Advances in Cryptology - ASIACRYPT 2005: 11th International by Pascal Paillier, Damien Vergnaud (auth.), Bimal Roy (eds.)

By Pascal Paillier, Damien Vergnaud (auth.), Bimal Roy (eds.)

This ebook constitutes the refereed court cases of the eleventh overseas convention at the thought and alertness of Cryptology and knowledge defense, ASIACRYPT 2005, held in Chennai, India in December 2005.

The 37 revised complete papers offered have been rigorously reviewed and chosen from 237 submissions. The papers are prepared in topical sections on algebra and quantity thought, multiparty computation, 0 wisdom and mystery sharing, info and quantum conception, privateness and anonymity, cryptanalytic concepts, flow cipher cryptanalysis, block ciphers and hash features, bilinear maps, key contract, provable defense, and electronic signatures.

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Extra 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

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Let E be an ordinary elliptic curve over Fq , with endomorphism ring End(E) of discriminant D. Let be a prime different from the characteristic of Fq . – Assume cE . Then there are exactly 1+ D horizontal isogenies φ : E → E of degree . • If cπ , there are no other isogenies E → E of degree over Fq . • If | cπ , there are − D down isogenies of degree . – Assume | cE . Then there is one up isogeny E → E of degree . • If • If | cπ cE , cπ cE , there are no other isogenies E → E of degree there are down isogenies of degree .

C) [OK : End(E)] = [OK : End(E )]. (d) [End(E) : Z[π]] = [End(E ) : Z[π]]. 4. Let φ : E → E be an isogeny from E to E of prime degree , defined over Fq . Then either End(E) contains End(E ) or End(E ) contains End(E), and the index of the smaller in the larger divides . 26 D. D. Miller, and R. Venkatesan 5. Suppose is a prime that divides one of [OK : End(E)] and [OK : End(E )], but not the other. Then every isogeny φ : E → E defined over Fq has degree equal to a multiple of . Proof. 2]. For any order O ⊆ OK , the conductor of O is defined to be the integer [OK : O].

L. Brown, Generic Groups, Collision Resistance and ECDSA, Des. Codes Cryptography 35 (2005), 119–152. 8. R. Canetti, O. Goldreich, and S. Halevi, The Random Oracle Methodology, Revisited. J. Assoc. Comput. Mach. 51 (2004), no. 4, 557–594. 9. FIPS 186. Digital Signature Standard, Federal Information Processing Standards Publication 186. US Department of Commerce/NIST, National Technical Information Service, Springfield, Virginia, 1994. 10. A. Dent, Adapting the weaknesses of the random oracle model to the generic model.

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