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

By Phong Q. Nguyen, Elisabeth Oswald

This ebook constitutes the complaints of the thirty third Annual overseas convention at the thought and purposes of Cryptographic ideas, 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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Example text

In addition, we have a complete description of these sets. Proposition 13. There are at least q 2 − n + 2 solutions for (S0 ) which are 1, −(q+1) x0 −(q+1) and the following vectors (1 − a)−(q+1) (x0 − a)q+1 x0 obtained with a ∈ Fq2 \ Lx . Similarly, there at least q − n + 2 solutions for (S1 ) which are 1, (x1 − 1)−(q+1) and the vectors a−(q+1) (x1 − a)q+1 (x1 − 1)−(q+1) also obtained with a ∈ Fq2 \ Lx : 2 Remark 3. It is possible to give a lower-bound for the probability P that (S0 ) (and (S1 )) has no other solution: P 1 − (q 3 + q) (q 2 − q)!

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 ).

Algebraic and Combinatorial Coding Theory, Voneshta Voda, pp. 113–117 (1992) 24. : An efficient attack of a mcEliece cryptosystem variant based on convolutional codes. In: Gaborit, P. ) PQCrypto 2013. 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.

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