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January 16, 2011

Quantum money from Knots

Peter Shor who developed a quantum algorithm for factoring primes, is now discussing quantum money. Money, either in the form of bills or information on a computer, should be impossible to copy and also should be verifiable as good money when tendered to a merchant. Quantum mechanics may make this possible to achieve with far greater security than can be achieved without quantum mechanics. Quantum money is a cryptographic protocol in which a mint can produce a quantum state, no one else can copy the state, and anyone (with a quantum computer) can verify that the state came from the mint without sending the money back to the mint. I will present a concrete quantum money scheme based on quantum superpositions of diagrams that encode knots. This scheme is hopefully secure against computationally bounded adversaries.



Quantum money from knots (22 pages)

Quantum money is a cryptographic protocol in which a mint can produce a quantum state, no one else can copy the state, and anyone (with a quantum computer) can verify that the state came from the mint. We present a concrete quantum money scheme based on superpositions of diagrams that encode oriented links with the same Alexander polynomial. We expect our scheme to be secure against computationally bounded adversaries.

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