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arXiv:2301.10832 · EPJ Quantum Technology

Quantum encryption of superposition states with quantum permutation pad in IBM quantum computers

Maria Perepechaenko, Randy Kuang

Published Feb 17, 2023• 34 citations
arXivHTMLPDF

Abstract

Abstract We present an implementation of Kuang and Bettenburg’s Quantum Permutation Pad (QPP) used to encrypt superposition states. The project was conducted on currently available IBM quantum systems using the Qiskit development kit. This work extends previously reported implementation of QPP used to encrypt basis states and demonstrates that application of the QPP scheme is not limited to the encryption of basis states. For this implementation, a pad of 56 2-qubit Permutation matrices was used, providing 256 bits of entropy for the QPP algorithm. An image of a cat was used as the plaintext for this experiment. The plaintext was randomized using a classical XOR function prior to the state preparation procedure. To create corresponding superposition states, we applied a novel operator defined in this paper. These superposition states were then encrypted using QPP, with 2-qubit Permutation Operators, producing superposition ciphertext states. Due to the lack of a quantum channel, we omitted the transmission and executed the decryption procedure on the same IBM quantum system. If a quantum channel existed, the superposition ciphertext states could be transmitted as qubits, and be directly decrypted on a different quantum system. We provide a brief discussion of the security, although the focus of the paper remains on the implementation. Previously we have demonstrated QPP operating in both classical and quantum computers, offering an interesting opportunity to bridge the security gap between classical and quantum systems. This work broadens the applicability of QPP for the encryption of basis states as well as superposition states. We believe that quantum encryption schemes that are not limited to basis states will be integral to a secure quantum internet, to reduce vulnerabilities introduced by using two separate algorithms for secure communication between a quantum and a classical computer.

DOI
10.1140/epjqt/s40507-023-00164-3

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Abstract We present an implementation of Kuang and Bettenburg’s Quantum Permutation Pad (QPP) used to encrypt superposition states. The project was conducted on currently available IBM quantum systems using the Qiskit development kit. This work extends previously reported implementation of QPP used to encrypt basis states and demonstrates that application of the QPP scheme is not limited to the encryption of basis states. For this implementation, a pad of 56 2-qubit Permutation matrices was used, providing 256 bits of entropy for the QPP algorithm. An image of a cat was used as the plaintext for this experiment. The plaintext was randomized using a classical XOR function prior to the state preparation procedure. To create corresponding superposition states, we applied a novel operator defined in this paper. These superposition states were then encrypted using QPP, with 2-qubit Permutation Operators, producing superposition ciphertext states. Due to the lack of a quantum channel, we omitted the transmission and executed the decryption procedure on the same IBM quantum system. If a quantum channel existed, the superposition ciphertext states could be transmitted as qubits, and be directly decrypted on a different quantum system. We provide a brief discussion of the security, although the focus of the paper remains on the implementation. Previously we have demonstrated QPP operating in both classical and quantum computers, offering an interesting opportunity to bridge the security gap between classical and quantum systems. This work broadens the applicability of QPP for the encryption of basis states as well as superposition states. We believe that quantum encryption schemes that are not limited to basis states will be integral to a secure quantum internet, to reduce vulnerabilities introduced by using two separate algorithms for secure communication between a quantum and a classical computer.
We present a functioning implementation of Kuang et al.’s Quantum Permutation Pad (QPP) using the Qiskit developmental kit on the currently available International Business Machines (IBM) quantum computers. For this implementation, we use a pad with 28 2-qubit permutation gates that provides 128 bits of entropy. In this implementation, we divide the plaintext into blocks of 2-bits each. Each such block is encrypted one at a time. For any given block of plaintext, a quantum circuit is created with qubits initialized according to the given plaintext 2-bit block. The plaintext qubits are then acted on with 2-qubit permutation operators chosen from a 28- permutation QPP pad. Due to the inability to send qubits directly, the ciphertext qubits are measured and transmitted to the decrypting side over a classical channel. The decryption can be performed on either a classical or quantum computer. The decryption uses an inverse Quantum Permutation Pad with the Hermitian conjugates of the corresponding permutation gates used for the encryption. We are currently working on advancing the implementation of QPP to include additional steps for security and efficiency.
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.
We demonstrate an early functional implementation of the Kuang and Barbeau’s Quantum Permutation Pad (QPP) algorithm on the IBMQ physical quantum computers using the Qiskit development kit. Our implementation of the quantum encryption QPP algorithm uses 2-qubit permutation operators created from the compositions of a few CNOT and NOT gates. With inability to physically transfer qubits between two IBMQ machines we acted as two separate IBMQ computers and described how ideally two quantum systems can securely communicate using QPP. Since the physical qubits are still noisy, we use a simple error correction technique by choosing the correct state with the highest probability. Our implementation can be extended to a hybrid system that consist of a quantum computer communicating with a classical computer securely using QPP. This work can be considered as a toy example of the fully secure implementation of quantum encryption using QPP. Nevertheless, it is a promising first step towards secure quantum communication.
Quantum logic gates represent certain quantum operations to perform quantum computations.Of those quantum gates, there is a category of classical behavior gates called quantum permutation gates.As a quantum algorithm, quantum permutation pad or QPP consists of multiple quantum permutation gates to be implemented both in a quantum computing system as a quantum circuit operating on n-qubits' states for transformations and in a classical computing system represented by a pad of n-bit permutation matrices.Since first time proposed in 2020, QPP has been recently applied to create a quantum safe lightweight block cipher by replacing SubBytes and AddRoundKey with QPP in AES called AES-QPP.In AES-QPP, QPP consists of 16 selected 8-bit permutation matrices based on the shared classical key materials.For quantum safe, the key length can be any size from 256 bits to 4 KB.That means, this QPP holds up to 4 KB of Shannon information entropy.Its code size is less than 2 KB with 4 KB of RAM memory.In this paper, we propose to apply QPP for a streaming cipher and carry out its encryption performance and the randomness analysis of this streaming cipher.The proposed QPP streaming cipher demonstrates not only good randomness in its ciphertexts but also huge performance improvement: 13x faster than AES-256, with an overall runtime space (6.8 KB).
This paper proposes an advanced quantum text encryption scheme based on an Enhanced Quantum Permutation Pad (QPP). The method begins by generating6×66 \times 66×6padded matrices derived from all possible permutations of four basis vectors inR4\mathbb{R}^{4}R4. These matrices are converted into binary strings and encrypted using two-qubit quantum circuits, whereXXXand CNOT gates enable quantum entanglement and conditional operations. A binary key is applied to influence the behavior of the quantum circuits during both encryption and decryption. The encryption logic is simulated using Qiskit's AerSimulator, and the resulting binary data is reconstructed into its original structure through matrix extraction. Experimental evaluation using the ENT test demonstrates a high entropy value of 7.66, indicating strong randomness and robustness of the encryption. This methodology presents a secure and structured approach to quantum encryption, combining permutation logic with quantum operations to ensure confidentiality and resistance to classical attacks.
Quantum computers can handle integer factorization and discrete logarithms more efficiently than their classical counterparts, which poses a threat to classical publickey cryptography. Also, quantum encryption systems and postquantum cryptography are gaining increasing attention due to the data vulnerability of classical systems. Hence, quantumnative encryption schemes are urgently needed. This work utilizes Quantum Permutation Pad (QPP), and it can be considered as an enhanced quantum extension of One Time Pad. A 2-qubit QPP is used to encrypt and decrypt an audio file using lowdepth gate permutations. The data file is segmented into 4bit blocks, each block is encoded as quantum states by using both basis and amplitude encoding, then encrypted with 2-qubit permutation circuits (depth≤5\leq 5≤5). The key needed for the permutation index is distributed by using the Greenberger-Horne-Zeilinger (GHZ)-based Quantum Secret Sharing scheme prior to the encoding stage. IBM Qiskit simulations showed that QPP can be a lightweight encryption scheme for NISQ devices.