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.
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.
Recently, there has been a growing interest among researchers in Pseudo-Random Binary Sequences (PRBS) for Quantum Key Distribution (QKD). QKD is a cryptographic protocol that distributes secret keys between senders and receivers, relying on random numbers to determine the basis for evaluating transmitted bits. Quantum Random Number Generators (QRNG) utilizing natural resources create random bit sequences for QKD. However, QRNGs are susceptible to natural noise, which compromises their security. Additionally, post-processing of QRNG-generated sequences is necessary to reduce noise, but this process slows down the random number generation speed in QKD. Non-deterministic Pseudo-Random Sequence Generators (ND-PRSG) may overcome the QRNG's constraints, post-processing, and speed. Lattice-based NDPRSG provides security and efficiency. The proposed work focuses on generating a uniform PRBS with non-deterministic entropy using Learning with Errors (LWE) and LFSR. NIST Statistical Tests are performed on generated PRBS for randomness analysis, and the results are reported. The proposed PRBS generation can be used for QKD, operating up to 20.17 Mbit/s.
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.
This paper explores the design of cryptographic algorithms leveraging the inherent randomness of quantum random number generators (QRNGs). Traditional cryptographic algorithms often rely on pseudo-random number generators (PRNGs), which are deterministic and therefore vulnerable to attacks if their internal state is compromised. QRNGs, on the other hand, derive their randomness from quantum mechanical phenomena, offering a fundamentally unpredictable source of numbers. This research investigates the application of QRNGs to enhance cryptographic security, focusing on constructing algorithms that exploit this unique property. The core claim is that utilizing QRNG characteristics allows for the design of more secure cryptographic algorithms. The proposed mechanism involves capitalizing on the non-deterministic nature of QRNGs to build algorithms with heightened security levels. This approach presents a novel security guarantee method by incorporating true randomness into cryptographic processes. We examine specific algorithm designs and analyze their security implications compared to traditional PRNG-based approaches. The paper concludes with a discussion on the challenges and future directions of utilizing QRNGs in cryptography.
The Gaussian Error, represented by random numbers with a Gaussian distribution, plays a critical role in the security of modern lattice-based cryptography. Lattice-based cryptography is the most important category of post-quantum cryptography capable of resisting attacks from both classical and quantum.While current schemes of generating Gaussian Error used in lattice cryptography face severe challenges. On the one hand, the current scheme produces an approximate Gaussian distribution rather than the rigorously proven Gaussian distribution required in lattice cryptography, posing a security risk. Meanwhile, the Gaussian Error of current schemes is obtained by using algorithms to compute uniformly distributed random numbers, which lack provable randomness and also pose security risks. On the other hand, the generation rate of Gaussian Error is not high enough for many applications of cryptographic systems in current schemes. To address these challenges, this paper proposes a novel scheme that uses a quantum random number generator(QRNG) to generate the Gaussian Error, which follows a theoretically proven Gaussian distribution and satisfies rigorous security justification in lattice cryptography. Furthermore, based on the quantum mechanical process of measuring vacuum fluctuations and the principle of minimum entropy under classical noise conditions, the Gaussian Error obtained by our scheme is theoretically unpredictable, further enhancing the security of lattice cryptography compared to the current schemes. Finally, an experiment for generating Gaussian Error was constructed, and our experimental results demonstrate that the Gaussian Error generation rate is 1 G/s, which achieves higher speed among existing works.
One of the solutions to the problem of secure communication is the Quantum Random Number Generators (QRNGs) which generate true randomness based on quantum mechanical principles.QRNGs are different from conventional pseudo random number generator in that they use quantum uncertainty to generate outputs which are very unpredictable.This work attempts to examine different QRNG architectures, study the possible integration of cryptographic frameworks with these architectures and highlight potential vulnerabilities in the integration of cryptographic frameworks with QRNG architectures.Post-processing techniques, i.e.Zero-Phase Component Analysis (ZPCA) and neural network based techniques are also studied to increase entropy and suppress environmental noise in QRNG systems.Key findings show that system jitter models based QRNG architectures are more scalable and less expensive for use in real world applications.Additionally, incorporating cryptographic protocols with the QRNGs endows them with the ability to resist quantum threats, and hence, provide better key distribution in the secure IoT communication frameworks.However, as security problems such as side channel attacks and hardware manipulation are still big issues.It also points out some of the emerging research trends including hybrid QRNG architectures, i.e., QRNG with classical PRNG to increase the entropy rate.As such, the proposed methodologies attempt to enhance QRNG scalability, security, and energy efficiency in cloud infrastructures, in mobile systems and in critical security environments.The advancement of these technologies will assume a crucial function in the advancement of quantum-safe frames for current advanced computerized foundation.
Even if the output of a Random Number Generator (RNG) is perfectly uniformly distributed, it may be correlated to pre-existing information and therefore be predictable. Statistical tests are thus not sufficient to guarantee that an RNG is usable for applications, e.g., in cryptography or gambling, where unpredictability is important. To enable such applications a stronger notion of randomness, termed "true randomness", is required, which includes independence from prior information. Quantum systems are particularly suitable for true randomness generation, as their unpredictability can be proved based on physical principles. Practical implementations of Quantum RNGs (QRNGs) are however always subject to noise, i.e., influences which are not fully controlled. This reduces the quality of the raw randomness generated by the device, making it necessary to post-process it. Here we provide a framework to analyse realistic QRNGs and to determine the post-processing that is necessary to turn their raw output into true randomness.