Applications of Semidefinite Programming in Quantum Cryptography

Abstract

Coin-flipping is the cryptographic task of generating a random coin-flip between two mistrustful parties. Kitaev discovered that the security of quantum coin-flipping protocols can be analyzed using semidefinite programming. This lead to his result that one party can force a desired coin-flip outcome with probability at least 1/√2.

We give sufficient background in quantum computing and semidefinite programming to understand Kitaev's semidefinite programming formulation for coin-flipping cheating strategies. These ideas are specialized to a specific class of protocols singled out by Nayak and Shor. We also use semidefinite programming to solve for the maximum cheating probability of a particular protocol which has the best known security.

Furthermore, we present a family of protocols where one party has a greater probability of forcing an outcome of 0 than an outcome of 1. We also discuss a computer search to find specific protocols which minimize the maximum cheating probability.