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2010

Quantum money from knots

Farhi, Edward, Gosset, David, Hassidim, Avinatan et al.

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Understand

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.

Quantum money from knots · Around

Built on

Topological invariants of knots and links
J. W. Alexander · 1928
Earlier work this paper cites.
Quantum cryptography, or unforgeable subway tokens
C.H. Bennett, G. Brassard, S. Breidbart, and S. Wiesner · 1983
Earlier work this paper cites.
Conjugate coding
Original
Stephen Wiesner · 1983
Earlier work this paper cites.
Creating superpositions that correspond to efficiently integrable probability distributions, 2002
Lov Grover and Terry Rudolph · 2002
Earlier work this paper cites.
Adiabatic quantum state generation and statistical zero knowledge, 2003
Dorit Aharonov and Amnon Ta-Shma · 2003
Earlier work this paper cites.

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Cited in the paper.

Then

Quantum state restoration and single-copy tomography
Edward Farhi, David Gosset, Avinatan Hassidim, Andrew Lutomirski, Daniel Nagaj, and Peter Shor · 2009
Later among the works it cites.
Quantum coins, 2009
Michele Mosca and Douglas Stebila · 2009
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Classical authenticated key exchange and quantum cryptography, 2009
Douglas Stebila · 2009
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Breaking and making quantum money: toward a new quantum cryptographic protocol, 2010
Andrew Lutomirski, Scott Aaronson, Edward Farhi, David Gosset, Avinatan Hassidim, Jon Kelner, and Peter Shor · 2010
Closest in time.

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