TY - GEN

T1 - Randomness condensers for efficiently samplable, seed-dependent sources

AU - Dodis, Yevgeniy

AU - Ristenpart, Thomas

AU - Vadhan, Salil

PY - 2012

Y1 - 2012

N2 - We initiate a study of randomness condensers for sources that are efficiently samplable but may depend on the seed of the condenser. That is, we seek functions Cond : {0,1} n × {0,1} d → {0,1} m such that if we choose a random seed S ← {0,1} d, and a source is generated by a randomized circuit of size t such that X has min-entropy at least k given S, then Cond(X;S) should have min-entropy at least some k′ given S. The distinction from the standard notion of randomness condensers is that the source X may be correlated with the seed S (but is restricted to be efficiently samplable). Randomness extractors of this type (corresponding to the special case where k′ = m) have been implicitly studied in the past (by Trevisan and Vadhan, FOCS '00). We show that: Unlike extractors, we can have randomness condensers for samplable, seed-dependent sources whose computational complexity is smaller than the size t of the adversarial sampling algorithm . Indeed, we show that sufficiently strong collision-resistant hash functions are seed-dependent condensers that produce outputs with min-entropy , i.e. logarithmic entropy deficiency. Randomness condensers suffice for key derivation in many cryptographic applications: when an adversary has negligible success probability (or negligible "squared advantage" [3]) for a uniformly random key, we can use instead a key generated by a condenser whose output has logarithmic entropy deficiency. Randomness condensers for seed-dependent samplable sources that are robust to side information generated by the sampling algorithm imply soundness of the Fiat-Shamir Heuristic when applied to any constant-round, public-coin interactive proof system.

AB - We initiate a study of randomness condensers for sources that are efficiently samplable but may depend on the seed of the condenser. That is, we seek functions Cond : {0,1} n × {0,1} d → {0,1} m such that if we choose a random seed S ← {0,1} d, and a source is generated by a randomized circuit of size t such that X has min-entropy at least k given S, then Cond(X;S) should have min-entropy at least some k′ given S. The distinction from the standard notion of randomness condensers is that the source X may be correlated with the seed S (but is restricted to be efficiently samplable). Randomness extractors of this type (corresponding to the special case where k′ = m) have been implicitly studied in the past (by Trevisan and Vadhan, FOCS '00). We show that: Unlike extractors, we can have randomness condensers for samplable, seed-dependent sources whose computational complexity is smaller than the size t of the adversarial sampling algorithm . Indeed, we show that sufficiently strong collision-resistant hash functions are seed-dependent condensers that produce outputs with min-entropy , i.e. logarithmic entropy deficiency. Randomness condensers suffice for key derivation in many cryptographic applications: when an adversary has negligible success probability (or negligible "squared advantage" [3]) for a uniformly random key, we can use instead a key generated by a condenser whose output has logarithmic entropy deficiency. Randomness condensers for seed-dependent samplable sources that are robust to side information generated by the sampling algorithm imply soundness of the Fiat-Shamir Heuristic when applied to any constant-round, public-coin interactive proof system.

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U2 - 10.1007/978-3-642-28914-9_35

DO - 10.1007/978-3-642-28914-9_35

M3 - Conference contribution

AN - SCOPUS:84858307660

SN - 9783642289132

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 618

EP - 635

BT - Theory of Cryptography - 9th Theory of Cryptography Conference, TCC 2012, Proceedings

T2 - 9th Theory of Cryptography Conference, TCC 2012

Y2 - 19 March 2012 through 21 March 2012

ER -