Download Advances in Cryptology – EUROCRYPT 2013: 32nd Annual by Sanjam Garg, Craig Gentry, Shai Halevi (auth.), Thomas PDF

By Sanjam Garg, Craig Gentry, Shai Halevi (auth.), Thomas Johansson, Phong Q. Nguyen (eds.)

This ebook constitutes the lawsuits of the thirty second Annual foreign convention at the idea and functions of Cryptographic innovations, EUROCRYPT 2013, held in Athens, Greece, in may perhaps 2013. The forty-one complete papers incorporated during this quantity have been conscientiously reviewed and chosen from 201 submissions. They care for cryptanalysis of hash services, side-channel assaults, quantity concept, lattices, public key encryption, electronic signatures, homomorphic cryptography, quantum cryptography, garage, instruments, and safe computation.

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Extra 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

Example text

However, this drawback is still quite mild compared to the super-polynomial inapproximability assumptions made in other works [GKPV10, BV11, Bra12]. We now state our main-theorem. 20 N. D¨ ottling and J. M¨ uller-Quade Theorem 1 (Main Theorem). Let n be a security parameter and let σ ∈ (0, 1) be an arbitrarily small constant. Let q = q(n) be a modulus and m = m(n) = poly(n) be a integer with m ≥ 3n. 5+σ m. If there exists a PPT-algorithm that solves LWE(n, m, q, U([−ρq, ρq])) with non-negligible probability, then there exists an efficient quantum-algorithm that approximates the decision-version of the shortest vector problem (GAPSVP) ˜ 1+σ m/ρ) in and the shortest independent vectors problem (SIVP) to within O(n the worst case.

C = [−r, r]n . 2 Min-Entropy Let χ be a probability distribution with finite support and let X be distributed according to χ. Define the min-entropy as H∞ (X) = − log(maxξ (Pr[X = ξ])). Let Y be random-variable (possibly correlated with X) and let y˜ be a measurement or outcome of Y . The conditional min-entropy H∞ (X|Y = y˜) is defined as H∞ (X|Y = y˜) = − log(maxξ (Pr[X = ξ|Y = y˜])). e. H∞ (X|Y = y˜) is at least δ, except with probability over the choice of the measurement y˜. e. it compresses δ and into one scalar).

5 Conclusion This work presented the first worst-to-average-case reduction for an LWE variant with polynomial modulus and uniformly distributed errors, thereby answering a question from Micciancio and Mol from Crypto 2011. The factor of this worst-to-average-case connection depends on the number of samples given to the adversary and we have to use a bounded LWE assumption where this number is fixed in advance. Overcoming this limitation poses an interesting open problem. , codes which lose information when decoding noisy code words.

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