Comparing Entropies in Statistical Zero Knowledge with Applications to the Structure of SZK
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
Testing that distributions are close
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Testing Random Variables for Independence and Identity
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Sublinear algorithms for testing monotone and unimodal distributions
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Testing monotone high-dimensional distributions
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Streaming and sublinear approximation of entropy and information distances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On optimal communication cost for gathering correlated data through wireless sensor networks
Proceedings of the 12th annual international conference on Mobile computing and networking
Approximating entropy from sublinear samples
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
An information-theoretic model for adaptive side-channel attacks
Proceedings of the 14th ACM conference on Computer and communications security
Testing symmetric properties of distributions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Formally Bounding the Side-Channel Leakage in Unknown-Message Attacks
ESORICS '08 Proceedings of the 13th European Symposium on Research in Computer Security: Computer Security
Testing monotone continuous distributions on high-dimensional real cubes
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Non-uniform distributions in quantitative information-flow
Proceedings of the 6th ACM Symposium on Information, Computer and Communications Security
Automatically deriving information-theoretic bounds for adaptive side-channel attacks
Journal of Computer Security
Proceedings of the forty-third annual ACM symposium on Theory of computing
On the complexity of computational problems regarding distributions
Studies in complexity and cryptography
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(MATH) We consider the problem of approximating the entropy of a discrete distribution under several models. If the distribution is given explicitly as an array where the i-th location is the probability of the i-th element, then linear time is both necessary and sufficient for approximating the entropy.We consider a model in which the algorithm is given access only to independent samples from the distribution. Here, we show that a &lgr;-multiplicative approximation to the entropy can be obtained in O(n(1+η)/&lgr;2 poly(log n)) time for distributions with entropy Ω(&lgr; η), where n is the size of the domain of the distribution and η is an arbitrarily small positive constant. We show that one cannot get a multiplicative approximation to the entropy in general in this model. Even for the class of distributions to which our upper bound applies, we obtain a lower bound of Ω(nmax(1/(2&lgr;2), 2/(5&lgr;2—2)).We next consider a hybrid model in which both the explicit distribution as well as independent samples are available. Here, significantly more efficient algorithms can be achieved: a &lgr;-multiplicative approximation to the entropy can be obtained in O(&lgr;2.Finally, we consider two special families of distributions: those for which the probability of an element decreases monotonically in the label of the element, and those that are uniform over a subset of the domain. In each case, we give more efficient algorithms for approximating the entropy.