We consider the task of extending a given coin toss. By this, we mean the two-party task of using a single instance of a given coin toss protocol in order to interactively generate more random coins. A bit more formally, our goal is to generate n common random coins from a single use of an ideal functionality that gives $m<n$ common random coins to both parties. In the framework of universal composability, we show the impossibility of securely extending a coin toss for statistical and perfect security. On the other hand, for computational security, the existence of a protocol for coin toss extension depends on the number m of random coins that can be obtained “for free.” For the case of stand-alone security, i.e., a simulation-based security definition without an environment, we present a protocol for statistically secure coin toss extension. Our protocol works for superlogarithmic m, which is optimal as we show the impossibility of statistically secure coin toss extension for smaller m. Combining our results with already known results, we obtain a (nearly) complete characterization under which circumstances coin toss extension is possible.We consider the task of extending a given coin toss. By this, we mean the two-party task of using a single instance of a given coin toss protocol in order to interactively generate more random coins. A bit more formally, our goal is to generate n common random coins from a single use of an ideal functionality that gives $$m<n$$ common random coins to both parties. In the framework of universal composability, we show the impossibility of securely extending a coin toss for statistical and perfect security. On the other hand, for computational security, the existence of a protocol for coin toss extension depends on the number m of random coins that can be obtained “for free.” For the case of stand-alone security, i.e., a simulation-based security definition without an environment, we present a protocol for statistically secure coin toss extension. Our protocol works for superlogarithmic m, which is optimal as we show the impossibility of statistically secure coin toss extension for smaller m. Combining our results with already known results, we obtain a (nearly) complete characterization under which circumstances coin toss extension is possible.

Journal of CryptologyApr 26, 20180 citations

Randomness and Probability

Andy Lawrence

Undergraduate lecture notes in physicsJan 1, 20190 citations

On the (Im-)Possibility of Extending Coin Toss

Dennis Hofheinz, Jörn Müller‐Quade, Dominique Unruh

Lecture notes in computer scienceJan 1, 200623 citations

m<n

common random coins to both parties. In the framework of universal composability, we show the impossibility of securely extending a coin toss for statistical and perfect security. On the other hand, for computational security, the existence of a protocol for coin toss extension depends on the number m of random coins that can be obtained “for free.” For the case of stand-alone security, i.e., a simulation-based security definition without an environment, we present a protocol for statistically secure coin toss extension. Our protocol works for superlogarithmic m, which is optimal as we show the impossibility of statistically secure coin toss extension for smaller m. Combining our results with already known results, we obtain a (nearly) complete characterization under which circumstances coin toss extension is possible.