Quantum cryptography based on an algorithm for determining simultaneously all the mappings of a Boolean function, by Koji Nagata and Renata Wong and Do Ngoc Diep and Tadao Nakamura

We study a quantum cryptography based on
an algorithm for determining simultaneously all the mappings
of a Boolean function using an
entangled state.
The security of our cryptography is based on the Ekert 1991 protocol,
which uses an entangled state.
Eavesdropping destroys the entanglement.
Alice selects a secret function from the number of possible function types.
Bob’s aim is then to determine the selected function
(a key) without an eavesdropper learning it.
In order for both Alice and Bob to be able to select the same function classically, in the worst case Bob requires multiple queries to Alice.
In the quantum case however, Bob requires just a single query.
By measuring the
single entangled state, which is sent to him by Alice, Bob can obtain
the function that Alice selected.
This quantum key distribution method is faster compared to
the multiple queries that would be required
in the classical case.