Quantum data communication protection with the quantum permutation pad block cipher in counter mode and Clifford operators

Abstract

Background: This article integrates two cryptographic schemes for quantum data protection. The result achieves authentification, confidentiality, integrity, and replay protection. The authentication, integrity, and replay aspects leverage quantum Clifford operators. Confidentiality of quantum messages is achieved using the quantum permutation pad (QPP) cryptographic scheme. Methods: Clifford operators and the QPP are combined into a block cipher in counter mode. A shared secret is used to seed a random number generator for the arbitrary selection of Clifford operators and quantum permutations to produce a signature field and perform encryption. An encryption and signature algorithm and a decryption and authentication algorithm are specified to protect quantum messages. Results: A symmetric key block cipher with authentication is described. The plain text is signed with a sequence of randomly selected Clifford operators. The signed plaintext is encrypted with a sequence of randomly selected permutations. The algorithms are analyzed. As a function of the values selected for the security parameters, there is an unavoidable risk of collision. The probability of block collision is modelled versus the number of blocks encrypted, for block sizes two, three, four, and five qubits. Conclusions: The scheme is practical but does not achieve perfect indistinguishability because of the risk of message collision. This is normal and unavoidable when fixed-size fields are assumed to make a scheme practical. The model can be used to determine the values of the security parameters and the lifetime of session keys to mitigate the risk of information leakage according to the needs of the scheme’s users. The session key can be renewed when a tolerable maximum number of messages has been sent.