We propose a coin-flip protocol which yields a string of strong, random coins and is fully simulatable against poly-sized quantum adversaries on both sides. It can be implemented with quantum-computational security without any set-up assumptions, since our construction only assumes mixed commitment schemes which we show how to construct in the given setting. We then show that the interactive generation of random coins at the beginning or during outer protocols allows for quantum-secure realizations of classical schemes, again without any set-up assumptions. As example applications we discuss quantum zero-knowledge proofs of knowledge and quantum-secure two-party function evaluation. Both applications assume only fully simulatable coin-flipping and mixed commitments. Since our framework allows to construct fully simulatable coin-flipping from mixed commitments, this in particular shows that mixed commitments are complete for quantum-secure two-party function evaluation. This seems to be the first completeness result for quantum-secure two-party function evaluation from a generic assumption.We propose a coin-flip protocol which yields a string of strong, random coins and is fully simulatable against poly-sized quantum adversaries on both sides. It can be implemented with quantum-computational security without any set-up assumptions, since our construction only assumes mixed commitment schemes which we show how to construct in the given setting. We then show that the interactive generation of random coins at the beginning or during outer protocols allows for quantum-secure realizations of classical schemes, again without any set-up assumptions. As example applications we discuss quantum zero-knowledge proofs of knowledge and quantum-secure two-party function evaluation. Both applications assume only fully simulatable coin-flipping and mixed commitments. Since our framework allows to construct fully simulatable coin-flipping from mixed commitments, this in particular shows that mixed commitments are complete for quantum-secure two-party function evaluation. This seems to be the first completeness result for quantum-secure two-party function evaluation from a generic assumption.

arXiv:1102.0887Feb 4, 20110 citations

Analytic quantum weak coin flipping protocols with arbitrarily small bias

Atul Singh Arora, Jérémie Roland, Chrysoula Vlachou

Weak coin flipping (WCF) is a fundamental cryptographic primitive for two-party secure computation, where two distrustful parties need to remotely establish a shared random bit whilst having opposite preferred outcomes. It is the strongest known primitive with arbitrarily close to perfect security quantumly while classically, its security is completely compromised (unless one makes further assumptions, such as computational hardness). A WCF protocol is said to have bias $\epsilon$ if neither party can force their preferred outcome with probability greater than $1/2+\epsilon$ . Classical WCF protocols are shown to have bias $1/2$ , i.e., a cheating party can always force their preferred outcome. On the other hand, there exist quantum WCF protocols with arbitrarily small bias, as Mochon showed in his seminal work in 2007 [arXiv:0711.4114]. In particular, he proved the existence of a family of WCF protocols approaching bias $\epsilon (k)=1/(4k+2)$ for arbitrarily large $k$ and proposed a protocol with bias $1/6$ . Last year, Arora, Roland and Weis presented a protocol with bias $1/10$ and to go below this bias, they designed an algorithm that numerically constructs unitary matrices corresponding to WCF protocols with arbitrarily small bias [STOC'19, p.205-216]. In this work, we present new techniques which yield a fully analytical construction of WCF protocols with bias arbitrarily close to zero, thus achieving a solution that has been missing for more than a decade. Furthermore, our new techniques lead to a simplified proof of existence of WCF protocols by circumventing the non-constructive part of Mochon's proof. As an example, we illustrate the construction of a WCF protocol with bias $1/14$ .Weak coin flipping (WCF) is a fundamental cryptographic primitive for two-party secure computation, where two distrustful parties need to remotely establish a shared random bit whilst having opposite preferred outcomes. It is the strongest known primitive with arbitrarily close to perfect security quantumly while classically, its security is completely compromised (unless one makes further assumptions, such as computational hardness). A WCF protocol is said to have bias $\epsilon$ if neither party can force their preferred outcome with probability greater than $1/2+\epsilon$. Classical WCF protocols are shown to have bias $1/2$, i.e., a cheating party can always force their preferred outcome. On the other hand, there exist quantum WCF protocols with arbitrarily small bias, as Mochon showed in his seminal work in 2007 [arXiv:0711.4114]. In particular, he proved the existence of a family of WCF protocols approaching bias $\epsilon (k)=1/(4k+2)$ for arbitrarily large $k$ and proposed a protocol with bias $1/6$. Last year, Arora, Roland and Weis presented a protocol with bias $1/10$ and to go below this bias, they designed an algorithm that numerically constructs unitary matrices corresponding to WCF protocols with arbitrarily small bias [STOC'19, p.205-216]. In this work, we present new techniques which yield a fully analytical construction of WCF protocols with bias arbitrarily close to zero, thus achieving a solution that has been missing for more than a decade. Furthermore, our new techniques lead to a simplified proof of existence of WCF protocols by circumventing the non-constructive part of Mochon's proof. As an example, we illustrate the construction of a WCF protocol with bias $1/14$.

arXiv:1911.13283Nov 29, 20191 citation

A Novel Quantum Coin Tossing Protocol with Computationally Secure

Guanghui Liu, Dong Cao

Communications in computer and information scienceJan 1, 20110 citations

Practical aspects of quantum coin flipping

Anna Pappa, Paul Jouguet, Thomas Lawson +4 more

Nov 1, 20120 citations

\epsilon

if neither party can force their preferred outcome with probability greater than

1/2+\epsilon

. Classical WCF protocols are shown to have bias

1/2

, i.e., a cheating party can always force their preferred outcome. On the other hand, there exist quantum WCF protocols with arbitrarily small bias, as Mochon showed in his seminal work in 2007 [arXiv:0711.4114]. In particular, he proved the existence of a family of WCF protocols approaching bias

\epsilon (k)=1/(4k+2)

for arbitrarily large

k

and proposed a protocol with bias

1/6

. Last year, Arora, Roland and Weis presented a protocol with bias

1/10

and to go below this bias, they designed an algorithm that numerically constructs unitary matrices corresponding to WCF protocols with arbitrarily small bias [STOC'19, p.205-216]. In this work, we present new techniques which yield a fully analytical construction of WCF protocols with bias arbitrarily close to zero, thus achieving a solution that has been missing for more than a decade. Furthermore, our new techniques lead to a simplified proof of existence of WCF protocols by circumventing the non-constructive part of Mochon's proof. As an example, we illustrate the construction of a WCF protocol with bias

1/14