A quantum key distribution on qudits using quantum operators
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Author list: Jirakitpuwapat, Wachirapong; Kumam, Poom; Deesuwan, Tanapat; Dhompongsa, Sompong;
Publisher: Wiley
Publication year: 2020
Journal: Mathematical Methods in the Applied Sciences (0170-4214)
ISSN: 0170-4214
eISSN: 1099-1476
Languages: English-Great Britain (EN-GB)
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Abstract
Cryptography is processing for securing communication between two people. The opponent wants to know the message that is encrypted using a secret key. Although the opponent can eavesdrop the message sent between the sender and the receiver, the opponent is unable to decrypt to read the message. Therefore, the secret key is very important. The sender and the receiver agree with the secret key in an insecure channel by using key distribution protocol such as the Diffie–Hellman protocol. Since quantum computer is coming soon, Diffie–Hellman protocol is not secure. We will develop a quantum key distribution protocol. The benefit of the quantum system is the quantum state that cannot copy by no-cloning theorem. Thus, the opponent does not copy and keeps the message that is quantum. In this paper, a novel quantum key distribution protocol between two people (Alice and Bob) based on quantum operators is developed. The opponent (Eve) wants to know the secret key. Although Eve knows this quantum key distribution protocol, Eve does not behave similarly to Alice and Bob. For example, Eve eavesdrops Alice's quantum state that was sent to Bob, and Eve sends another quantum state. Therefore, we cannot control Eve's behavior. So we give the upper bound of mutual information between the user and opponent by using Holevo's bound. We verify the usual security definition for quantum key distribution that is equality-and-uniformity and privacy in the mutual information sense. © 2020 John Wiley & Sons, Ltd.
Keywords
B92 protocol, BB84 protocol, Holevo's Bound, No-cloning theorem, Quantum Key Distribution, three-stage quantum cryptography
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