By Martin Hirt, Ueli Maurer, Vassilis Zikas (auth.), Josef Pieprzyk (eds.)
This ebook constitutes the refereed lawsuits of the 14th foreign convention at the concept and alertness of Cryptology and knowledge protection, ASIACRYPT 2008, held in Melbourne, Australia, in December 2008.
The 33 revised complete papers awarded including the summary of one invited lecture have been conscientiously reviewed and chosen from 208 submissions. The papers are prepared in topical sections on muliti-party computation, cryptographic protocols, cryptographic hash services, public-key cryptograhy, lattice-based cryptography, private-key cryptograhy, and research of movement ciphers.
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Extra resources for Advances in Cryptology - ASIACRYPT 2008: 14th International Conference on the Theory and Application of Cryptology and Information Security, Melbourne, Australia, December 7-11, 2008. Proceedings
The conditions for 34 Z. Zhang et al. 3-multiplicativity are easy to verify, while veriﬁcation for strong multiplicativity involves checking an exponential number of equations (each subset in the adversary structure corresponds to an equation). With 3-multiplicative LSSS, or more generally λ-multiplicative LSSS, we can simplify local computation for each player and reduce the round complexity in MPC protocols. For example, using the technique of Bar-Ilan and Beaver , l we can compute i=1 xi , xi ∈ Fq , in a constant number of rounds, independent of l.
Using an identical argument for the case of strongly multiplicative LSSS, we have a general construction for 3-multiplicative LSSS based on Shamir’s threshold secret sharing schemes, with exponential complexity. For any λ vectors xi = (xi1 , . . , xid ) ∈ Kd , 1 ≤ i ≤ λ, we deﬁne λi=1 xi to n λ be the i=1 dλi -dimensional vector which contains entries of the form i=1 xiji with ψ(j1 ) = · · · = ψ(jλ ). Deﬁnition 3 (λ-Multiplicativity). Let M(K, M, ψ, e1 ) be an LSSS realizing the access structure AS, and let λ > 1 be an integer.
Suppose M(K, M, ψ, e1 ) is a 3-multiplicative LSSS realizing AS, and suppose to the contrary, that AS is not Q3 , so there exist A1 , A2 , A3 ∈ A = 2P − AS such that A1 ∪ A2 ∪ A3 = P . By Proposition 1, there exists ρi ∈ Kl−1 such that MAi (1, ρi )τ = 0τ for 1 ≤ i ≤ 3. Since A1 ∪ A2 ∪ A3 = P , we have M (1, ρ1 )τ M (1, ρ2 )τ M (1, ρ3 )τ = 0τ , which contradicts Deﬁnition 2. On the other hand, a general construction for building a 3-multiplicative LSSS from a strongly multiplicative LSSS is given in the next section, thus suﬃciency is guaranteed by Proposition 2.
Advances in Cryptology - ASIACRYPT 2008: 14th International Conference on the Theory and Application of Cryptology and Information Security, Melbourne, Australia, December 7-11, 2008. Proceedings by Martin Hirt, Ueli Maurer, Vassilis Zikas (auth.), Josef Pieprzyk (eds.)