By Henri Gilbert
This booklet constitutes the refereed complaints of the twenty ninth Annual overseas convention at the thought and functions of Cryptographic suggestions, EUROCRYPT 2010, hung on the French Riviera, in May/June 2010. The 33 revised complete papers offered including 1 invited lecture have been conscientiously reviewed and chosen from 188 submissions. The papers tackle all present foundational, theoretical and study elements of cryptology, cryptography, and cryptanalysis in addition to complex purposes. The papers are geared up in topical sections on cryptosystems; obfuscation and part channel defense; 2-party protocols; cryptanalysis; automatic instruments and formal equipment; versions and proofs; multiparty protocols; hash and MAC; and foundational primitives.
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Asymptotically eﬃcient lattice-based digital signatures. In: Canetti, R. ) TCC 2008. LNCS, vol. 4948, pp. 37–54. : SWIFFT: A modest proposal for FFT hashing. In: Nyberg, K. ) FSE 2008. LNCS, vol. 5086, pp. 54–72. : Generalized compact knapsacks, cyclic lattices, and eﬃcient oneway functions. : Worst-case to average-case reductions based on Gaussian measures. SIAM J. Comput. : Statistical zero-knowledge proofs with eﬃcient provers: Lattice problems and more. In: Boneh, D. ) CRYPTO 2003. LNCS, vol.
Van Dijk et al. The technical details, of course, are very diﬀerent than in factoring-based cryptography. Perhaps the main diﬀerence is that our random self-reduction entails a loss in parameters. Speciﬁcally, we show that a noticeable advantage in guessing the encrypted bit in a random “high noise ciphertext” – where the noise is ρ bits – can be converted into the ability to predict reliably the parity bit of the quotient in an arbitrary “low noise integer” – where the noise is ρ bits. ” Note that the diﬀerence between “high noise” and “low noise” is rather small: only ω(log λ) bits.
Ct ). We need to establish that c∗ /p = si z i (mod 2) i where the zi ’s are computed as [c∗ · yi ]2 with only log θ + 3 bits of precision after the binary point, so [c∗ · yi ]2 = zi − Δi with |Δi | ≤ 1/16θ. We have Fully Homomorphic Encryption over the Integers (c∗ /p) − si z i 2 = (c∗ /p) − si [c∗ · yi ]2 + = (c∗ /p) − c∗ · 2 + 2 si Δi = (c /p) − c · (1/p − Δp ) + si Δi ∗ ∗ si y i si Δi ∗ = c · Δp + si Δi 39 2 2 2 We claim that the ﬁnal quantity inside the brackets has magnitude at most 1/8.