By Sanjam Garg, Craig Gentry, Shai Halevi (auth.), Thomas Johansson, Phong Q. Nguyen (eds.)
This booklet constitutes the court cases of the thirty second Annual overseas convention at the conception and purposes of Cryptographic suggestions, EUROCRYPT 2013, held in Athens, Greece, in may well 2013. The forty-one complete papers integrated during this quantity have been rigorously reviewed and chosen from 201 submissions. They care for cryptanalysis of hash features, side-channel assaults, quantity idea, lattices, public key encryption, electronic signatures, homomorphic cryptography, quantum cryptography, garage, instruments, and safe computation.
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Additional resources for Advances in Cryptology – EUROCRYPT 2013: 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Athens, Greece, May 26-30, 2013. Proceedings
Moreover, with this we can deﬁne a meaningful ”norm” on Zq by x mod q ∞ = x ∞ . 6 Learning-With-Errors As mentioned above, we will consider an m-bounded LWE-problem, where the adversary is given m(n) = poly(n) samples (which we can write conveniently in matrix-form). Problem 1. m-bounded LWE Search-Problem, Average-Case Version. Let n be a security parameter, let m = m(n) = poly(n) and q = q(n) ≥ 2 be integers and χ be a distribution on Zq . Let x ∈ Znq be chosen uniformly at random, let A ∈ Zm×n be chosen uniformly at random an let e be chosen according to χm .
Regarding the choice of ring, the class of cyclotomic rings R ∼ = Z[X]/Φm (X), where Φm (X) is the mth cyclotomic polynomial (which has degree n = ϕ(m) and is monic and irreducible over the rationals), has many attractive features that have proved very useful in cryptography. , [32, 8, 17, 18, 16]). , ). , [25, 24, 21, 14, 15, 26, 33, 9, 8, 17, 18, 22, 5, 28, 20, 16]), often to the exclusion of all other rings. While power-of-two cyclotomic rings are very convenient to use, there are several reasons why it is essential to consider other cyclotomics as well.
Say that a solution x for an instance (A, y) is valid, if y − A · x is in the support of the error-distribution χ. There are two diﬀerent behaviors that algorithm A could exhibit when receiving inputs of the form (A, y), where A is chosen from Cn,m,q and y = Ax + e. In the ﬁrst case, the probability that A outputs a valid solution x is negligible. In the second case, there exists a non-negligible such that the probability that A outputs a valid solution x with probability at least . In the ﬁrst case we can construct D as follows.