A robust noncrytographic protocol for collective coin flipping
SIAM Journal on Discrete Mathematics
Journal of the ACM (JACM)
Simple and efficient leader election in the full information model
STOC '94 Proceedings of the twenty-sixth 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
Fault-tolerant Computation in the Full Information Model
SIAM Journal on Computing
Lower bounds for leader election and collective coin-flipping in the perfect information model
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Perfect-Information Leader Election with Optimal Resilience
SIAM Journal on Computing
Oblivious Transfer with a Memory-Bounded Receiver
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Perfect Information Leader Election in log^* n + O(1) Rounds
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Noncryptographic Selection Protocols
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
High Entropy Random Selection Protocols
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Random selection with an adversarial majority
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
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We study the round complexity of two-party protocols for generating a random n-bit string such that the output is guaranteed to have bounded bias (according to some measure) even if one of the two parties deviates from the protocol (even using unlimited computational resources). Specifically, we require that the output's statistical difference from the uniform distribution on zon is bounded by a constant less than 1.We present a protocol for the above problem that has 2 log*n+O(1) rounds, improving a 2n-round protocol that follows from the work of Goldreich, Goldwasser, and Linial (FOCS'91). Like the GGL protocol, our protocol actually provides a stronger guarantee, ensuring that the output lands in any set T⊆zon of density μ with probability at most O(√μ+δ), where δ is an arbitarily small constant.We then prove a matching lower bound, showing that any protocol guaranteeing bounded statistical difference requires at least log*n - log* log*n-O(1) rounds. As far as we know, this is the first nontrivial lower bound on the round complexity of random selection protocols (of any type) that does not impose additional constraints (e.g. on communication or "simulatability").We also state several results for the case when the output's bias is measured by the maximum multiplicative factor by which a party can increase the probability of a set T ⊆ zon.