By Antoine Joux (auth.), David Pointcheval, Thomas Johansson (eds.)
This ebook constitutes the refereed complaints of the thirty first Annual foreign convention at the thought and purposes of Cryptographic ideas, EUROCRYPT 2012, held in Cambgridge, united kingdom, in April 2012.
The forty-one papers, provided including 2 invited talks, have been rigorously 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, totally homomorphic encryption, uneven cryptanalysis, effective discounts, public-key schemes, defense versions, and lattices.
Read or Download Advances in Cryptology – EUROCRYPT 2012: 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, Cambridge, UK, April 15-19, 2012. Proceedings PDF
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Additional 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
The general linearization strategy and our analysis below rely on a heuristic assumption formalized below: Assumption 1. With a probability exponentially close to one, the equations generated by Algorithm 1 are linearly independent. Particularly, the assumption states that the solutions of Slin are in one-to-one correspondence with the solutions of Problem 2. 5 Complexity Bounds for Solving Problem 2 We now derive an upper bound on the complexity of Algorithm 1. The main task is to estimate the values of M (d) (number of columns in Slin ) and E(d) (number of equations in Slin ).
Math. 7, 167–192 (2004) (electronic) 17. : Weil descent attacks. In: Advances in Elliptic Curve Cryptography. London Math. Soc. Lecture Note Ser, vol. 317, pp. 151–180. Cambridge Univ. Press, Cambridge (2005) Improved Index Calculus on Some Elliptic Curves 23 18. : Elliptic curve discrete logarithm problem over small degree extension ﬁelds. J. 1007/s00145-011-9116-z 19. : A Variant of the F4 Algorithm. In: Kiayias, A. ) CT-RSA 2011. LNCS, vol. 6558, pp. 356–375. Springer, Heidelberg (2011) 20. : Elliptic curve cryptosystems.
While the complexity of solving bi-linear systems using Gröbner bases – that is to say polynomials of bi-degree (1, 1) – is now well understood , the general case is not known. Consequently, we propose a simple ad-hoc algorithm to take advantage of the multihomogeneous structure. This is of independent interest in the more general context of computer algebra. The main idea is to show that starting from the unique equation f = 0, we can generate many low-degree equations by deploying the equations mf = 0 over F2 for a large number of appropriately chosen monomials m.