Quantum fingerprinting
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Quantum fingerprinting is a proposed technique that uses a quantum computer to generate a string with a similar function to the cryptographic hash function.
If unconditional guarantees of security are needed, and if it is impractical for the communicating parties to arrange to share a secret that can be used in a Carter-Wegman MAC, this technique might one day be faster than classical techniques given a quantum computer with 5 to 10 qubits. However, these circumstances are very unusual and it is unlikely the technique will ever have a practical application; it is largely of theoretical interest.