Simple, near-optimal quantum protocols for die-rolling

TL;DR

This paper introduces simple classical and quantum protocols for die-rolling that achieve near-optimal security, contrasting with the complexity of previous quantum protocols based on coin-flipping, and explores their applications and theoretical bounds.

Contribution

The paper presents simple classical die-rolling protocols with strong security and quantum protocols based on integer-commitment that approach Kitaev's lower bound.

Findings

Classical die-rolling protocols can have optimal or decent security.

Quantum protocols based on integer-commitment approach optimal bounds.

Protocols have potential applications in quantum state discrimination.

Abstract

Die-rolling is the cryptographic task where two mistrustful, remote parties wish to generate a random $D$-sided die-roll over a communication channel. Optimal quantum protocols for this task have been given by Aharon and Silman (New Journal of Physics, 2010) but are based on optimal weak coin-flipping protocols which are currently very complicated and not very well understood. In this paper, we first present very simple classical protocols for die-rolling which have decent (and sometimes optimal) security which is in stark contrast to coin-flipping, bit-commitment, oblivious transfer, and many other two-party cryptographic primitives. We also present quantum protocols based on integer-commitment, a generalization of bit-commitment, where one wishes to commit to an integer. We analyze these protocols using semidefinite programming and finally give protocols which are very close to Kitaev's lower bound for any $D \geq 3$. Lastly, we briefly discuss an application of this work to the quantum state discrimination problem.