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## Applications of Semidefinite Programming in Quantum Cryptography

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.

Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/3056 |

Date | January 2007 |

Creators | Sikora, Jamie William Jonathon |

Source Sets | University of Waterloo Electronic Theses Repository |

Language | English |

Detected Language | English |

Type | Thesis or Dissertation |

Format | 659000 bytes, application/pdf |

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