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

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 ecu- pean meetings at the thought and alertness of Cryptographic recommendations. The convention was once backed via 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 obtained of which 188 have been retained as legitimate submissions. those have been each one assigned to at the very least 3 application Committee participants and a complete of 606 evaluation studies have been produced. the broadcast list of the reports and huge on-line discussions that will be nearly as voluminous as those complaints. in any case 35 submissions have been authorised with twosubmissionpairsbeingmergedtogive33paperspresentedattheconference. The ?nal papers in those court cases weren't topic to a moment assessment ahead of ebook and the authors are liable for their contents. The ProgramCommittee, indexed at the subsequent web page, deservesparticular thank you for all their labor, their striking services, and their consistent c- mitment to all features of the evaluate procedure. 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 evaluate process.It was once additionally a greatpleasure to honor and welcome Moti Yung who gave the 2010 IACR special 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

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Lemma 11 (Search to Decision). For any i ∈ Z∗m , there is a probabilistic polynomial-time reduction from qi -LWEq,Ψ to DecLWEiq,Ψ . Proof. The idea for recovering s ∈ Rq∨i is to try each of its possible values, modifying the samples we receive from As,ψ so that on the correct value the modified samples are distributed according to Ai− s,ψ , whereas on all the other values the modified samples are distributed according to Ais,ψ . We can then use the DecLWEiq,Ψ oracle to tell us which distribution was generated.

282–298. : Public-key cryptosystems from the worst-case shortest vector problem. In: STOC, pp. : Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices. , Rabin, T. ) TCC 2006. LNCS, vol. 3876, pp. 145–166. : Lattices that admit logarithmic worst-case to average-case connection factors. In: STOC, pp. : A framework for efficient and composable oblivious transfer. In: Wagner, D. ) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. : Lossy trapdoor functions and their applications.

So, clearly, the main bottleneck is the multiplicative depth of the circuit, or the degree of the multivariate polynomial computed by the circuit. We have the following lemma. Lemma 3. Let C be a boolean circuit with t inputs, and let C † be the associated integer circuit (where boolean gates are replaced with integer operations). Let f (x1 , . . , xt ) be the multivariate polynomial computed by C † ; let d be its degree. If |f | · (2ρ +2 )d ≤ 2η−4 (where |f | is the l1 norm of the coefficient vector of f ) then C ∈ CE .

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