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Constant-Round Simulation-Secure Coin Tossing Extension with Guaranteed Output
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| Conference: | EUROCRYPT 2024 |
| Abstract: | Common randomness is an essential resource in many applications. However, a celebrated result of Cleve (STOC 86) rules out the possibility of tossing a fair coin from scratch in the presence of a dishonest majority. A second-best alternative is a Coin Tossing Extension (CTE) protocol, which uses an "online" oracle that produces a small number of common random bits to generate a large number of common random-looking bits.This work initiates the systematic study of fully-secure CTE, which guarantees output even in the presence of malicious behavior. A fully-secure two-party statistical CTE protocol with black-box simulation was implicit in Hofheinz et al. (Eurocrypt 06), but its round complexity is nearly linear in its output length. The problem of constant-round CTE with superlogarithmic stretch remained open. We prove that any statistical CTE with full black-box security and superlogarithmic stretch must have superconstant rounds. To circumvent this impossibility we investigate fully-secure computational CTE, and prove that with N parties and any polynomial stretch: • One round suffices for CTE under subexponential LWE, even with Universally Composable security against adaptive corruptions. • One-round CTE is implied by DDH or the hidden subgroup assumption in class groups, with a short, reusable Uniform Random String, and by both DCR and QR, with a reusable Structured Reference String. • One-way functions imply CTE with O(N) rounds, and thus constant-round CTE for any constant number of parties. Such results were not known even in the two-party setting with standalone, static security. Furthermore, we extend one-round CTE to sample from any efficient distribution, via strong assumptions that include indistinguishability obfuscation. Our one-round CTE protocols can be interpreted as explainable variants of classical randomness extractors, wherein a (short) seed and a source instance can be efficiently reverse-sampled given a random output. Such explainable extractors may be of independent interest. |
BibTeX
@inproceedings{eurocrypt-2024-33930,
title={Constant-Round Simulation-Secure Coin Tossing Extension with Guaranteed Output},
publisher={Springer-Verlag},
author={Damiano Abram and Jack Doerner and Yuval Ishai and Varun Narayanan},
year=2024
}