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

By Phong Q. Nguyen, Elisabeth Oswald

This publication constitutes the complaints of the thirty third Annual foreign convention at the conception and functions of Cryptographic ideas, EUROCRYPT 2014, held in Copenhagen, Denmark, in could 2014. The 38 complete papers integrated during this quantity have been conscientiously 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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Extra 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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Proposition 5. Let x be an n–tuple of pairwise distinct elements of Fq and y, y be two n–tuples of nonzero elements of Fq . Then, (i) GRSk (x, y) GRSk (x, y ) = GRSk+k −1 (x, y y ); 2 (ii) GRSk (x, y) = GRS2k−1 (x, y y). Remark 1. This proposition shows that the dimension of GRSk (x, y) GRSk (x, y ) does not scale multiplicatively as kk but additively as k + k − 1. It has been used the first time in cryptanalysis in [48] and appears for instance 24 A. Couvreur, A. –P. Tillich explicitly as Proposition 10 in [31].

Yn−1 f (xn−1 )) ∈ GRSk (x, y) and c = (y0 g(x0 ), . . , yn−1 g(xn−1 )) ∈ GRSk (x, y ) where deg(f ) k − 1 and deg(g) k − 1. Then, c c is of the form: c c = (y0 y0 f (x0 )g(x0 ), . . , 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.

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