By Pascal Paillier, Damien Vergnaud (auth.), Bimal Roy (eds.)
This e-book constitutes the refereed complaints of the eleventh foreign convention at the idea and alertness of Cryptology and knowledge safeguard, 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, details and quantum concept, privateness and anonymity, cryptanalytic innovations, circulate cipher cryptanalysis, block ciphers and hash capabilities, bilinear maps, key contract, provable defense, and electronic signatures.
Read Online or Download 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 PDF
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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
Sample text
1. A table of curves recommended as international standards [16, 36]. Note that the value of cπ for each of the standards curves is small (at most 3), except for the curves in the NIST K (Koblitz curve) family. These phenomena are to be expected and are explained in Section 6. Any curve with cπ = 1 has the property that its isogeny class consists of only one level. 1 that randomly generated elliptic curves with cπ = 1 (or, more generally, with smooth cπ ) will have discrete logarithm problems of typical difficulty amongst all elliptic curves in their isogeny class.
1. For a holomorphic modular form f one has ap log p + O(m1/2 ). ψ(m, f ) = p≤m Proof. The error term represents the contribution of proper prime powers. 3) which is O(m1/2 ) by the Prime Number Theorem. 2. (Iwaniec [20, p. 114]) Assume that f is a holomorphic modular cusp form of level3 N and that L(s, f ) satisfies GRH. Then ψ(m, f ) = O(m1/2 log(m) log(mN )). 3 Actually in [20] N equals the conductor of the L-function, which in general may be smaller than the level. The lemma is of course nevertheless valid.
The following are equivalent: (a) End(E) = End(E ). (b) There exist two isogenies φ : E → E and ψ : E → E of relatively prime degree, both defined over Fq . (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.
