Phong Q. Nguyen, Elisabeth Oswald's Advances in Cryptology – EUROCRYPT 2014: 33rd Annual PDF

By Phong Q. Nguyen, Elisabeth Oswald

ISBN-10: 3642552196

ISBN-13: 9783642552199

ISBN-10: 364255220X

ISBN-13: 9783642552205

This ebook constitutes the lawsuits of the thirty third Annual foreign convention at the concept and purposes of Cryptographic options, EUROCRYPT 2014, held in Copenhagen, Denmark, in might 2014. The 38 complete papers incorporated during this quantity have been rigorously reviewed and chosen from 197 submissions. They take care of public key cryptanalysis, identity-based encryption, key derivation and quantum computing, secret-key research and implementations, obfuscation and multi linear maps, authenticated encryption, symmetric encryption, multi-party encryption, side-channel assaults, signatures and public-key encryption, sensible encryption, foundations and multi-party computation.

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Additional resources for Advances in Cryptology – EUROCRYPT 2014: 33rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Copenhagen, Denmark, May 11-15, 2014. Proceedings

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The classical Goppa code G (x, Γ ) over Fq associated to Γ and supported by s is defined as def G (x, Γ ) = Ar (x, Γ (x)−1 ). We call Γ the Goppa polynomial, x the support and m the extension degree of the Goppa code. 22 A. Couvreur, A. –P. Tillich As for alternant codes, the following description of Goppa codes, which is due to Proposition 2 will be extremely useful in this article. Lemma 2 G (x, Γ ) = Γ (xi )f (xi ) πx (xi ) f ∈ Fq2 [z]

Yn−1 yn−1 f (xn−1 )g(xn−1 )) = (y0 y0 r(x0 ), . . , yn−1 yn−1 r(xn−1 )) where deg(r) k + k − 2. Conversely, any element (y0 y0 r(x0 ), . . , yn−1 yn−1 r(xn−1 )) where deg(r) k + k − 2, is a linear combination of star products of two elements of GRSk (x, y). Statement (ii) is a consequence of (i) by putting y = y and k = k. Since an alternant code is a subfield subcode of a GRS code, we might suspect that products of alternant codes have also an abnormal low dimension. This is is true but in a very attenuated form as shown by: Theorem 2.

N − 1}. The classical Goppa code G (x, Γ ) over Fq associated to Γ and supported by s is defined as def G (x, Γ ) = Ar (x, Γ (x)−1 ). We call Γ the Goppa polynomial, x the support and m the extension degree of the Goppa code. 22 A. Couvreur, A. –P. Tillich As for alternant codes, the following description of Goppa codes, which is due to Proposition 2 will be extremely useful in this article. Lemma 2 G (x, Γ ) = Γ (xi )f (xi ) πx (xi ) f ∈ Fq2 [z]

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Advances in Cryptology – EUROCRYPT 2014: 33rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Copenhagen, Denmark, May 11-15, 2014. Proceedings by Phong Q. Nguyen, Elisabeth Oswald


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