Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2303.01315 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Pseudo Quantum Random Number Generator with Quantum Permutation Pad

Randy Kuang, Dafu Lou, Alex He, Chris McKenzie, Michael Redding

Published Oct 1, 2021• 22 citations
arXivHTMLPDF

Abstract

Cryptographic random number generation is critical for any quantum-safe encryption. Based on the natural uncertainty of some quantum processes, a variety of quantum random number generators, or QRNGs, have been created with physical quantum processes. These typically generate random numbers with good unpredictable randomness. Of course, physical QRNGs are costic and require physical integrations with computing systems. This paper proposes a pseudo quantum random number generator with a quantum algorithm called a quantum permutation pad, or QPP, leveraging the high entropy of quantum permutation space for its bijective transformation. Unlike Boolean algebra, where the size of information space is 2nfor an n-bit system, an n-bit quantum permutation space consists of 2n! quantum permutation matrices, representing all quantum permutation gates over an n-bit computational basis. This permutation space holds an equivalent Shannon information entropy of log2(2n!). A QPP can be used to create a pseudo-QRNG or pQRNG capable of integration with any classical computing system, or directly with any application, for good-quality deterministic random number generation. Using a QPP pad with 64 8-bit permuation matrices, a pQRNG holds 107,776 bits of entropy for pseudo-random number generation, compared with 4,096 bits of entropy in Linux /dev/random. It can be used as a deterministic PRNG or as an entropy booster for other PRNGs. It can also be used as a whitening algorithm for any hardware random number generator, including QRNGs, without discarding physical bias bits.

DOI
10.1109/qce52317.2021.00053

Related papers

Quantum encryption with quantum permutation pad in IBMQ systems

Randy Kuang, Maria Perepechaenko

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.

EPJ Quantum Technology•Oct 12, 2022•34 citations

Quantum Secure Lightweight Cryptography with Quantum Permutation Pad

Randy Kuang, Dafu Lou, Alex He +1 more

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).

Advances in Science Technology and Engineering Systems Journal•Aug 1, 2021•7 citations

Entropy Transformation and Expansion with Quantum Permutation Pad for 5G Secure Networks

Dafu Lou, Randy Kuang, Alex He

This paper proposes a quantum safe solution for 5G networks using a quantum permutation pad (or QPP) algorithm, originated from quantum computing logic gates or quantum permutation gates. All permutation gates form a unique permutation space, just like a classical key space. An n-bit permutation space consists of the entire 2n! permutation gates, or permutation matrices over its computational basis. The huge equivalent Shannon entropy of this permutation space would be a nice entropy source for information security. Kuang and Bettenburg in 2020 first proposed QPP and proved it to be the Shannon type of perfect secrecy. Here, we extend its capability of entropy transformations for distribution over the Internet to entropy expansions for 5G networks. We analyze the randomnesses following transformations and expansions with QPP, using industry randomness testing suites. Testing results confirm that QPP can maintain the original randomness of QRNG random numbers for transformations and expansions. Leveraging its strong diffusion capability, QPP may also improve the byte-level randomness of input random numbers.

IEEE International Conference on Communication Technology (ICCT)•Oct 13, 2021•10 citations

Benchmark Performance of Digital QKD Platform Using Quantum Permutation Pad

Dafu Lou, Alex He, Michael Redding +5 more

Quantum permutation pad or QPP is a set of quantum permutation gates. QPP has been demonstrated for quantum secure encryption in both classical and quantum computing systems recently, even at a noisy 5-qubit IBMQ systems. In a classical computing system, QPP encryption is implemented as a permutation gate matrix multiplication with information state vectors. In a quantum computing system, QPP is compiled into a quantum encryption circuit in a native quantum computer and encryption is performed through QPP circuit. Leveraging its quantum mechanical characteristics, we report a digital QKD or D-QKD platform using QPP as a quantum mechanical algorithm implemented in classical systems to distribute quantum entropy, generated from physical quantum random number generators or QRNG, and quantum key over the internet. D-QKD interfaces have been developed to support the photonic QKD standard ETSI-014. This makes any systems with ETSI QKD standards compatible with D-QKD. D-QKD offers point-to-point quantum entropy and quantum key distributions as well as point-to-multi-points quantum key synchronizations with speeds 1000x faster than photonic QKD. This paper reports benchmark performance tests and randomness quality tests for pure quantum entropy generated by a QRNG and expanded entropy using the QPP protocol. The work has been funded by the PlanQK1project and deployed within the OpenQKD2testbed Berlin, operated by Deutsche Telekom.

IEEE Access•Jan 1, 2022•10 citations

IID-Based QPP-RNG: A Random Number Generator Utilizing Qpp Generated from System Jitter

Randy Kuang, Dafu Lou

We propose a groundbreaking random number generator that achieves truly uniform, independent, and identically distributed (IID) randomness by integrating Quantum Permutation Pads (QPP) with system jitter-derived entropy, herein called IID-based QPP-RNG. Unlike conventional RNGs that use raw timing variations, our design uses system jitter solely to generate ephemeral QPP pads and derives 8-bit outputs directly from permutation counts, eliminating the need for post-processing. This approach leverages the factorial complexity of permutation sorting to systematically accumulate entropy from dynamic hardware interactions, ensuring non-deterministic outputs even from fixed seeds. Notably, IID-based QPP-RNG achieves a min-entropy of 7.85-7.95 bits per byte from IID minentropy estimate, surpassing ID Quantique's QRNG (7.157042 bits per byte), which marks a breakthrough in randomness quality. Our implementation employs a dynamic seed evolution protocol that continuously refreshes the internal state with unpredictable system jitter, effectively decoupling the QPP sequence from the initial seed. Cross-platform validation on macOS (x86 and ARM) and Windows (x86) confirms uniformly distributed outputs, while evaluations compliant with NIST SP 800-90B show a Shannon entropy of 7.9999 bits per byte. Overall, IID-based QPP-RNG represents a significant advancement in random number generation, offering a scalable, system-based, software-only, postquantum secure solution for a wide range of cryptographic applications.

International Conference on Communications, Circuits and Systems•May 23, 2025•0 citations

Non Deterministic Pseudorandom Generator for Quantum Key Distribution

Arun Mishra, Kanaka Raju P., Anupama Arjun Pandit +1 more

Quantum Key Distribution(QKD) thrives to achieve perfect secrecy of One time Pad (OTP) through quantum processes. One of the crucial components of QKD are Quantum Random Number Generators(QRNG) for generation of keys. Unfortunately, these QRNG does not immediately produce usable bits rather it produces raw bits with high entropy but low uniformity which can be hardly used by any cryptographic system. A lot of pre-processing is required before the random numbers generated by QRNG to be usable. This causes a bottle neck in random number generation rate as well as QKD system relying on it. To avoid this lacuna of post-processing methods employed as a central part of Quantum Random Number Generators alternative approaches that satisfy the entropy(non determinism) and quantum security is explored. Pseudorandom generators based on quantum secure primitives could be an alternative to the post-processing problem as PRNGs are way more faster than any random number generator employing physical randomness (quantum mechanical process in QRNG) as well as it can provide uniform bits required for cryptography application. In this work we propose a pseudorandom generator based on post quantum primitives. The central theme of this random number generator is designing PRNG with non deterministic entropy generated through hard lattice problem - Learning with errors. We leverage the non determinism by Gaussian errors of LWE to construct non-deterministic PRNG satisfying the entropy requirement of QKD. Further, the paper concludes by evaluating the PRNG through Die-Harder Test.

arXiv:2311.03024•Nov 6, 2023•0 citations
Cryptographic random number generation is critical for any quantum-safe encryption. Based on the natural uncertainty of some quantum processes, a variety of quantum random number generators, or QRNGs, have been created with physical quantum processes. These typically generate random numbers with good unpredictable randomness. Of course, physical QRNGs are costic and require physical integrations with computing systems. This paper proposes a pseudo quantum random number generator with a quantum algorithm called a quantum permutation pad, or QPP, leveraging the high entropy of quantum permutation space for its bijective transformation. Unlike Boolean algebra, where the size of information space is 2nfor an n-bit system, an n-bit quantum permutation space consists of 2n! quantum permutation matrices, representing all quantum permutation gates over an n-bit computational basis. This permutation space holds an equivalent Shannon information entropy of log2(2n!). A QPP can be used to create a pseudo-QRNG or pQRNG capable of integration with any classical computing system, or directly with any application, for good-quality deterministic random number generation. Using a QPP pad with 64 8-bit permuation matrices, a pQRNG holds 107,776 bits of entropy for pseudo-random number generation, compared with 4,096 bits of entropy in Linux /dev/random. It can be used as a deterministic PRNG or as an entropy booster for other PRNGs. It can also be used as a whitening algorithm for any hardware random number generator, including QRNGs, without discarding physical bias bits.
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).
This paper proposes a quantum safe solution for 5G networks using a quantum permutation pad (or QPP) algorithm, originated from quantum computing logic gates or quantum permutation gates. All permutation gates form a unique permutation space, just like a classical key space. An n-bit permutation space consists of the entire 2n! permutation gates, or permutation matrices over its computational basis. The huge equivalent Shannon entropy of this permutation space would be a nice entropy source for information security. Kuang and Bettenburg in 2020 first proposed QPP and proved it to be the Shannon type of perfect secrecy. Here, we extend its capability of entropy transformations for distribution over the Internet to entropy expansions for 5G networks. We analyze the randomnesses following transformations and expansions with QPP, using industry randomness testing suites. Testing results confirm that QPP can maintain the original randomness of QRNG random numbers for transformations and expansions. Leveraging its strong diffusion capability, QPP may also improve the byte-level randomness of input random numbers.
Quantum permutation pad or QPP is a set of quantum permutation gates. QPP has been demonstrated for quantum secure encryption in both classical and quantum computing systems recently, even at a noisy 5-qubit IBMQ systems. In a classical computing system, QPP encryption is implemented as a permutation gate matrix multiplication with information state vectors. In a quantum computing system, QPP is compiled into a quantum encryption circuit in a native quantum computer and encryption is performed through QPP circuit. Leveraging its quantum mechanical characteristics, we report a digital QKD or D-QKD platform using QPP as a quantum mechanical algorithm implemented in classical systems to distribute quantum entropy, generated from physical quantum random number generators or QRNG, and quantum key over the internet. D-QKD interfaces have been developed to support the photonic QKD standard ETSI-014. This makes any systems with ETSI QKD standards compatible with D-QKD. D-QKD offers point-to-point quantum entropy and quantum key distributions as well as point-to-multi-points quantum key synchronizations with speeds 1000x faster than photonic QKD. This paper reports benchmark performance tests and randomness quality tests for pure quantum entropy generated by a QRNG and expanded entropy using the QPP protocol. The work has been funded by the PlanQK1project and deployed within the OpenQKD2testbed Berlin, operated by Deutsche Telekom.
We propose a groundbreaking random number generator that achieves truly uniform, independent, and identically distributed (IID) randomness by integrating Quantum Permutation Pads (QPP) with system jitter-derived entropy, herein called IID-based QPP-RNG. Unlike conventional RNGs that use raw timing variations, our design uses system jitter solely to generate ephemeral QPP pads and derives 8-bit outputs directly from permutation counts, eliminating the need for post-processing. This approach leverages the factorial complexity of permutation sorting to systematically accumulate entropy from dynamic hardware interactions, ensuring non-deterministic outputs even from fixed seeds. Notably, IID-based QPP-RNG achieves a min-entropy of 7.85-7.95 bits per byte from IID minentropy estimate, surpassing ID Quantique's QRNG (7.157042 bits per byte), which marks a breakthrough in randomness quality. Our implementation employs a dynamic seed evolution protocol that continuously refreshes the internal state with unpredictable system jitter, effectively decoupling the QPP sequence from the initial seed. Cross-platform validation on macOS (x86 and ARM) and Windows (x86) confirms uniformly distributed outputs, while evaluations compliant with NIST SP 800-90B show a Shannon entropy of 7.9999 bits per byte. Overall, IID-based QPP-RNG represents a significant advancement in random number generation, offering a scalable, system-based, software-only, postquantum secure solution for a wide range of cryptographic applications.
Quantum Key Distribution(QKD) thrives to achieve perfect secrecy of One time Pad (OTP) through quantum processes. One of the crucial components of QKD are Quantum Random Number Generators(QRNG) for generation of keys. Unfortunately, these QRNG does not immediately produce usable bits rather it produces raw bits with high entropy but low uniformity which can be hardly used by any cryptographic system. A lot of pre-processing is required before the random numbers generated by QRNG to be usable. This causes a bottle neck in random number generation rate as well as QKD system relying on it. To avoid this lacuna of post-processing methods employed as a central part of Quantum Random Number Generators alternative approaches that satisfy the entropy(non determinism) and quantum security is explored. Pseudorandom generators based on quantum secure primitives could be an alternative to the post-processing problem as PRNGs are way more faster than any random number generator employing physical randomness (quantum mechanical process in QRNG) as well as it can provide uniform bits required for cryptography application. In this work we propose a pseudorandom generator based on post quantum primitives. The central theme of this random number generator is designing PRNG with non deterministic entropy generated through hard lattice problem - Learning with errors. We leverage the non determinism by Gaussian errors of LWE to construct non-deterministic PRNG satisfying the entropy requirement of QKD. Further, the paper concludes by evaluating the PRNG through Die-Harder Test.