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Download e-book for iPad: Advances in Cryptology - EUROCRYPT 2010: 29th Annual by Henri Gilbert

By Henri Gilbert

ISBN-10: 3642131891

ISBN-13: 9783642131899

This e-book constitutes the refereed lawsuits of the twenty ninth Annual overseas convention at the idea and functions of Cryptographic options, EUROCRYPT 2010, hung on the French Riviera, in May/June 2010. The 33 revised complete papers offered including 1 invited lecture have been conscientiously reviewed and chosen from 188 submissions. The papers tackle all present foundational, theoretical and examine facets of cryptology, cryptography, and cryptanalysis in addition to complicated functions. The papers are equipped in topical sections on cryptosystems; obfuscation and part channel defense; 2-party protocols; cryptanalysis; automatic instruments and formal equipment; versions and proofs; multiparty protocols; hash and MAC; and foundational primitives.

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Extra resources for Advances in Cryptology - EUROCRYPT 2010: 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, French Riviera, ... Computer Science / Security and Cryptology)

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We proved that our somewhat homomorphic scheme was correct for the set C(PE ) of circuit that compute permitted polynomials, and we now show that this is true also of the modified scheme. Lemma 4. The modified scheme from above is correct for C(PE ). Moreover, for every ciphertext (c∗ , z) that is generated by evaluating a permitted polynomial, it holds that si zi is within 1/4 of an integer. Proof. Fix public and secret keys, generated with respect to security parameter Θ λ, with {yi }Θ i=1 the rational numbers in the public key and {si }i=1 the secretkey bits.

Because there are only N(qi ) = q = poly(n) possible values for s ∈ Rq∨i , we can enumerate over all of them efficiently and discover the correct value. 1, we can transform our input distribution As,ψ to i− ∨ Ai− s,ψ . We now give the transformation that takes some g ∈ Rq and maps As,ψ i ∨ to either Ai− s,ψ or As,ψ , depending on whether or not g = s ∈ Rqi (its values in i− ∨ the other Rqj are irrelevant). Given a sample (a, b) ← As,ψ , the transformation produces a sample (a , b ) = (a + v, b + vg/q) ∈ Rq × T, On Ideal Lattices and Learning with Errors over Rings 21 where v ∈ Rq is uniformly random modulo qi and is 0 modulo the other qj .

It is clear that as defined above, fully homomorphic encryption can be trivially realized from any secure encryption scheme, by an algorithm Evaluate that simply attaches a description of the circuit C to the ciphertext tuple, and a Decrypt procedure that first decrypts all the ciphertexts and then evaluates C on the corresponding plaintext bits. Two properties of homomorphic encryption that rule out this trivial solution are circuit-privacy and compactness. Circuit privacy roughly means that the ciphertext generated by Evaluate does not reveal anything about the circuit that it evaluates beyond the output value of that circuit, even for someone who knows the secret key.

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Advances in Cryptology - EUROCRYPT 2010: 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, French Riviera, ... Computer Science / Security and Cryptology) by Henri Gilbert


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