Advances in Cryptology – EUROCRYPT 2012: 31st Annual by Antoine Joux (auth.), David Pointcheval, Thomas Johansson

By Antoine Joux (auth.), David Pointcheval, Thomas Johansson (eds.)

This booklet constitutes the refereed court cases of the thirty first Annual overseas convention at the idea and purposes of Cryptographic thoughts, EUROCRYPT 2012, held in Cambgridge, united kingdom, in April 2012.
The forty-one papers, offered including 2 invited talks, have been rigorously reviewed and chosen from 195 submissions. The papers are equipped in topical sections on index calculus, symmetric buildings, safe computation, protocols, lossy trapdoor capabilities, instruments, symmetric cryptanalysis, totally homomorphic encryption, uneven cryptanalysis, effective discount rates, public-key schemes, defense types, and lattices.

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Additional resources 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

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Math. , Providence (2010) 28. : Monte Carlo methods for index computation (mod p). Math. Comp. 32(143), 918–924 (1978) 29. pdf 30. : Summation polynomials and the discrete logarithm problem on elliptic curves. Cryptology ePrint Archive, Report 2004/031 (2004) 31. : Lower Bounds for Discrete Logarithms and Related Problems. In: Fumy, W. ) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997) 32. : Weil descent attack for Kummer extensions. J. Ramanujan Math. Soc. 1 Genus 3 Cover Odd Characteristic We consider elliptic curves defined over Fq3 of the form y 2 = h(x)(x − α)(x − σ(α)) (5) where σ is the Frobenius automorphism of Fq3 /Fq , α ∈ Fq3 \Fq and h ∈ Fq [x] is of degree 1 or 2.

Then, we compute βreal = logn (dreal ). According to Lemma 2, the theoretical value predicted for β = logn (d) is βtheo = 1 α − log(n) . The last column columns shows that βtheo is extremely close to βreal . Finally, we obtain an estimate on the complexity: Theorem 2. Let α, n , m, t be as in Lemma 2. Under Assumption 1, Problem 2 can asymptotically be solved in time O(2ωτ ) and memory O(22τ ), where ω is the linear algebra constant and τ ≈ n2 . 1 Note that we assume that d ≥ t. -C. Faugère et al.

LNCS, vol. 6197, pp. 285–300. Springer, Heidelberg (2010) 27. : Genus 3 curves with many involutions and application to maximal curves in characteristic 2. In: Arithmetic, Geometry, Cryptography and Coding Theory 2009. Contemp. , vol. 521, pp. 71–85. Amer. Math. , Providence (2010) 28. : Monte Carlo methods for index computation (mod p). Math. Comp. 32(143), 918–924 (1978) 29. pdf 30. : Summation polynomials and the discrete logarithm problem on elliptic curves. Cryptology ePrint Archive, Report 2004/031 (2004) 31.

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