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 court cases of the thirty third Annual foreign convention at the thought and functions of Cryptographic suggestions, 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 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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Read Online or Download Advances in Cryptology – EUROCRYPT 2014: 33rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Copenhagen, Denmark, May 11-15, 2014. Proceedings PDF

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Additional 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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Keywords: ECDLP, elliptic curves, decomposition method, index calculus, Semaev polynomials, multivariate polynomial systems, invariant theory. 1 Introduction In the past decade, the resolution of the discrete logarithm problem (DLP) on elliptic curves defined over extension fields has made important theoretical advances. Besides transfer attacks such as GHS [7], a promising approach is the This work has been partially supported by the LabExPERSYVAL-Lab(ANR-11LABX-0025) and the HPAC grant of the French National Research Agency (HPAC ANR-11-BS02-013).

I ← rand. subset of {1, . . } C 0,I (t) ← D ∩ A B ⊥ C 0 (t) ← C 0 (t) + C 0,I (t) end while end for return C 0 (q + 1) In Algorithm 1 it is essential to choose the sizes a(t) of the set of indices I used to compute C 0,I (t) appropriately. Let us denote by k the dimension of C and bring in the quantity: def kAlt (s, t, a) = 3(n − a) − 4r(q + 1) − 2(s + t) − 1 def 1 kRand (s, t, a) = (k − 2s − a + 1) (k − 4t + 2s − a + 2) 2 (9) (10) then we choose we choose a(t) such that: a(t) > n − 2r(q + 1) − t kAlt ( t/2 , t/2 , a(t)) < kRand ( t/2 , t/2 , a(t)) (11) (12) The reasons for this choice are explained in a forthcoming long version of this paper.

Star Product. Vectors and matrices are respectively denoted in bold letters and bold capital letters such as a and A. We always denote the entries of a vector u ∈ Fnq by u0 , . . , un−1 . Given a subset I ⊂ {0, . . , n − 1}, we denote by uI the vector u punctured at I, that is to say, indexes that are in I are removed. When I = {j} we allow ourselves to write uj instead of u{j} . The component-wise def product u v of two vectors u, v ∈ Fnq is defined as: u v = (u0 v0 , . . , un−1 vn−1 ). The i–th power u · · · u is denoted by ui .

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