Download Advances in Cryptology – EUROCRYPT 2010: 29th Annual by Vadim Lyubashevsky, Chris Peikert, Oded Regev (auth.), Henri PDF

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

These are the court cases of Eurocrypt 2010, the twenty ninth within the sequence of european- pean meetings at the conception and alertness of Cryptographic suggestions. The convention was once subsidized by way of the overseas organization for Cryptologic examine and hung on the French Riviera, may perhaps 30–June three, 2010. a complete of 191 papers have been acquired of which 188 have been retained as legitimate submissions. those have been every one assigned to no less than 3 application Committee individuals and a complete of 606 overview studies have been produced. the published list of the stories and vast on-line discussions that will be virtually as voluminous as those lawsuits. finally 35 submissions have been authorised with twosubmissionpairsbeingmergedtogive33paperspresentedattheconference. The ?nal papers in those court cases weren't topic to a moment assessment ahead of booklet and the authors are chargeable for their contents. The ProgramCommittee, indexed at the subsequent web page, deservesparticular thank you for all their labor, their extraordinary services, and their consistent c- mitment to all features of the assessment strategy. those thank you are in fact prolonged to the very many exterior reviewers who took the time to assist out throughout the assessment process.It was once additionally a greatpleasure to honor and welcome Moti Yung who gave the 2010 IACR wonderful Lecture.

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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, May 30 – June 3, 2010. Proceedings

Example text

Namely, set c = pq + 2r + m, where the integers q, r are chosen at random in some other prescribed intervals, such that 2r is smaller than p/2 in absolute value. Decrypt(p, c): Output (c mod p) mod 2. It is easy to see that when the noise r is sufficiently smaller than the secret key p, this simple scheme is both additively and multiplicatively homomorphic for shallow arithmetic circuits. , “bootstrapping” and “squashing the decryption circuit”) to morph this scheme into a fully homomorphic encryption scheme [20].

71 . The depth of the circuit needed to compute the final sum of two numbers is logarithmic in their bit-lengths, but if we are only interested in s1 + s2 mod 2 and have the promise that s1 + s2 is within 1/4 of an integer, this value can be computed by multivariate polynomial of degree 4 (and only nine terms). Overall, the circuit for computing k i=1 ri mod 2 corresponds to a polynomial of degree at most d ≤ 32k . with coefficient vector having l1 -norm at most 27d . Unfortunately, this degree (with k = Θ) is still too large for our scheme to handle.

The proof is similar to Gentry’s [5,6]. By Theorem 1, we obtain homomorphic encryption schemes for circuits of any depth. Proof. , one satisfying Equation (1)), and show that there is a polynomial-size circuit that computes this polynomial. Recall that c∗ is an integer, the si ’s are bits, and the zi ’s are rational numbers in [0, 2), in binary representation with n = log θ + 3 bits of precision after the binary point. Also, our parameter setting implies two promises – namely, that si · zi is within 1/4 of an integer, and that only θ of the bits s1 , .

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