Quantum cryptography based on an algorithm for determining simultaneously all the mappings of a Boolean function

• Published in: Quantum Studies : Mathematics and Foundations Vol. 10; no. 2; pp. 279 - 291
• Main Authors: Nagata, Koji, Wong, Renata, Diep, Do Ngoc, Nakamura, Tadao
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.05.2023; Springer Nature B.V
• Subjects: Algorithms; Boolean functions; Eavesdropping; Entangled states; History and Philosophical Foundations of Physics; Mathematical and Computational Physics; Mathematical Physics; Mathematics; Mathematics and Statistics; Quantum cryptography; Quantum entanglement; Quantum Physics; Queries; Regular Paper; Theoretical; Quantum algorithms; Quantum computation; Boolean algebra; Quantum cryptography; Quantum communication
• ISSN: 2196-5609; 2196-5617
• DOI: 10.1007/s40509-023-00294-4

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.