Highly Nonlinear Balanced S-Boxes With Good Differential Properties

Zhang, Weiguo; Pašalić, Enes

doi:10.1109/tit.2014.2360880

Cited by 38 publications

(17 citation statements)

References 13 publications

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“…Designing powerful S-boxes is an important critereon for realisation of secure cryptosystems and it is a major component of nonlinear transformations, which are the fulcrum of confusion and diffusion analysis for assessing well-designed ciphers 41 . Therefore, designing S-boxes based on secure mechanisms plays an important part in modern cryptographic tasks 42,43 . Consequently, it is widely investigated.…”

Section: S-box Constructionmentioning

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

116

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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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Section: S-box Constructionmentioning

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

116

View full text Add to dashboard Cite

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“…, f m } is a basis of an mdimensional vector space of bent functions over F 2 . Classical examples of vectorial bent functions arise from the Maiorana-McFarland class and the partial spread class, see for instance [2,9,15]. As already shown by Nyberg in [9, Theorem 3.2], for a vectorial Boolean bent function m can be at most n/2.…”

Section: Vectorial Gbent Functionsmentioning

confidence: 92%

Partial spread and vectorial generalized bent functions

Martinsen

Meidl

Stănică

2016

Des. Codes Cryptogr.

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In this paper we generalize the partial spread class and completely describe it for generalized Boolean functions from F n 2 to Z 2 t . Explicitly, we describe gbent functions from F n 2 to Z 2 t , which can be seen as a gbent version of Dillon's P S ap class. For the first time, we also introduce the concept of a vectorial gbent function from F n 2 to Z m q , and determine the maximal value which m can attain for the case q = 2 t . Finally we point to a relation between vectorial gbent functions and relative difference sets.

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“…For instance, the best affine approximation attack [3] and linear approximation attack [4] both reflect the importance of designing highly nonlinear Sboxes. The construction of resilient S-boxes with high nonlinearity has been an important challenge in cryptography since mid 1990s, and it was extensively studied in [6,7,8,9,10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Construction of resilient S‐boxes with higher‐dimensional vectorial outputs and strictly almost optimal non‐linearity

Zhang

Pašalić

2017

IET Information Security

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Resilient substitution boxes (S-boxes) with high nonlinearity are important cryptographic primitives in the design of certain encryption algorithms. There are several trade-offs between the most important cryptographic parameters and their simultaneous optimization is regarded as a difficult task. In this paper we provide a construction technique to obtain resilient S-boxes with so-called strictly almost optimal (SAO) nonlinearity for a larger number of output bits m than previously known. This is the first time that the nonlinearity bound 2 n−1 − 2 n/2 of resilient (n, m) S-boxes, where n and m denote the number of the input and output bits respectively, has been exceeded for m > n 4. Thus, resilient S-boxes with extremely high nonlinearity and a larger output space compared to other design methods have been obtained.

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Highly Nonlinear Balanced S-Boxes With Good Differential Properties

Cited by 38 publications

References 13 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

Partial spread and vectorial generalized bent functions

Construction of resilient S‐boxes with higher‐dimensional vectorial outputs and strictly almost optimal non‐linearity

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