Quantum Permutation Pad (QPP) is a symmetric-key quantum block data encryption scheme. Central to QPP is using value permutations in the encryption and decryption procedures. A plaintext is encrypted with a sequence of randomly selected permutations and decrypted by their inverses. Implementing QPP requires a random dispatching operation determining the permutation operators used for encryption. The efficient implementation of the dispatching operation remains an open question. We propose an efficient solution to the dispatching operation. A detailed circuit design is presented, analyzed, and implemented.
Quantum Permutation Pad (QPP) is a symmetric-key quantum block data encryption scheme. Central to QPP is using value permutations in the encryption and decryption procedures. A plaintext is encrypted with a sequence of randomly selected permutations and decrypted by their inverses. Implementing QPP requires a random dispatching operation determining the permutation operators used for encryption. The efficient implementation of the dispatching operation remains an open question. We propose an efficient solution to the dispatching operation. A detailed circuit design is presented, analyzed, and implemented.
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 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.
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).
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.
This paper proposes an advanced quantum text encryption scheme based on an Enhanced Quantum Permutation Pad (QPP). The method begins by generating6×6padded matrices derived from all possible permutations of four basis vectors inR4. These matrices are converted into binary strings and encrypted using two-qubit quantum circuits, whereXand 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.
This review delves into the latest advancements in quantum-secure cryptography, focusing on the quantum permutation pad (QPP), a pivotal innovation proposed by Kuang et al. QPP harnesses the non-commutativity and generalized uncertainty derived from the Galois permutation group, making it highly suitable for cryptographic applications. The review underscores QPP’s versatility across both symmetric and asymmetric cryptography through three core representations: matrix-based for classical encryption, quantum gates for quantum-native encryption, and arithmetic-based for multivariate public key systems such as Merkle–Hellman cryptosystems, multivariate public key cryptography (MPKC), and the most recent homomorphic polynomial public key (HPPK). In particular, QPP strengthens the security of HPPK’s key encapsulation mechanism (KEM) and digital signature (DS) schemes, thus offering robust quantum resistance. This work further examines QPP’s integration with various encryption techniques for enhancing resilience against quantum attacks. By addressing challenges in cryptographic complexity, key size optimization, and security enhancement, the review presents a thorough evaluation of QPP’s role in fortifying cryptographic protocols for ensuring strong security foundations in the quantum computing era.