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Chinese Physics B

Effect of pseudo-random number on the security of quantum key distribution protocol

Xiaoliang Yang, Yu-Qing 毓擎 Li 李, Hong-Wei Li

Published Dec 3, 2024• 4 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/ad99c9

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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.
Abstract Quantum random key distribution based on physical properties of quantum mechanics has high security and true randomness, but it has the disadvantages of low key generation efficiency and high cost. The classic pseudo-random number generator has the advantages of simple algorithm and high key generation efficiency, but it has extremely strict requirements on the security and randomness of the "seed". Based on the analysis of two unrelated technologies, this paper proposes a pseudo-random number generation scheme based on quantum key distribution. This scheme makes full use of quantum key distribution to share a short quantum random number-seed between the two communicating parties, then inputs the seed into a pseudo-random number generator. Finally, the two communicating parties share a long random number to encrypt the communication content. Research shows that compared with classic quantum key distribution and classic pseudo-random number generator, this scheme has stronger security, better randomness, and higher key generation efficiency.
Quantum key distribution (QKD) relies on randomness to exchange secret keys among the communicating parties. While ensuring the secrecy of the keys being distributed, independent randomness also causes to reduce the number of key bits that can be shared per quantum signal exchanged. Recently it was shown that it is possible to use pseudo-randomness in place of true randomness in the QKD without compromising the integrity of a QKD scheme. By the virtue of a short secret key — called a control key — shared among the key sharing parties, same pseudo-randomness can be generated at the transmitter and the receiver end that allow to obtain a higher key exchange rate. However, there are certain modifications which are necessary before pseudo-randomness can be safely employed in a QKD procedure. In this paper, we provide a modification of QKD schemes for a secure use with the control key. We modify the prepare-and-measure (BB84) type, and measurement-device independent protocols. We then verify the advantages of use of control key in terms of key rates for the modification of two QKD schemes.
Quantum key distribution (QKD) schemes rely on the randomness to exchange secret keys between two parties. A control key to generate the same (pseudo)-randomness for the key exchanging parties increases the key exchange rate. However, the use of pseudo-randomness where true randomness is required makes a classical system vulnerable to the known plain-text attack. Contrary to the belief of unavailability of this attack in QKD, we show that this attack is actually possible whenever a control key is employed. In this paper, we show that it is possible to make use of the uncertainty principle to not only avoid this attack, but also remove the hazards of photon-number splitting attack in quantum setting. We define the secrecy of control key based on the guessing probability, and propose a scheme to achieve this defined secrecy. We show the general applicability of our framework on the most common QKD schemes.
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.
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.