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

By Phong Q. Nguyen, Elisabeth Oswald

This booklet constitutes the court cases of the thirty third Annual foreign convention at the conception and functions of Cryptographic thoughts, EUROCRYPT 2014, held in Copenhagen, Denmark, in could 2014. The 38 complete papers incorporated during this quantity have been rigorously reviewed and chosen from 197 submissions. They care for 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 info 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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Inform. Theory 46(4), 1193–1203 (2000) 43. : A public-key cryptosytem based on Reed-Muller codes. Discrete Math. Appl. 4(3), 191–207 (1994) 44. : On the insecurity of cryptosystems based on generalized Reed-Solomon codes. Discrete Math. Appl. 1(4), 439–444 (1992) 45. : A method for finding codewords of small weight. , Cohen, G. ) Coding Theory 1988. LNCS, vol. 388, pp. 106–113. Springer, Heidelberg (1989) 46. : Further results on Goppa codes and their applications to constructing efficient binary codes.

C 0,I (t − 1) have been found, we might be tempted to use the “Equation”: C 0,I (0) C 0,I (t) = C 0,I ( t/2 ) C 0,I ( t/2 ). Unfortunately, this equality does not hold in general. However, we have the following related statement. def Lemma 4. Let I be a subset of {1, . . , n − 1} such that r = r( t/2 , t/2 ) = −n + |I| + 2r(q + 1) + t > 0. We have: (i) Any codeword s in C 0,I (t − 1) such that s C 0,I (0) ⊆ C 0,I ( t/2 ) C 0,I ( t/2 ), necessarily belongs to C 0,I (t). (ii) Conversely, C 0,I (t) is equal to the set of codewords s in C 0,I (t − 1) such that s C 0,I (0) ⊆ Ar (xI∪{0} , y).

However, when m > 1, the right hand term of (3) is in general the full space Fnq . Indeed, assume that m > 1 and that the dimension of As (x, y) is n − sm whereas the dimension of As (x, y ) is equal to n − s m. If we assume that both codes have non trivial dimension then we should have n − sm > 0 and n n/2. Therefore we have s n/2 − 1 n − s m > 0 which implies that s < m and s n/2 − 1. This implies that (s + s ) − n + 2 0, which entails that As+s −n+1 (x, y ) is the full space Fnq . e. As (x, y) = As (x, y) for s > s, then the right-hand term of (3) can be smaller than the full space (at least for small dimensions).

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