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Scientific Reports

Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption

Yu‐Guang Yang, Peng Xu, Rui Zhe Yang, Yi‐Hua Zhou, Wei‐Min Shi

Published Jan 29, 2016• 106 citations
Publisher

Abstract

Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.

DOI
10.1038/srep19788

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Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.
Quantum computation has achieved a tremendous success during the last decades. In this paper, we investigate the potential application of a famous quantum computation model, i.e., quantum walks (QW) in image encryption. It is found that QW can serve as an excellent key generator thanks to its inherent nonlinear chaotic dynamic behavior. Furthermore, we construct a novel QW-based image encryption algorithm. Simulations and performance comparisons show that the proposal is secure enough for image encryption and outperforms prior works. It also opens the door towards introducing quantum computation into image encryption and promotes the convergence between quantum computation and image processing.
This paper examines classical privacy amplification using a universal family of hash functions. In quantum key distribution, the adversary's measurement can wait until the choice of hash functions is announced, and so the adversary's information may depend on the choice. Therefore the existing result on classical privacy amplification, which assumes the independence of the choice from the other random variables, is not applicable to this case. This paper provides a security proof of privacy amplification which is valid even when the adversary's information may depend on the choice of hash functions. The compression rate of the proposed privacy amplification can be taken to be the same as that of the existing one with an exponentially small loss in secrecy of a final key.
The hash functions have been at the center of the data security algorithms for the last two decades. However, with the emergence of quantum computing, conventional methods of data security are under review and scrutiny. At this juncture, the concept of quantum hash function comes to the rescue with its immensely important uses in the field of post quantum data security, especially in quantum key distribution. In this chapter we will present the theory behind quantum hash functions, followed by its uses for post quantum cryptography models, particularly for image data. The algorithms using quantum hash function are also discussed, along with their individual performance.
Privacy amplification is an indispensable step in the post-processing of quantum key distribution, which can be used to compress the redundancy of shared key and improve the security level of the key. The commonly used privacy amplification is based on the random selection of universal hash functions, which needs the help of an additional random source, while it does not exist in general. In this paper, we propose a privacy amplification scheme based on composite coding, which is an extension of quantum CSS codes to classical linear codes. Compared with the universal hashing function, the proposed scheme does not need other random sources, and the randomness can be completely provided by the qubit string. Furthermore, the information-theoretic bound for the extraction of the key is obvious in composite coding.
Secure image transmission has become critical in the emerging quantum computing landscape. This research introduces a hybrid key quantum encryption approach that combines Quantum True Random Number Generation (QTRNG) and Quantum Pseudo Random Number Generation (QPRNG) to enhance security and efficiency. The proposed Quantum Hybrid Random Number Generator (QHRNG) integrates entanglement-based true randomness with structured pseudo-randomness using Hadamard, controlled rotation and Clifford gates to generate high-entropy encryption keys. The generated Quantum keys are applied to encrypt grayscale images using the Novel Enhanced Quantum Image Representation (NEQR). The encryption process is strengthened by quantum bit-level scrambling and selective Quantum Fourier Transform. The proposed method is implemented on Qiskit’s Aer and Basic simulators and validated on IBM’s torino quantum hardware. Compared to standalone QTRNG and QPRNG methods, QHRNG consistently provides higher randomness and stronger security in noisy and noiseless environments. This work offers a robust and future-ready framework for quantum secure image encryption.
Quantum Key Distribution (QKD) protocols typically involve two separate steps of error-verification and privacy amplification. Both steps involve the application of a hash function sampled from a suitable hash family to classical data. A potentially simpler alternative is to implement a single-step hashing procedure, announce and compare a fixed number of bits of its output for error-verification, and retain the remaining bits as the final output key. This reduces the complexity of classical postprocessing, the amount of classical communication, and the amount of randomness needed in the protocol. While this construction has appeared in the literature, a suitable mathematical justification is lacking. In this work, we show that the security of such protocols, under certain simple conditions, follows from a slightly modified notion of secrecy of the protocol without the final error-verification step. In particular, we show that for most entropy-based proofs, the combined protocol can be implemented with no change to the key rate, and a minor change to the security parameter.