Advances in Cryptology - EUROCRYPT 2010: 29th Annual by Henri Gilbert PDF

By Henri Gilbert

ISBN-10: 3642131891

ISBN-13: 9783642131899

This publication constitutes the refereed lawsuits of the twenty ninth Annual overseas convention at the conception and purposes of Cryptographic suggestions, EUROCRYPT 2010, hung on the French Riviera, in May/June 2010. The 33 revised complete papers provided including 1 invited lecture have been rigorously reviewed and chosen from 188 submissions. The papers tackle all present foundational, theoretical and study facets of cryptology, cryptography, and cryptanalysis in addition to complex functions. The papers are equipped in topical sections on cryptosystems; obfuscation and part channel safeguard; 2-party protocols; cryptanalysis; automatic instruments and formal tools; versions and proofs; multiparty protocols; hash and MAC; and foundational primitives.

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B then outputs a public key pk = x0 , x1 , . . , xτ . Clearly, if rp (x0 ) happens to be even then the distribution induced on the public key is identical to that of the scheme. Step 2: A subroutine for high-accuracy LSB predictor. Next, B produces a sequence of integers, and attempts to recover p by utilizing A to learn the leastsignificant bit of the quotients of these integers with respect to p. For this, B uses the following subroutine: Fully Homomorphic Encryption over the Integers 33 Subroutine Learn-LSB(z, pk): Input: z ∈ [0, 2γ ) with |rp (z)| < 2ρ , a public key pk = x0 , x1 , .

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. In: STOC, pp. : On lattices, learning with errors, random linear codes, and cryptography. J. : Efficient public key encryption based on ideal lattices. In: Matsui, M. ) ASIACRYPT 2009. LNCS, vol. 5912, pp. 617–635. edu/papers/ant/ (last accessed October 12, 2009) Fully Homomorphic Encryption over the Integers Marten van Dijk1 , Craig Gentry2 , Shai Halevi2 , and Vinod Vaikuntanathan2 1 2 MIT CSAIL IBM Research Abstract.

Choose a random subset S ⊆ {1, 2, . . , τ } and a random integer r in (−2ρ , 2ρ ), and output c ← m + 2r + 2 i∈S xi x0 . Evaluate(pk, C, c1 , . . , ct ). Given the (binary) circuit CE with t inputs, and t ciphertexts ci , apply the (integer) addition and multiplication gates of CE to the ciphertexts, performing all the operations over the integers, and return the resulting integer. Decrypt(sk, c). Output m ← (c mod p) mod 2. Remark 1. Recall that (c mod p) = c − p · c/p , and as p is odd we can instead decrypt using the formula m ← [c − c/p ]2 = (c mod 2) ⊕ ( c/p mod 2).

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Advances in Cryptology - EUROCRYPT 2010: 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, French Riviera, ... Computer Science / Security and Cryptology) by Henri Gilbert


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