Quantum encryption with quantum permutation pad in IBMQ systems

Abstract Quantum permutation pad or QPP is a quantum-safe symmetric cryptographic algorithm proposed by Kuang and Bettenburg in 2020. The theoretical foundation of QPP leverages the linear algebraic representations of quantum gates which makes QPP realizable in both, quantum and classical systems. By applying the QPP with 64 of 8-bit permutation gates, holding respective entropy of over 100,000 bits, we accomplished quantum random number distributions digitally over today’s classical internet. The QPP has also been used to create pseudo quantum random numbers and served as a foundation for quantum-safe lightweight block and streaming ciphers. This paper continues to explore numerous applications of QPP, namely, we present an implementation of QPP as a quantum encryption circuit on today’s still noisy quantum computers. With the publicly available 5-qubit IBMQ devices, we demonstrate quantum secure encryption (256 bits of entropy) using 2-qubit QPP with 56 permutation gates, and 3-qubit QPP with 17 permutation gates respectively. Initial qubits of the encryption circuit correspond to the plaintext and after applying quantum encryption operations, cipher qubits are measured with probabilistic distributions, and the results with the highest probability are recorded as cipher bits. The cipher bits are then decrypted with an inverse QPP circuit. The output state plaintext qubits are measured and the most frequent count measurement results are recorded as plaintext bits. This quantum encryption and decryption process clearly demonstrates that QPP quantum implementations works exactly as symmetric encryption and decryption schemes should. The plaintext and ciphertext bits can also be encrypted and decrypted respectively by any classical computing device with the corresponding QPP algorithm as in quantum computers. This work reveals that it is possible to build quantum-secure communications between quantum-to-quantum and quantum-to-classical computers over today’s internet and the future quantum internet.