Discrete-time interacting quantum walks and quantum Hash schemes

Li, Dan; Zhang, Jie; Guo, Fen-Zhuo; Huang, Wei; Wen, Qiaoyan; Chen, Hui

doi:10.1007/s11128-012-0421-8

Cited by 60 publications

(44 citation statements)

References 25 publications

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“…Hence, the quantum mechanical implementation of quantum walks is deemed outside the purview of this present work. Nevertheless, we enrich our bibliography by including interesting studies on such implementation 19,20,[31][32][33][34][35][36][37][38][39][40] from where interested readers can obtain further details.…”

mentioning

confidence: 99%

Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications

El‐Latif

Abd-El-Atty

Amin

et al. 2020

Sci Rep

109

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Designing efficient and secure cryptosystems has been a preoccupation for many scientists and engineers for a long time wherein they use chaotic systems to design new cryptosystems. While one dimensional (1-D) chaotic maps possess powerful properties compared to higher dimension ones, they are vulnerable to various attacks due to their small key space, chaotic discontinuous ranges, and degradation in chaotic dynamical behaviours. Moreover, when simulated on a computer, every such chaotic system produces a periodic cycle. Meanwhile, quantum random walks exhibit the potential for deployment in efficient cryptosystem design, which makes it an excellent solution for this problem. In this context, we present a new method for constructing substitution boxes (S-boxes) based on cascaded quantum-inspired quantum walks and chaos inducement. the performance of the proposed S-box scheme is investigated via established S-box evaluation criterion and outcomes suggest that the constructed S-box has significant qualities for viable applications information security. Further, we present an efficient scheme for pseudo-random numbers generation (PRNG) whose sustainability over long periods remedies the periodicity problem associated with traditional cryptographic applications. Furthermore, by combining the two mechanisms, an atypical image encryption scheme is introduced. Simulation results and analysis validate that the proposed image encryption algorithm will offer gains in many cryptographic applications. Chaotic systems have attracted a great deal of attention across different scientific and engineering disciplines, especially in designing new cryptosystems and cryptanalysis. A chaotic system is an evolution map of a deterministic dynamical system that reconstructs the state of a system S 0 to a new state S 1 depending on the initial state of S 0 , a control parameter C, and time T 1. Chaotic maps exhibit the desired properties of ergodicity, unpredictability, and sensitivity to their control parameter(s) and initial value(s) that satisfy the requirements for cryptosystem confusion-diffusion properties 2-4. In fact, an inappropriate initial control parameter of a chaotic system can lead to non-chaotic behaviours, which implies the reduction in nonlinearity levels as well as circumvention of insecurity pitfalls 5,6. Currently, chaotic dynamical systems play a vital role in designing modern cryptographic applications, such as constructing S-boxes, generating pseudo-random numbers, designing image encryption algorithms and so on 7-16 , which are based on the unproven assumptions pertaining to computational complexity and that their constructions are based on mathematical models. However, with the development of quantum technologies, some of these traditional security mechanisms, and cryptographic applications may be effortlessly violated and abused 17-19. Among the computational models developed in quantum computation, quantum walks (QWs), which is a universal model of quantum computation that has been traditionally employed to de...

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mentioning

confidence: 99%

Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications

El‐Latif

Abd-El-Atty

Amin

et al. 2020

Sci Rep

109

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“…CAQW based quantum hash function doesn't have predictable collisions in Ref. [2]. Furthermore, implementing CAQW based quantum hash function significantly reduces the resources necessary for its feasible experimental realization than implementing CIQW based quantum hash functions in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…al. presented a kind of quantum hash function based on two-particle controlled interacting quantum walks (CIQW) [2,3] . This quantum hash function guarantees the security of hash function by infinite possibilities of the initial state and the irreversibility of measurement rather than hard mathematic problems.…”

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confidence: 99%

Controlled Alternate Quantum Walks based Quantum Hash Function

Yang

et al. 2018

Sci Rep

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Through introducing controlled alternate quantum walks, we present controlled alternate quantum walks (CAQW) based quantum hash function. CAQW based quantum hash function have excellent security, outstanding statistical performance and splendid expansibility. Furthermore, due to the structure of alternate quantum walks, implementing CAQW based quantum hash function significantly reduces the resources necessary for its feasible experimental realization than implementing other quantum hash functions.

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“…One of the first considerations of a quantum function as a cryptographic primitive, having the one-way property and the collision resistance property, is due to [31], where the quantum fingerprinting function from [26] was used. Another approach towards constructing quantum hash functions from quantum walks was considered in [51,52,66], and it resulted in privacy amplification in quantum key distribution and other useful applications.…”

Section: Quantum Hashingmentioning

confidence: 99%

Classical and Quantum Computations with Restricted Memory

Ablayev

Khadiev

et al. 2018

Adventures Between Lower Bounds and Higher Altitudes

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Automata and branching programs are known models of computation with restricted memory. These models of computation were in focus of a large number of researchers during the last decades. Streaming algorithms are a modern model of computation with restricted memory. In this paper, we present recent results on the comparative computational power of quantum and classical models of branching programs and streaming algorithms. In addition to comparative complexity results, we present a quantum branching program for computing a practically important quantum function (quantum hash function) and prove optimality of this algorithm.

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Discrete-time interacting quantum walks and quantum Hash schemes

Cited by 60 publications

References 25 publications

Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications

Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications

Controlled Alternate Quantum Walks based Quantum Hash Function

Classical and Quantum Computations with Restricted Memory

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