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

ISBN-10: 3540772715

ISBN-13: 9783540772712

ISBN-10: 3540772723

ISBN-13: 9783540772729

This booklet constitutes the refereed complaints of the eleventh IMA overseas convention on Cryptography and Coding, held in Cirencester, united kingdom in December 2007.

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

**Read Online or Download Cryptography and Coding: 11th IMA International Conference, Cirencester, UK, December 18-20, 2007. Proceedings PDF**

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**Sample text**

If there are 0 < w < N/2 invalid signatures in a batch of N signatures, the worst-case cost is 2(2 log2 w − 1 + w( log2 N − log2 w )) batch veriﬁcations when the tree is perfectly balanced. If w > N/2 then the worst-case cost is the same as the cost for w = N/2. Pastuszak et al. [11] also observed that if the veriﬁer knows in advance that the batch contains exactly one invalid signature, then the number of veriﬁcations can be reduced to log2 N . In the following section, we will show how to modify Simple Binary Search to ﬁnd a single invalid signature with log2 N veriﬁcations without advance knowledge of the number of invalid signatures.

Pw that will solve equation (4). Once we know p1 , . . , 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).

Xw . If a match is found then output the list of w invalid signatures and exit. If no match is found, then there are more that w invalid signatures in the batch. Set w ← w + 1 and go to the next step. 2. Compute γw as in equation (7) with i = w. Compute the inverses of γ’s as needed and search for a w-subset of signatures x1 , . . , xw , x1 < x2 < . . < xw to solve equation (8). If a match is found then output the list of w invalid signatures and exit. If no match is found, then there are more than w invalid signatures in the batch.

### 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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