Advances in Cryptology - ASIACRYPT 2008: 14th International by Martin Hirt, Ueli Maurer, Vassilis Zikas (auth.), Josef

By Martin Hirt, Ueli Maurer, Vassilis Zikas (auth.), Josef Pieprzyk (eds.)

This booklet constitutes the refereed lawsuits of the 14th overseas convention at the concept and alertness of Cryptology and data safeguard, ASIACRYPT 2008, held in Melbourne, Australia, in December 2008.

The 33 revised complete papers provided including the summary of one invited lecture have been rigorously reviewed and chosen from 208 submissions. The papers are prepared in topical sections on muliti-party computation, cryptographic protocols, cryptographic hash features, public-key cryptograhy, lattice-based cryptography, private-key cryptograhy, and research of circulate ciphers.

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Extra info 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

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Player simulation and general adversary structures in perfect multiparty computation. : On combining privacy with guaranteed output delivery in secure multiparty computation. In: Dwork, C. ) CRYPTO 2006. LNCS, vol. 4117, pp. 483–500. : Secure multi-party computation made simple. , Persiano, G. ) SCN 2002. LNCS, vol. 2576, pp. 14–28. : Secure multi-party computation made simple. : Verifiable secret sharing and multiparty protocols with honest majority. In: STOC 1989, pp. : Protocols for secure computations.

Thus M is multiplicative if and only if (e1 − zM )(ss , ρ )τ = 0. (2) Because of the arbitrariness of s, s , ρ and ρ , equality (2) holds if and only if e1 − zM = 0. Thus e1 ∈ span{M }. The latter part of the proposition can be proved similarly. Now we are ready to give the definition of 3-multiplicative LSSS. We extend the diamond product “ ” and define x y z to be the vector containing all entries of the form xi yj zk with ψ(i) = ψ(j) = ψ(k), where the entries of x y z are written in some fixed order.

26 Z. Zhang et al. Definition 2 (3-Multiplicativity). Let M(K, M, ψ, e1 ) be an LSSS realizing the access structure AS. Then M is called 3-multiplicative if there exn 3 ists a recombination vector z ∈ K i=1 di such that for all s1 , s2 , s3 ∈ K and ρ1 , ρ2 , ρ3 ∈ Kl−1 , we have s1 s2 s3 = z(M (s1 , ρ1 )τ M (s2 , ρ2 )τ M (s3 , ρ3 )τ ). We can derive an equivalent definition for 3-multiplicative LSSS, similar to Proposition 3: M is 3-multiplicative if and only if e1 ∈ span{(M M M )}. The following proposition gives a necessary and sufficient condition for the existence of 3-multiplicative LSSS.

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