Advances in Cryptology - EUROCRYPT 2010: 29th Annual by Henri Gilbert
By Henri Gilbert
This ebook constitutes the refereed lawsuits of the twenty ninth Annual foreign convention at the thought and functions of Cryptographic ideas, EUROCRYPT 2010, hung on the French Riviera, in May/June 2010. The 33 revised complete papers awarded including 1 invited lecture have been rigorously reviewed and chosen from 188 submissions. The papers tackle all present foundational, theoretical and examine features of cryptology, cryptography, and cryptanalysis in addition to complicated purposes. The papers are geared up in topical sections on cryptosystems; obfuscation and part channel defense; 2-party protocols; cryptanalysis; automatic instruments and formal tools; versions and proofs; multiparty protocols; hash and MAC; and foundational primitives.
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Encrypt(pk, m ∈ {0, 1}). 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).
Encrypt(pk, m ∈ {0, 1}). 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).
If we were to forget our current schemes and start from scratch, perhaps something like the following scheme would be a good candidate for a simple symmetric encryption scheme: KeyGen: The key is an odd integer, chosen from some interval p ∈ [2η−1 , 2η ). Encrypt(p, m): To encrypt a bit m ∈ {0, 1}, set the ciphertext as an integer whose residue mod p has the same parity as the plaintext. Namely, set c = pq + 2r + m, where the integers q, r are chosen at random in some other prescribed intervals, such that 2r is smaller than p/2 in absolute value.