The complexity of promise problems with applications to public-key cryptography
Information and Control
The complexity of perfect zero-knowledge
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Journal of the ACM (JACM)
On relationships between statistical zero-knowledge proofs
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Honest-verifier statistical zero-knowledge equals general statistical zero-knowledge
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
The complexity of approximating entropy
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Can Statistical Zero Knowledge Be Made Non-interactive? or On the Relationship of SZK and NISZK
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
On the (Im)possibility of Obfuscating Programs
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
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
A Complete Promise Problem for Statistical Zero-Knowledge
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
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
A study of statistical zero-knowledge proofs
A study of statistical zero-knowledge proofs
Perfect zero-knowledge languages can be recognized in two rounds
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
| Hi-index | 0.00 |
We consider two basic computational problems regarding discrete probability distributions: (1) approximating the statistical difference (aka variation distance) between two given distributions, and (2) approximating the entropy of a given distribution. Both problems are considered in two different settings. In the first setting the approximation algorithm is only given samples from the distributions in question, whereas in the second setting the algorithm is given the "code" of a sampling device (for the distributions in question). We survey the know results regarding both settings, noting that they are fundamentally different: The first setting is concerned with the number of samples required for determining the quantity in question, and is thus essentially information theoretic. In the second setting the quantities in question are determined by the input, and the question is merely one of computational complexity. The focus of this survey is actually on the latter setting. In particular, the survey includes proof sketches of three central results regarding the latter setting, where one of these proofs has only appeared before in the second author's PhD Thesis.