By Vadim Lyubashevsky, Chris Peikert, Oded Regev (auth.), Henri Gilbert (eds.)

ISBN-10: 3642131891

ISBN-13: 9783642131899

ISBN-10: 3642131905

ISBN-13: 9783642131905

These are the lawsuits of Eurocrypt 2010, the twenty ninth within the sequence of european- pean meetings at the concept and alertness of Cryptographic concepts. The convention was once subsidized via the foreign organization for Cryptologic examine and hung on the French Riviera, may well 30–June three, 2010. a complete of 191 papers have been got of which 188 have been retained as legitimate submissions. those have been each one assigned to at the least 3 application Committee participants and a complete of 606 evaluate experiences have been produced. the published list of the stories and wide on-line discussions that will be nearly as voluminous as those lawsuits. finally 35 submissions have been authorized with twosubmissionpairsbeingmergedtogive33paperspresentedattheconference. The ?nal papers in those court cases weren't topic to a moment overview earlier than book and the authors are liable for their contents. The ProgramCommittee, indexed at the subsequent web page, deservesparticular thank you for all their exertions, their amazing services, and their consistent c- mitment to all elements of the assessment technique. those thank you are in fact prolonged to the very many exterior reviewers who took the time to aid out in the course of the overview process.It used to be additionally a greatpleasure to honor and welcome Moti Yung who gave the 2010 IACR distinctive Lecture.

**Read Online or Download Advances in Cryptology – EUROCRYPT 2010: 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, French Riviera, May 30 – June 3, 2010. Proceedings PDF**

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**Additional info for Advances in Cryptology – EUROCRYPT 2010: 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, French Riviera, May 30 – June 3, 2010. Proceedings**

**Sample text**

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.

Namely, we assume that given two smooth numbers p1 , p2 as above and given N such that one of the pi ’s divides φ(N ), it is hard to determine which of the two pi ’s divides φ(N ). In the full version we describe this optimization in more details, and provide a proof of security for it under this φ-hiding variant. 4 Security of the Somewhat Homomorphic Scheme We reduce the security of the scheme from Section 3 to the hardness of the approximate-gcd problem. Namely, given a set of integers x0 , x1 , .

3. Set cj ← z + mj + 2rj + 2 4. 5. Call A to get a prediction aj ← A(pk, cj ) Set bj ← aj ⊕ parity(z) ⊕ mj // bj should be the parity of qp (z) ρ ρ k∈Sj xk x0 6. Output the majority vote among the bj ’s. In the full version [21] we show that for all but a negligible fraction of the public keys generated by the scheme, the “ciphertext” cj in line 3 is distributed almost identically to a valid encryption of the bit [rp (z)]2 ⊕ mj . Note also that since p is odd, we always have [qp (z)]2 = [rp (z)]2 ⊕ parity(z).

### Advances in Cryptology – EUROCRYPT 2010: 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, French Riviera, May 30 – June 3, 2010. Proceedings by Vadim Lyubashevsky, Chris Peikert, Oded Regev (auth.), Henri Gilbert (eds.)

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