By Phong Q. Nguyen, Elisabeth Oswald

This e-book constitutes the court cases of the thirty third Annual foreign convention at the conception and functions of Cryptographic options, EUROCRYPT 2014, held in Copenhagen, Denmark, in might 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, useful 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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Thus, the computation of C a (q + 1) costs O(n4 n). 3 Other Computations The resolution of Problems (13) in Step 2, costs O(n4 ) (see (14)). Since the solution spaces D and D in (14) have Fq –dimension 4, the exhaustive search in them costs O(q 4 ) = O(n2 ) which is negligible. The computation of the map φ and that of minimal polynomials is also negligible. Finally, the resolution of Problem 2 costs O(n4 ) since it is very similar to Problem 1. Since Final step should be iterated q 2 − n + 1 times in the worst case, we see that the part of the attack after the computation of the filtration costs at worst O(n5 ).

LNCS, vol. 7932, pp. 102–117. Springer, Heidelberg (2013) 25. : An observation on the security of McEliece’s publickey cryptosystem. G. ) EUROCRYPT 1988. LNCS, vol. 330, pp. 275–280. Springer, Heidelberg (1988) 26. : A probabilistic algorithm for computing minimum weights of large error-correcting codes. IEEE Trans. Inform. Theory 34(5), 1354–1359 (1988) 27. : Weak keys in the McEliece public-key cryptosystem. IEEE Trans. Inform. Theory 47(3), 1207–1211 (2001) 28. : A new version of mcEliece PKC based on convolutional codes.

This leads to the definition of alternant codes ([29, Chap. 12, §2]). Definition 2 (Alternant code). Let x, y ∈ Fnqm be two vectors such that the entries of x are pairwise distinct and those of y are all nonzero. The alternant code Ar (x, y) defined over Fq where x, y ∈ Fnqm is the subfield subcode over Fq of the code GRSr (x, y)⊥ defined over Fqm , that is: def Ar (x, y) = GRSr (x, y)⊥ ∩ Fnq . The integer r is referred to as the degree of the alternant code, the integer m as its extension degree and the vector x as its support.

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