Generating quasi-random sequences from semi-random sources
Journal of Computer and System Sciences
A robust noncrytographic protocol for collective coin flipping
SIAM Journal on Discrete Mathematics
Coin-flipping games immune against linear-sized coalitions
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
Perfect-Information Leader Election with Optimal Resilience
SIAM Journal on Computing
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
The influence of variables on Boolean functions
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
On the impossibility of extracting classical randomness using a quantum computer
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
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We introduce a new imperfect random source that realistically generalizes the SV-source of Santha and Vazirani [SV86] and the bit-fixing source of Lichtenstein, Linial and Saks [LLS89]. Our source is expected to generate a known sequence of (possibly dependent) random variables (for example, a stream of unbiased random bits). However, the realizations/observations of these variables could be imperfect in the following two ways: (1) inevitably, each of the observations could be slightly biased (due to noise, small measurements errors, imperfections of the source, etc.), which is characterized by the "statistical noise" parameter δ ∈ [0, 1/2], and (2) few of the observations could be completely incorrect (due to very poor measurement, improper setup, unlikely but certain internal correlations, etc.), which is characterized by the "number of errors" parameter b ≥ 0. While the SV-source considered only scenario (1), and the bit-fixing source - only scenario (2), we believe that our combined source is more realistic in modeling the problem of extracting quasi-random bits from physical sources. Unfortunately, we show that dealing with the combination of scenarios (1) and (2) is dramatically more difficult (at least from the point of randomness extraction) than dealing with each scenario individually. For example, if bδ = ω(1), the adversary controlling our source can force the outcome of any bit extraction procedure to a constant with probability 1 - o(1), irrespective of the random variables, their correlation and the number of observations. We also apply our source to the question of producing n-player collective coin-flipping protocols secure against adaptive adversaries. While the optimal non-adaptive adversarial threshold for such protocols is known to be n/2 [BN00], the optimal adaptive threshold is conjectured by Ben-Or and Linial [BL90] to be only O(√n). We give some evidence towards this conjecture by showing that there exists no black-box transformation from a non-adaptively secure coin-flipping protocol (with arbitrary conceivable parameters) resulting in an adaptively secure protocol tolerating ω(√n) faulty players.