By Antoine Joux (auth.), David Pointcheval, Thomas Johansson (eds.)
This ebook constitutes the refereed court cases of the thirty first Annual foreign convention at the concept and purposes of Cryptographic options, EUROCRYPT 2012, held in Cambgridge, united kingdom, in April 2012.
The forty-one papers, provided including 2 invited talks, have been conscientiously reviewed and chosen from 195 submissions. The papers are geared up in topical sections on index calculus, symmetric buildings, safe computation, protocols, lossy trapdoor features, instruments, symmetric cryptanalysis, absolutely homomorphic encryption, uneven cryptanalysis, effective discount rates, public-key schemes, protection types, and lattices.
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Extra info for Advances in Cryptology – EUROCRYPT 2012: 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, Cambridge, UK, April 15-19, 2012. Proceedings
In particular, we validated the assumption for Problem 3 using Semaev’s summation polynomials with m + 1 variables (m = 2, . . , 4). These validations represent a huge computational eﬀort since some of the matrices M encountered during the experiments had more than 10000 columns. 2 Gröbner Basis Computations We performed actual Gröbner basis computation using the FGb software  to compare the theoretical number of operations with a more realistic value. 5 opera67 2 tions using a variant of the hybrid 97 2 method .
We solve it by means of Gröbner basis techniques and analyze its complexity using the multi-homogeneous structure of the equations. A direct consequence of our results is an index calculus algorithm solving ECDLP over any binary ﬁeld F2n in time O(2ω t ), with t ≈ n/2 (provided that a certain heuristic assumption holds). This has to be compared with Diem’s  index calculus based approach for solving ECDLP over Fqn which has complexity exp O(n log(n)1/2 ) for q = 2 and n a prime (but this holds without any heuristic assumption).
F ∈ R (with ≤ n) is D = 1 + i=1 (deg(fi ) − 1). Ideals with special structures – typically arising in cryptography – may have a much lower regularity degree, hence a much better time complexity. g. the Hidden Field Equation cryptosystem (HFE) [38,31,18,29], Multi-HFE ). In many cases, the algebraic systems appearing in these applications were not generic and could be solved more eﬃciently than generic systems, sometimes using dedicated Gröbner basis algorithms. In our case, the algebraic system considered in Problem 2 has a multihomogeneous structure (more precisely multi-linear ).
Advances in Cryptology – EUROCRYPT 2012: 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, Cambridge, UK, April 15-19, 2012. Proceedings by Antoine Joux (auth.), David Pointcheval, Thomas Johansson (eds.)