Download Advances in Cryptology – EUROCRYPT 2011: 30th Annual by Ronald Cramer (auth.), Kenneth G. Paterson (eds.) PDF

By Ronald Cramer (auth.), Kenneth G. Paterson (eds.)

This publication constitutes the refereed lawsuits of the thirtieth Annual foreign convention at the thought and purposes of Cryptographic innovations, EUROCRYPT 2011, held in Tallinn, Estonia, in may perhaps 2011.
The 31 papers, awarded including 2 invited talks, have been conscientiously reviewed and chosen from 167 submissions. The papers are equipped in topical sections on lattice-base cryptography, implementation and aspect channels, homomorphic cryptography, signature schemes, information-theoretic cryptography, symmetric key cryptography, assaults and algorithms, safe computation, composability, key established message defense, and public key encryption.

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Example text

A key typically contains a random matrix defined over Zq for a small q, whose dimension is linear in the security parameter; consequently, the space and time requirements seem bound to be at least quadratic with respect to the security parameter. In 2002, Micciancio [22] succeeded in restricting SIS to structured matrices while preserving a worst-case to average-case reduction. The worst-case problem is a restriction of a standard lattice problem to the specific family of cyclic lattices. The structure of Micciancio’s matrices allows for an interpretation in terms of arithmetic in the ring Zq [x]/(xn − 1), where n is the dimension of the worst-case lattices and q is a small prime.

Rq× ) is isomomorphic to (Zq )n n (resp. (Z× q ) ) via the isomorphism t → (t mod Φi )i≤m . Let gIS = i∈S Φi : it is a degree |S| generator of IS . Making NTRU as Secure as Worst-Case Problems over Ideal Lattices 37 Let p denote the probability (over the randomness of a) that L(a, IS ) contains a non-zero vector t of infinity norm < B, where B = √1n q β . We upper bound p by the union bound, summing the probabilities p(t, s) = Pra [∀i, ti = ai s mod IS ] over all possible values for t of infinity norm < B and s ∈ Rq /IS .

We denote by ρσ (x) (resp. νσ ) the standard n-dimensional Gaussian function (resp. , ρσ (x) = exp(−π x 2 /σ 2 ) (resp. νσ (x) = ρσ (x)/σ n ). We denote by Exp(μ) the exponential distribution on R with mean μ and by U (E) the uniform distribution over a finite set E . If D1 and D2 are two distributions on discrete domain E, their statistical distance is Δ(D1 ; D2 ) = 12 x∈E |D1 (x) − D2 (x)|. We write z ← D when the random variable z is sampled from the distribution D. Remark. Due to space limitations, some proofs have been omitted; they may be found in the full version of this paper, available on the authors’ web pages.

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