By Shai Halevi
This booklet constitutes the refereed court cases of the twenty ninth Annual overseas Cryptology convention, CRYPTO 2009, held in Santa Barbara, CA, united states in August 2009. The 38 revised complete papers awarded have been rigorously reviewed and chosen from 213 submissions. Addressing all present foundational, theoretical and study elements of cryptology, cryptography, and cryptanalysis in addition to complicated purposes, the papers are prepared in topical sections on key leakage, hash-function cryptanalysis, privateness and anonymity, interactive proofs and zero-knowledge, block-cipher cryptanalysis, modes of operation, elliptic curves, cryptographic hardness, merkle puzzles, cryptography within the actual international, assaults on signature schemes, mystery sharing and safe computation, cryptography and game-theory, cryptography and lattices, identity-based encryption and cryptographers’ toolbox.
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Extra info for Advances in Cryptology - CRYPTO 2009: 29th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2009, Proceedings (Lecture ... Computer Science Security and Cryptology)
Speciﬁcally, we present the notions of an average-case strong extractor and hash proof systems. 1 Randomness Extraction The statistical distance between two random variables X and Y over a ﬁnite domain Ω is SD(X, Y ) = 12 ω∈Ω |Pr [X = ω] − Pr [Y = ω] |. We say that two variables are -close if their statistical distance is at most . The min-entropy of a random variable X is H∞ (X) = − log(maxx Pr [X = x]). Dodis et al.  formalized the notion of average min-entropy that captures the remaining unpredictability of a random variable X conditioned on the value of a random variable Y , formally deﬁned as follows: H∞ (X|Y ) = − log Ey←Y 2−H∞ (X|Y =y) .
When considering the length of the ciphertexts and the number of exponentiations per ciphertext, the ﬁrst proposal performs better than the second proposal when roughly λ < L(1−1/ log q), where L is the length of the secret key (note that such a λ is a considerable amount of leakage). For example, by setting k = 2 in the ﬁrst proposal one obtains the simple instantiation described in Section 4 which is resilient to any leakage of L(1/2 − o(1)) bits, and requires only 3 exponentiations per ciphertext.
That is, in a “weak” key-leakage attack the leakage function f is chosen independently of pk. Akavia et al. proved that Regev’s encryption scheme is resilient to any weak key leakage of L(1 − o(1)) bits. Although this notion of key leakage seems rather limited, it still captures many realistic attacks in which the leakage does not depend on the parameters of the encryption scheme. Speciﬁcally, this notion captures the cold boot attack of Halderman et al. , in which the leakage depends only on the properties of the hardware devices that are used for storing the secret key.