C. Cachin, "Smooth entropy and R'enyi entropy." In preparation, 1996. Home/Search Document Details and Download
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Smoothing Probability Distributions and Smooth Entropy.. - Cachin, al. (1996) (Correct)
....log jX j. These characterizations of spoiling knowledge do not translate directly into simple bounds on smooth entropy. However, bounds using non optimal side information show that smooth entropy is lower bounded by R enyi entropy of order ff for any ff 1 up to an asymptotically vanishing term [4] . ....
C. Cachin, "Smooth entropy and R'enyi entropy." In preparation, 1996.
Oblivious Transfers and Privacy Amplification - Brassard, Crépeau (1997) (6 citations) (Correct)
....1 ) UOT, provided n fi ff (k s) for an appropriate constant fi ff to be determined, where s is the safety parameter. Conjecture 6. If conjecture 5 fails as stated, it works if Shannon entropy is replaced with R enyi entropy of order ae in the definition of ff ( 2 1 ) UOT for all ae 1 [Cac97] or perhaps merely for ae = 2 [BBCM95] Acknowledgements We thank Dominic Mayers and Louis Salvail for their help, comments, suggestions and support. ....
C. Cachin, "Smooth entropy and R'enyi entropy", Advances in Cryptology: Proceedings of Eurocrypt '97, Springer-Verlag, 1997.
Oblivious Transfer with a Memory-Bounded Receiver - Cachin, Crepeau, Marcil (1998) (14 citations) Self-citation (Cachin) (Correct)
....= 1; l. Privacy amplification [7, 6] is a method to eliminate partial information about a random variable and extract a shorter, almost uniformly distributed value. The following theorem [23, 5] is formulated using min entropy, but it can be generalized to Renyi entropy of any order 1 [9]. Theorem 2 (Privacy Amplification [5] Let X be a random variable over the alphabet X , let G be the random variable corresponding to the random choice (with uniform distribution) from a 2 universal class G of hash functions X Y , and let Y = G(X) Then H(Y jG) lg jY j 2 lg jYj H1 (X) ....
C. Cachin. Smooth entropy and Renyi entropy. In W. Fumy, editor, Advances in Cryptology: EUROCRYPT '97, volume 1233 of Lecture Notes in Computer Science, pages 193--208. Springer-Verlag, 1997.
Oblivious Transfer with a Memory-Bounded Receiver - Cachin, Crepeau, Marcil (1998) (14 citations) Self-citation (Cachin) (Correct)
....Privacy amplification [BBR86, BBR88] is a method to eliminate partial information about a random variable and extract a shorter, almost uniformly distributed value. The following theorem [ILL89, BBCM95] is formulated using min entropy, but it can be generalized to Renyi entropy of any order = [Cac97b]. Theorem 2 ( BBCM95] Let W be a random variable over the alphabet [ let be the random variable corresponding to the random choice (with uniform distribution) from a 2 universal class of hash functions [ and let o y W . Then Rop NmO b Mt k Y Nm I (1) 3 The ....
Christian Cachin, Smooth entropy and R enyi entropy, Advances in Cryptology: EUROCRYPT '97 (Walter Fumy, ed.), Lecture Notes in Computer Science, vol. 1233, SpringerVerlag, 1997, pp. 193--208.
Oblivious Transfer with a Memory-Bounded Receiver - Cachin, Crepeau, Marcil (1998) (14 citations) Self-citation (Cachin) (Correct)
....Privacy amplification [BBR86, BBR88] is a method to eliminate partial information about a random variable and extract a shorter, almost uniformly distributed value. The following theorem [ILL89, BBCM95] is formulated using min entropy, but it can be generalized to Renyi entropy of any order ff 1 [Cac97b]. Theorem 2 ( BBCM95] Let X be a random variable over the alphabet X , let G be the random variable corresponding to the random choice (with uniform distribution) from a 2 universal class G of hash functions X Y , and let Y = G(X) Then H(Y jG) lg #Y Gamma 2 lg #Y GammaH 1 (X) ln 2 : ....
Christian Cachin, Smooth entropy and R enyi entropy, Advances in Cryptology: EUROCRYPT '97 (Walter Fumy, ed.), Lecture Notes in Computer Science, vol. 1233, SpringerVerlag, 1997, pp. 193--208.
Oblivious Transfer with a Memory-Bounded Receiver - Cachin, Crepeau, Marcil (1998) (14 citations) Self-citation (Cachin) (Correct)
....1; l. Privacy amplification [7, 6] is a method to eliminate partial information about a random variable and extract a shorter, almost uniformly distributed value. The following theorem [23, 5] is formulated using min entropy, but it can be generalized to Renyi entropy of any order ff 1 [9]. Theorem 2 (Privacy Amplification [5] Let X be a random variable over the alphabet X , let G be the random variable corresponding to the random choice (with uniform distribution) from a 2 universal class G of hash functions X Y , and let Y = G(X) Then H(Y jG) lg jY j Gamma 2 lg ....
C. Cachin. Smooth entropy and Renyi entropy. In W. Fumy, editor, Advances in Cryptology: EUROCRYPT '97, volume 1233 of Lecture Notes in Computer Science, pages 193--208. Springer-Verlag, 1997.
Smoothing Probability Distributions and Smooth Entropy - Christian Cachin (1997) Self-citation (Cachin) (Correct)
....entropy and the smooth entropy within 2 Gammas=2 in terms of L1 distance with probability 1 are at least the minimum R enyi entropy of order 2 of any X 2 X. Using a spoiling knowledge argument [1] a recent result shows that smooth entropy is lower bounded by R enyi entropy of any order ff 1 [2]: Let r; t 0, and let m be an integer such that m Gamma log(m 1) log jX j t. For ff 1, the smooth entropy of X within 2 Gammas = ln 2 in terms of relative entropy with probability 1 Gamma 2 Gammar Gamma 2 Gammat satisfies Psi(X) min X2X H ff (X) Gamma log(m 1) Gamma r ....
C. Cachin, "Smooth entropy and R'enyi entropy," in Advances in Cryptology --- EUROCRYPT '97 (W. Fumy, ed.), Lecture Notes in Computer Science, Springer-Verlag, 1997.
Unconditional Security Against Memory-Bounded Adversaries - Cachin, Maurer (1997) (7 citations) Self-citation (Cachin) (Correct)
....G : X Y, and let Y = G(X) Then H(Y jG) log jYj Gamma 2 log jY j GammaH 2 (X) ln 2 : 1) To apply the theorem in the described scenario, replace PX by the conditional probability distribution P W jV =v . Cachin has recently extended the theorem to R enyi entropy of order ff for any ff 1 [6]. 4 Extracting a Secret Key from a Randomly Selected Subset We are now going to show how and why Alice and Bob can exploit the fact that an adversary Eve cannot store the complete output of a public random source that is broadcast to the participants. The security proof consists of three steps. ....
C. Cachin, "Smooth entropy and R'enyi entropy," in Advances in Cryptology --- EUROCRYPT '97 (W. Fumy, ed.), vol. 1233 of Lecture Notes in Computer Science, pp. 193--208, Springer-Verlag, 1997.
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