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IEEE International Carnahan Conference on Security Technology (ICCST)

Pseudo Random Binary Sequence using Lattice-based Hard Problem for Quantum Key Distribution

Anupama Arjun Pandit, Arun Mishra

Published Oct 11, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.1109/iccst59048.2023.10474268

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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.
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.
Abstract In the process of quantum key distribution (QKD), the communicating parties need to randomly determine quantum states and measurement bases. To ensure the security of key distribution, we aim to use true random sequences generated by true random number generators as the source of randomness. In practical systems, due to the difficulty of obtaining true random numbers, pseudo-random number generators are used instead. Although the random numbers generated by pseudo-random number generators are statistically random, meeting the requirements of uniform distribution and independence, they rely on an initial seed to generate corresponding pseudo-random sequences. Attackers may predict future elements from the initial elements of the random sequence, posing a security risk to quantum key distribution. This paper analyzes the problems existing in current pseudo-random number generators and proposes corresponding attack methods and applicable scenarios based on the vulnerabilities in the pseudo-random sequence generation process. Under certain conditions, it is possible to obtain the keys of the communicating parties with very low error rates, thus effectively attacking the quantum key system. This paper presents new requirements for the use of random numbers in quantum key systems, which can effectively guide the security evaluation of quantum key distribution protocols.
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.
Topicality. Reliable random number generation is one of the key requirements for modern cryptographic systems and cybersecurity applications. Traditional pseudo-random number generators are based on deterministic algorithms and may exhibit limited entropy and predictability, which can negatively affect information security. The subject of study in the article is methods of quantum random number generation and approaches to evaluating the quality of generated random sequences. The purpose of the article is to analyze modern methods of quantum random number generation, develop a software tool for obtaining quantum random numbers based on the ANU Quantum Random Number Generator service, perform statistical testing of the generated sequences, and analyze the obtained results. The following results were obtained. Modern quantum random number generation systems were analyzed and compared. A software tool was implemented in Python for automatic retrieval of quantum random numbers through the ANU QRNG API. The generated binary sequences were evaluated using Frequency Test and Block Frequency Test from the NIST SP 800-22 statistical test suite. The obtained p-values were 0.977181 and 0.200659 respectively, confirming successful completion of both tests. Additionally, visual analysis of the generated sequences revealed no noticeable patterns or repetitive structures. Conclusion. The obtained results confirm the high quality of quantum random sequences generated using ANU QRNG and demonstrate the applicability of the developed software tool for cryptographic and cybersecurity applications requiring high-quality randomness.
Random Numbers determine the security level of cryptographic applications as they are used to generate padding schemes in the encryption/decryption process as well as used to generate cryptographic keys. This paper utilizes the QKD to generate a random quantum bit rely on BB84 protocol, using the NIST and DIEHARD randomness test algorithms to test and evaluate the randomness rates for key generation. The results show that the bits generated using QKD are truly random, which in turn, overcomes the distance limitation (associated with QKD) issue, its well-known challenges with the sending/ receiving data process between different communication parties
Random Numbers determine the security level of cryptographic applications as they are used to generate padding schemes in the encryption/decryption process as well as used to generate cryptographic keys.This paper utilizes the QKD to generate a random quantum bit rely on BB84 protocol, using the NIST and DIEHARD randomness test algorithms to test and evaluate the randomness rates for key generation.The results show that the bits generated using QKD are truly random, which in turn, overcomes the distance limitation (associated with QKD) issue, its well-known challenges with the sending/ receiving data process between different communication parties.