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

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

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

The 37 revised complete papers awarded have been conscientiously reviewed and chosen from 237 submissions. The papers are equipped in topical sections on algebra and quantity thought, multiparty computation, 0 wisdom and mystery sharing, details and quantum idea, privateness and anonymity, cryptanalytic ideas, movement cipher cryptanalysis, block ciphers and hash capabilities, bilinear maps, key contract, provable defense, and electronic signatures.

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3. 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.

Two mutually exclusive cases may occur. 1. ∀ i, j ∈ [1, n] with i = j, one has i = j. Then by Lemma 4, we get Pr [det(β 1 , . . , βn ) = 0] = z(n, q) . Then with probability 1 − z(n, q), M recovers k and succeeds in solving n-DL. 2. ∃ i, j ∈ [1, n] with i = j such that i = j . Then the reduction M may fail because it might be the case that βi = βj while si − ci xi ≡ sj − cj xj mod q resulting in that the system above is not solvable. The probability of this event is unknown and depends on how R modified its simulation of H between two executions of A.

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.

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