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.

Quantum Encryption of superposition states with Quantum Permutation Pad in IBM Quantum Computers

“…This work goes beyond academic interest and exhibits potential to be used in the future quantum internet where the states of quantum systems may generally be superposition states transmitted over a quantum channel. This paper builds on and extends our previous research [24,25,26]. In [24,25,26] we describe how QPP can be used to encrypt basis states in an IBM Quantum device using Qiskit.…”

“…In this work, we explore whether superposition states can be encrypted using the QPP algorithm with Qiskit on the IBM Quantum systems, and what are the implications of introducing the superposition in the framework of the QPP algorithm. Our previous work [25,26,24] described encryption of basis states with QPP, which can be considered a quantum counterpart of the classical QPP encryption algorithm from [23]. We were then curious to examine whether the quantum implementation of QPP can be extended to the framework that can not be replicated on a classical computer, such as encryption of the superposition states and entangled states using QPP.…”

“…We will demonstrate the encryption of the image given in Figure 4. Similar to our previous work [24,25,26], the current implementation is done using 2-qubit Permutations Operators. Such 2-qubit Permutation Operators act simultaneously on 2 qubits, in other words, these permutations permute 4 state vectors.…”

“…However, one of the main attributes of QPP is that it can be implemented in both classical and quantum devices. Previous implementations of QPP have shown that it is lightweight and can be run today on a free-of-charge IBM Quantum system as well as any classical computer, unlocking the potential of being widely used for quantum encryption in classical systems, quantum systems, as well as hybrid systems, with significant potential use-cases such as quantum internet [25,26,24,19,20,21]. Having a hybrid encryption scheme reduces the limitations and vulnerabilities of a scenario where two different schemes are used on quantum and classical devices, and therefore we continue advancing QPP to ensure that both quantum and classical QPP implementations are efficient and secure.…”

Benchmark Performance of Digital QKD Platform Using Quantum Permutation Pad

“…They demonstrated that in addition to classical computing systems, QPP can also be implemented in quantum computers because it is essentially a set of quantum permutation gates. Recently, Perepechaenko and Kuang implemented QPP in IBMQ quantum computer to decompose permutation gates into quantum circuits, consisting of basic quantum logic gates, to perform encryption and decryption at qubit level [32,33]. The encrypted cipher qubits can be measured with measurement gates to create ciphertext and then the ciphertext can be further turned into cipher qubits and decrypted into plaintext qubits with the inversed QPP and finally measured to form the plaintext.…”