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 ebook constitutes the refereed court cases of the 14th foreign 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 features, public-key cryptograhy, lattice-based cryptography, private-key cryptograhy, and research of movement ciphers.

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Additional 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

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Let S and R denote random variables Strongly Multiplicative and 3-Multiplicative Linear Secret Sharing Schemes 23 taking values in S and R, respectively. Then Π : S × R → S1 × · · · × Sn is called a secret sharing scheme (SSS) with respect to the access structure AS, if the following two conditions are satisfied: 1. for all A ∈ AS, H(S | Π(S, R)|A ) = 0; 2. for all B ∈ AS, H(S | Π(S, R)|B ) = H(S), where H(·) is the entropy function. Furthermore, the secret sharing scheme Π is called linear if we have S = K, R = Kl−1 , and Si = Kdi for some positive integers l and di , 1 ≤ i ≤ n, and the reconstruction of the secret can be performed by taking a linear combination of shares from the authorized players.

The main idea of their protocol is to keep the intermediate results secretly shared among the players with the underlying LSSS. Due to the nature of linearity, secure additions (and linear operations) can be easily achieved. For instance, if player Pi holds the share x1i for input x1 and x2i for input x2 , he can locally compute x1i + x2i which is actually Pi ’s share for x1 + x2 . Unfortunately, the above homomorphic property does not hold for multiplication. In order to securely compute multiplications, Cramer et al.

We then define 3-multiplicative LSSS and give a necessary and sufficient condition for its existence. The notion of 3-multiplicativity is also extended to λmultiplicativity for all integer λ > 1. Finally, we present a generic (but inefficient) construction of λ-multiplicative LSSS. 2, it is straightforward to see that n we have an induced labeling map ψ : {1, . . , i=1 d2i } → {P1 , . . , Pn } on the entries of x y, distributing the entry xij yik to Pi , since both xij and yik are labeled by Pi under ψ.

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