ 4q and λtriv ∼ e log m . 1 is λχ = O(λβtriv ) 1 for any β > 12 + δ+2 . 1. 2). The Theorem shows that a random walk from any ﬁxed curve E probabilistically reaches the proportion where the algorithm A succeeds, in at most polylog(q) steps. Since each step is a low degree isogeny, their composition can be computed in polylog(q) steps.
This claim follows using the smallness of diameter of our graphs and the smoothness of the degrees of isogenies involved. We omit the details. 24 D. D. Miller, and R. Venkatesan Curve NIST P-192 NIST P-256 NIST P-384 NIST P-521 NIST K-163 NIST K-233 NIST K-283 NIST K-409 NIST K-571 NIST B-163 NIST B-233 NIST B-283 NIST B-409 NIST B-571 IPSec 3rd OG,F 155 2 IPSec 4th OG, F 185 2 (maximal conductor gap in isogeny class) P(cπ ) = largest prime factor of cπ 1 1 3 3 1 1 1 1 45641·82153·56498081·P (cπ ) 86110311 5610641·85310626991·P (cπ ) 150532234816721999 1697·162254089·P (cπ ) 1779143207551652584836995286271 21262439877311·22431439539154506863·P (cπ ) 57030553306655053533734286593 9021184135396238924389891(contd) 3952463·P (cπ ) 9451926768145189936450898(contd) 07769277009849103733654828039 1 1 1 1 1 1 1 1 1 1 cπ 1 1 1 1 Fig.
Advances in Cryptology - ASIACRYPT 2005: 11th International Conference on the Theory and Application of Cryptology and Information Security, Chennai, India, December 4-8, 2005. Proceedings by Pascal Paillier, Damien Vergnaud (auth.), Bimal Roy (eds.)