By Vadim Lyubashevsky, Chris Peikert, Oded Regev (auth.), Henri Gilbert (eds.)
These are the complaints of Eurocrypt 2010, the twenty ninth within the sequence of european- pean meetings at the thought and alertness of Cryptographic suggestions. The convention used to be subsidized through the overseas organization for Cryptologic study 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 each one assigned to at the least 3 application Committee contributors and a complete of 606 evaluate studies have been produced. the broadcast list of the stories and broad on-line discussions that will be nearly as voluminous as those lawsuits. in spite of everything 35 submissions have been authorised with twosubmissionpairsbeingmergedtogive33paperspresentedattheconference. The ?nal papers in those complaints weren't topic to a moment overview ahead of book and the authors are chargeable for their contents. The ProgramCommittee, indexed at the subsequent web page, deservesparticular thank you for all their exertions, their remarkable services, and their consistent c- mitment to all elements of the overview procedure. those thank you are after all prolonged to the very many exterior reviewers who took the time to aid out in the course of the review process.It was once additionally a greatpleasure to honor and welcome Moti Yung who gave the 2010 IACR unusual Lecture.
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Extra 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
Xτ , all randomly chosen close to multiples of a large integer p, ﬁnd this “common near divisor” p. , Alexi et al. ): Fixing a randomly-chosen public key, we roughly show that an adversary who can predict the encrypted bit in a random ciphertext under this public key can be used to ﬁnd the secret key (for this ﬁxed public key). As in , we describe a random-self-reduction and accuracy-ampliﬁcation step that uses the promised adversary to get a reliable oracle for the least-signiﬁcant bit, and then a binary-GCD algorithm that uses that reliable oracle to ﬁnd p.
Let CE denote the set of permitted circuits. Clearly, we have: Lemma 2. The scheme from above is correct for CE . Remark 3. Since “fresh” ciphertexts output by Encrypt have noise at most 2ρ +2 , the ciphertext output by Evaluate applied to a permitted circuit has noise at most 2η−4 < p/8. The bound 2η−2 < p/2 would suﬃce for correct decryption. But we will later use the fact that the noise remains below p/8 in Section 6 to perform the decryption operation using a very shallow arithmetic circuit.
1 Homomorphic Encryption Our deﬁnitions are adapted from Gentry . Below we only consider encryption schemes that are homomorphic with respect to boolean circuits consisting of gates for addition and multiplication mod 2. ” A homomorphic public key encryption scheme E has four algorithms: the usual KeyGen, Encrypt, and Decrypt, and an additional algorithm Evaluate. The algorithm Evaluate takes as input a public key pk, a circuit C, a tuple of ciphertexts c = c1 , . . , ct (one for every input bit of C), and outputs another ciphertext c.