How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
How to construct random functions
Journal of the ACM (JACM)
The knowledge complexity of interactive proof-systems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
The complexity of perfect zero-knowledge
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
One-way functions and Pseudorandom generators
Combinatorica - Theory of Computing
How to construct pseudorandom permutations from pseudorandom functions
SIAM Journal on Computing - Special issue on cryptography
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Pseudo-random generation from one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Proofs that yield nothing but their validity and a methodology of cryptographic protocol design
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Random self-reducibility and zero knowledge interactive proofs of possession of information
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
On the cunning power of cheating verifiers: Some observations about zero knowledge proofs
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
On the existence of pseudorandom generators
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Homogeneous measures and polynomial time invariants
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
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Pseudorandom distributions on n-bit strings are ones which cannot be efficiently distinguished from the uniform distribution on strings of the same length. Namely, the expected behavior of any polynomial-time algorithm on a pseudorandom input is (almost) the same as on a random (i.e. uniformly chosen) input. Clearly, the uniform distribution is a pseudorandom one. But do such trivial cases exhaust the notion of pseudorandomness? Under certain intractability assumptions the existence of pseudorandom generators was proven, which in turn implies the existence of non-trivial pseudorandom distributions. In this paper we investigate the existence of pseudorandom distributions, using no unproven assumptions.We show that sparse pseudorandom distributions do exist. A probability distribution is called sparse if it is concentrated on a negligible fraction of the set of all strings (of the same length). It is shown that sparse pseudorandom distributions can be generated by probabilistic (non-polynomial time) algorithms, and some of them are not statistically close to any distribution induced by probabilistic polynomial-time algorithms.Finally, we show the existence of probabilistic algorithms which induce pseudorandom distributions with polynomial-time evasive support. Any polynomial-time algorithm trying to find a string in their support will succeed with negligible probability. A consequence of this result is a proof that the original definition of zero-knowledge is not robust under sequential composition. (This was claimed before, leading to the introduction of more robust formulations of zero-knowledge.)