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

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

This ebook constitutes the refereed complaints of the 14th foreign convention at the thought and alertness of Cryptology and knowledge 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 conscientiously 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 flow 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

Example text

M =⎜ . ⎟, ⎠ ⎝ md1 · · · mdl v0 v1 · · · vk ⎛ ⎛ ⎞ m11 · · · m1l ⎜ ⎟ where ⎝ ... . ... ⎠ = M and the blanks in M denote zeros. Define a labeling md1 · · · mdl map ψ on the rows of M which labels the first d rows of M according to ψ n and the other i=1 d2i rows according to ψ . As mentioned above, M (K, M , ψ , e1 ) obviously realizes the access structure AS. We now verify its 3-multiplicativity. n 2 Let N = (v 0 , v 1 , . . , v k ), a matrix over K with i=1 di rows and k + 1 l−1 k × K , 1 ≤ i ≤ 3, denote columns.

Then there exists an LSSS of size d that realizes AS if and only if there exists an MSP of size d that computes fAS . Since an MSP computes the same Boolean function under linear transformations, we can always assume that the target vector is e1 = (1, 0, . . , 0). From an MSP M(K, M, ψ, e1 ) that computes fAS , we can derive an LSSS realizing AS as follows: to share a secret s ∈ K, the dealer randomly selects ρ ∈ Kl−1 , computes M (s, ρ)τ and sends MPi (s, ρ)τ to Pi as his share, where 1 ≤ i ≤ n and τ denotes the transpose.

4]. More importantly, we show that 3-multiplicative LSSS are closely related to strongly multiplicative LSSS. The latter is known to be a powerful tool for constructing secure MPC protocols against active adversaries. More precisely, we show the following: (i) 3-multiplicative LSSS are also strongly multiplicative; (ii) there exists an efficient algorithm that transforms a strongly multiplicative LSSS into a 3-multiplicative LSSS; (iii) an example of a strongly multiplicative LSSS that is not 3-multiplicative.

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