Advances in Cryptology - ASIACRYPT 2003: 9th International by Duong Hieu Phan, David Pointcheval (auth.), Chi-Sung Laih

By Duong Hieu Phan, David Pointcheval (auth.), Chi-Sung Laih (eds.)

This booklet constitutes the refereed court cases of the ninth overseas convention at the idea and alertness of Cryptology and data safeguard, ASIACRYPT 2003, held in Taipei, Taiwan in November/December 2003.

The 32 revised complete papers offered including one invited paper have been rigorously reviewed and chosen from 188 submissions. The papers are equipped in topical sections on public key cryptography, quantity conception, effective implementations, key administration and protocols, hash capabilities, workforce signatures, block cyphers, broadcast and multicast, foundations and complexity conception, and electronic signatures.

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Additional info for Advances in Cryptology - ASIACRYPT 2003: 9th International Conference on the Theory and Application of Cryptology and Information Security, Taipei, Taiwan, November 30 – December 4, 2003. Proceedings

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Using the factorization of the modulus we compute a mod N , b mod N and c mod N , then we check whether the following relation holds: ab ≡ c mod N. (1) Note that if G is a Diffie-Hellman triplet, the relation (1) is in fact satisfied with probability 1. On the other hand if G is not a Diffie-Hellman triplet, the probability that the relation (1) is verified is: Pr[ab ≡ c mod N ∧ ab ≡ c mod p q N ]. Since a, b and c are random elements in ZN 2 they can be written as a = a1 +a2 N , b = b1 + b2 N and c = c1 + c2 N where a1 , a2 , b1 , b2 , c1 , c2 ∈ ZN .

In particular, to commit to a message m the sender has to compute only two modular multiplications (using a previously computed value). Such a value is completely independent of m and for this reason can be computed before even knowing to which message to commit to. Furthermore we point out that such a preprocessing step requires a single modular exponentiation. Thus even when the precomputation time is considered, our new scheme is basically as efficient as all the other trapdoor commitment schemes known in the literature.

It can be seen in Section 5 that although the different methods do not produce identical results, the actual smoothness tests do inspire a high level of confidence in the numerical approximations. Furthermore, we computed similar estimates for the multiple number field approach from [5], under the untested and possibly over-optimistic assumption that all number fields are about equally ‘good’ as the number fields we generated (cf. Section 6). In the same section we estimated the yield under the assumption that we are able to find much better number fields than we found, for instance by adapting the Franke/Kleinjung program to higher degrees.

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