New PDF release: Advances in Cryptology - ASIACRYPT 2008: 14th International

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

ISBN-10: 3540892540

ISBN-13: 9783540892540

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

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

Example text

Proof. We give a constructive proof. Let M be the matrix defined in Section 3, and ψ be the induced labeling map on the rows of M . Then we have an LSSS M (K, M , ψ , e1 ) that realizes an access structure AS . Because M is strongly multiplicative, by Proposition 3 we have e1 ∈ span{(M )A } for all A ∈ AS. Therefore A ∈ AS and it follows that AS ∗ ⊆ AS , where AS ∗ denotes the dual access structure of AS, defined by AS ∗ = {A ⊆ P | P − A ∈ AS}. The equality (1) in the proof of Proposition 3 shows that the diamond product of two share vectors equals sharing the product of the two secrets by the MSP M (K, M , ψ , e1 ), that is, (M (s1 , ρ1 )τ ) (M (s2 , ρ2 )τ ) = M (s1 s2 , ρ)τ , for some ρ1 , ρ2 , ρ ∈ Kl−1 .

Then there exists a (λ + 1)-multiplicative LSSS for AS of size O(dλ ). 2 From 3-Multiplicativity to Strong Multiplicativity Theorem 3. Any 3-multiplicative LSSS is strongly multiplicative. Proof. Let M(K, M, ψ, e1 ) be a 3-multiplicative LSSS realizing the access structure AS over P . For all A ∈ A = 2P − AS, by Proposition 1, we can choose a fixed vector ρ ∈ Kl−1 such that MA (1, ρ )τ = 0τ . There exists a recombination n 3 vector z ∈ K i=1 di such that for all s, s ∈ K and ρ, ρ ∈ Kl−1 , we have ss = z(M (s, ρ)τ M (s , ρ )τ M (1, ρ )τ ).

7 Conclusions In this paper, we propose the new concept of 3-multiplicative LSSS, which form a subclass of strongly multiplicative LSSS. The 3-multiplicative LSSS are easier to Strongly Multiplicative and 3-Multiplicative Linear Secret Sharing Schemes 35 construct compared to strongly multiplicative LSSS. They can also simplify the computation and reduce the round complexity in secure multiparty computation protocols. We believe that 3-multiplicative LSSS are a more appropriate primitive as building blocks for secure multiparty computations, and deserve further investigation.

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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.)


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