Cryptography and Coding: 10th IMA International Conference, by Ueli Maurer (auth.), Nigel P. Smart (eds.)

By Ueli Maurer (auth.), Nigel P. Smart (eds.)

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"This e-book comprises chosen refereed complaints of the 10th Institute of arithmetic and its functions (IMA) foreign convention. … The ebook covers a few vital learn components in coding and cryptography. … i feel a person who desires to research or layout a method for crypto-protecting delicate info will locate helpful info during this booklet. … Books resembling this are important to making sure the growth of theoretical and functional reports on cryptography, the most vital applied sciences within the box of desktop and community security." (Patriciu Victor-Valeriu, Computing experiences, August, 2006)

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Extra resources for Cryptography and Coding: 10th IMA International Conference, Cirencester, UK, December 19-21, 2005. Proceedings

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Miyaji, M. Nakabayashi, and S. Takano, New explicit conditions of elliptic curve traces for FR-reduction, IEICE Trans. Fundamentals, E84-A (5), 2001. 41. D. Naccache and J. Stern, Signing on a postcard, Financial Cryptography – FC 2000, LNCS 1962, 2001, 121-135. 42. National Institute of Standards and Technology, Special Publication 800-56: Recommendation for pair-wise key establishment schemes using discrete logarithm cryptography, Draft, 2005. 43. L. Pintsov and S. Vanstone, Postal revenue collection in the digital age, Financial Cryptography – FC 2000, LNCS 1962, 2001, 105-120.

Shokrollahi Recently, Bleichenbacher et al. [1] invented a new decoding algorithm for Interleaved Reed-Solomon Codes over the Q-ary symmetric channel. As the name suggests, the codes are constructed with an interleaving technique from m Reed-Solomon codes defined over Fq , if Q = q m . These codes are similar to well-known product code constructions with Reed-Solomon codes as inner codes, but there is an important improvement: interleaved codes model the Q-ary channel more closely than a standard decoder for the product code would.

N, ∀ j = 1, . . , m : vj (Pi ) = yij · w(Pi ). (2) Furthermore, since we are assuming that the zero codeword was transmitted, we have yij = 0 for i > e (since i is not an error position). From this and (2) we can deduce that ∀i = e + 1, . . , n, ∀ j = 1, . . , m, : vj (Pi ) = 0. (3) This implies that n ∀ j = 1, . . , m : vj ∈ L (t + α + g)D − Pi =: L T . (4) i=e+1 In particular, this proves part (1) of the theorem: if t+α+g −n+e < 0, or equivalently, if t + e < n − α − g, then this linear space is trivial, and hence any element in the right kernel of A is non-erroneous (since it has the property that vj = 0 for all j = 1, .

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