Cryptanalysis increases the level of confidence in cryptographic algorithms. We analyze the security of a symmetric cryptographic algorithm - quantum permutation pad (QPP) [8]. We found the instances of ciphertext the same as plaintext even after the action of QPP with the probability 1/N when the entire set of permutation matrices of dimension N is used and with the probability 1/N^m when an incomplete set of m permutation matrices of dimension N are used. We visually show such instances in a cipher image created by QPP of 256 permutation matrices of different dimensions. For any practical usage of QPP, we recommend a set of 256 permutation matrices of a dimension more or equal to 2048.
Cryptanalysis increases the level of confidence in cryptographic algorithms. We analyze the security of a symmetric cryptographic algorithm - quantum permutation pad (QPP) [8]. We found the instances of ciphertext the same as plaintext even after the action of QPP with the probability 1/N when the entire set of permutation matrices of dimension N is used and with the probability 1/N^m when an incomplete set of m permutation matrices of dimension N are used. We visually show such instances in a cipher image created by QPP of 256 permutation matrices of different dimensions. For any practical usage of QPP, we recommend a set of 256 permutation matrices of a dimension more or equal to 2048.
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 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).
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.
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.
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 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.