Cryptography and Coding: 11th IMA International Conference, - download pdf or read online

By Jonathan Katz (auth.), Steven D. Galbraith (eds.)

ISBN-10: 3540772715

ISBN-13: 9783540772712

ISBN-10: 3540772723

ISBN-13: 9783540772729

This e-book constitutes the refereed complaints of the eleventh IMA foreign convention on Cryptography and Coding, held in Cirencester, united kingdom in December 2007.

The 22 revised complete papers awarded including invited contributions have been conscientiously reviewed and chosen from forty eight submissions. The papers are prepared in topical sections on signatures, boolean services, block cipher cryptanalysis, aspect channels, linear complexity, public key encryption, curves, and RSA implementation.

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Example text

Pw , it is easy to solve for the signature identifiers x1 , . . , xw . If a match is found, then output “signatures x1 , . . , and xw are invalid” and exit. If no match is found, then there are at least w + 1 bad signatures in the batch. Set w ← w + 1 and repeat Step 3, or stop and switch to a different method. Cost. We will assume that the number of invalid signatures, w, is small. We need to compute each αi , for i = 1 to w, and to then solve equation (4). N To compute each αi in (3), we first need to compute the quantities k i Bk k=1 N and k=1 k i Dk .

M −2 times to test equation (9). w−2 Therefore, for w ≥ 2, the cost of all calls to the Factor method is bounded by The Factor method is used a maximum of M −2 w−2 8M < 8 M w−1 (w − 2)! multiplications in Fqd . We can establish a tighter upper bound if we consider the fact that x1 and x2 must lie in the range [1, x3 − 1] instead of [1, M ]. The number of times the M − x3 . Factor method is called for any given value of x3 is no more than w−3 Therefore, excluding the cost of computing the δ’s, the cost of the using the Factor method for w ≥ 3 is M−(w−3) 8 x3 =3 ≤ 8 (w − 3)!

6] proposed a batch signature scheme for a variant of the Cha-Cheon scheme. Their scheme is partially aggregate, meaning that a portion of each signature can be combined into into a single short string. Aggregate signatures Finding Invalid Signatures in Pairing-Based Batches 37 are shorter than batch signatures, but when a batch verification fails they do not provide enough information to allow identification of the bad signatures. Cheon et al. claimed that batch verification is not secure for Cha-Cheon and demonstrated an attack.

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Cryptography and Coding: 11th IMA International Conference, Cirencester, UK, December 18-20, 2007. Proceedings by Jonathan Katz (auth.), Steven D. Galbraith (eds.)

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