By Vadim Lyubashevsky, Chris Peikert, Oded Regev (auth.), Henri Gilbert (eds.)
These are the lawsuits of Eurocrypt 2010, the twenty ninth within the sequence of european- pean meetings at the concept and alertness of Cryptographic thoughts. The convention used to be subsidized via the foreign organization for Cryptologic learn and hung on the French Riviera, could 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 a minimum of 3 software Committee contributors and a complete of 606 evaluation studies have been produced. the broadcast list of the experiences and vast on-line discussions that will be virtually as voluminous as those court cases. after all 35 submissions have been authorized with twosubmissionpairsbeingmergedtogive33paperspresentedattheconference. The ?nal papers in those lawsuits weren't topic to a moment assessment earlier than booklet and the authors are answerable for their contents. The ProgramCommittee, indexed at the subsequent web page, deservesparticular thank you for all their labor, their amazing services, and their consistent c- mitment to all elements of the review procedure. those thank you are in fact prolonged to the very many exterior reviewers who took the time to assist out in the course of the assessment process.It used to be additionally a greatpleasure to honor and welcome Moti Yung who gave the 2010 IACR uncommon Lecture.
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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
Amazingly, it seems √ 3 that with judicious choice of parameters (say r ≈ 2 η and q ≈ 2η ), this simple scheme may even be secure!! H. ): EUROCRYPT 2010, LNCS 6110, pp. 24–43, 2010. c International Association for Cryptologic Research 2010 Fully Homomorphic Encryption over the Integers 25 So far we only described a symmetric scheme, but turning it into a public key scheme is easy: The public key consists of many “encryptions of zero”, namely integers xi = qi ·p+2ri where qi , ri are chosen from the same prescribed intervals as above.
Van Dijk et al. 3 Optimizations Modular-reduction during Evaluate. Note that while Encrypt reduces the ciphertext modulo the public key element x0 , we cannot do the same in Evaluate. The reason is that after just one multiplication the ciphertext becomes much larger than x0 , so modular reduction will include a large multiple of x0 hence introducing intolerable error. To reduce the ciphertext size during Evaluate, we can add to the public key more elements of the form xi = qi p + 2ri where the ri ’s are chosen as usual from the interval (−2ρ , 2ρ ) but the qi ’s are chosen much larger than for the other public key elements.
However, the second and third steps require more complicated sub-circuits. k The problem of using a shallow boolean circuit to compute the sum i=1 ri of k rational numbers in binary representation is well-studied. A well-known technique uses the three-for-two trick (see ), whereby a constant-depth circuit is used to transform three numbers of arbitrary bit-length into two numbers that are at most 1 bit longer, such that the sum of the two output numbers is the same as the sum of the three input numbers.
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.)