By Xiang Xie, Rui Xue, Rui Zhang (auth.), Ivan Visconti, Roberto De Prisco (eds.)
This ebook constitutes the complaints of the eighth overseas convention on safeguard and Cryptography, SCN 2012, held in Amalfi, Italy, in September 2012.
The 31 papers offered during this quantity have been rigorously reviewed and chosen from seventy two submissions. they're equipped 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 buildings; and protocols and combiners.
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Extra resources for Security and Cryptography for Networks: 8th International Conference, SCN 2012, Amalfi, Italy, September 5-7, 2012. Proceedings
Ring Switching in BGV-Style Homomorphic Encryption 25 Lemma 1. For any a ∈ K and i ∈ Z∗w , σi (TrK/K (a)) = σj (a). j=i mod w In matrix form, σ (TrK/K (a)) = P · σ(a), where P is the ϕ(w)-by-ϕ(m) matrix (with rows indexed by i ∈ Z∗w and columns by j ∈ Z∗m ) whose (i, j)th entry is 1 if j = i mod w, and is 0 otherwise. Proof. Recall that for any i ∈ Z∗m such that i = i mod w, the K -embedding σi and the K-embedding σi coincide on K . In particular, σi (TrK/K (a)) = σi (TrK/K (a)) because TrK/K (a) ∈ K .
In this case, as long as we have at least 16 slots in small-ring elements, we can continue working with a single small-ring ciphertext (as opposed to the u ciphertexts that the technique of the previous section gives us). 1 Ring-Switching with Plaintext Encoding Below we describe our method for converting the plaintext encoding between the diﬀerent rings, for the special case where the order of 2 is the same in Z∗m and Z∗w . As sketched in the introduction, the basic observation underlying our approach is that the transformation T (a) = (a0 , a1 , .
Ring-LWE. 5 For a “secret” element s ∈ R , a sample from the RLWE distribution As ,χ is generated by choosing α ∈ Rq uniformly at random and ← χ , computing β ← α · s + in Rq , then outputting the pair (α, β) ∈ (Rq )2 . The decision RLWE problem in Rq is: given arbitrarily many pairs (αi , βi ) ∈ (Rq )2 , distinguish the case where the samples are chosen independently from As ,χ (for a single s ← χ ) from the case where they are uniformly random and independent. To set up the key-switching technique, we ﬁrst prove a lemma of independent interest about the hardness of RLWE over the big ring Rq when the secret is chosen according to χ from the subring R .