By Xiang Xie, Rui Xue, Rui Zhang (auth.), Ivan Visconti, Roberto De Prisco (eds.)
This booklet constitutes the lawsuits of the eighth overseas convention on protection and Cryptography, SCN 2012, held in Amalfi, Italy, in September 2012.
The 31 papers awarded during this quantity have been conscientiously reviewed and chosen from seventy two submissions. they're geared up in topical sections on cryptography from lattices; signature schemes; encryption schemes; effective two-party and multi-party computation; safety within the UC framework; cryptanalysis; effective structures; and protocols and combiners.
Read Online or Download Security and Cryptography for Networks: 8th International Conference, SCN 2012, Amalfi, Italy, September 5-7, 2012. Proceedings PDF
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Additional resources for Security and Cryptography for Networks: 8th International Conference, SCN 2012, Amalfi, Italy, September 5-7, 2012. Proceedings
7293, pp. 34–51. org/2012/235 8. : Predicting Lattice Reduction. P. ) EUROCRYPT 2008. LNCS, vol. 4965, pp. 31–51. Springer, Heidelberg (2008) 9. : Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. ) STOC 2009, pp. 169–178. ACM (2009) 10. org/2012/240 Ring Switching in BGV-Style Homomorphic Encryption 37 11. : Fully Homomorphic Encryption with Polylog Overhead. , Johansson, T. ) EUROCRYPT 2012. LNCS, vol. 7237, pp. 465–482. org/2011/566 12. : Better Bootstrapping in Fully Homomorphic Encryption.
However, coming in the middle of homomorphic evaluation, we may need to get small-ring ciphertexts encrypting elements other than the a(k) ’s. Speciﬁcally, if the original a encodes several plaintext values in its plaintext slots (as in [18, 11]), we may want to get encryptions of small-ring elements that encode the very same values in their slots. We note that the plaintext values encoded in the element a ∈ R are the evaluations a(ρi ), where the ρi ’s are primitive m-th roots of unity in some extension ﬁeld F2d .
Similarly m Ring Switching in BGV-Style Homomorphic Encryption 35 let x = Enc−1 m (x). Observe that since multiplication in R2 implies pointwise multiplication on the slots, then the product a·x ∈ R2 encodes in its slots exactly α times the slots of x. In other words, we have Enc−1 m (α · x ∈ F2d ) = a · x ∈ R2 . Since a has the same element α in all its slots then it satisﬁes the condition of Lemma 5 and Corollary 1. Let b ∈ F2 [X]/Φw (X) ∼ = R2 be the polynomial promised by Lemma 5. Then from Corollary 1 we have that T2 (a · x) = b · T (x).