A group theoretic construction of highly nonlinear substitution box and its applications in image encryption

Razaq, Abdul; Akhter, Shumaila; Yousaf, Awais; Shuaib, Umer; Ahmad, Musheer

doi:10.1007/s11042-021-11635-z

Cited by 18 publications

(7 citation statements)

References 53 publications

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“…In an identical way, we find all remaining cycles of the permutations 𝑥 and 𝑦 and given as: 𝑥 = (𝜉 1 , 𝜉 126 )(𝜉 2 , 𝜉 125 )(𝜉 3 , 𝜉 124 )(𝜉 4 , 𝜉 123 )(𝜉 5 , 𝜉 122 )(𝜉 6 , 𝜉 121 )(𝜉 7 , 𝜉 120 )(𝜉 8 , 𝜉 119 )(𝜉 9 , 𝜉 118 ) (𝜉 , 𝜉 117 )(𝜉 11 , 𝜉 116 )(𝜉 12 , 𝜉 115 )(𝜉 13 , 𝜉 114 )(𝜉 14 , 𝜉 113 )(𝜉 15 , 𝜉 112 )(𝜉 16 , 𝜉 111 )(𝜉 17 , 𝜉 110 )(𝜉 18 , 𝜉 109 ) (𝜉 , 𝜉 108 )(𝜉 20 , 𝜉 107 )(𝜉 21 , 𝜉 106 )(𝜉 22 , 𝜉 105 )(𝜉 23 , 𝜉 104 )(𝜉 24 , 𝜉 103 )(𝜉 25 , 𝜉 102 )(𝜉 26 , 𝜉 101 )(𝜉 27 , 𝜉 100 ) (𝜉 28 , 𝜉 99 )(𝜉 29 , 𝜉 98 )(𝜉 30 , 𝜉 97 )(𝜉 31 , 𝜉 96 )(𝜉 32 , 𝜉 95 )(𝜉 33 , 𝜉 94 )( 𝜉 34 , 𝜉 93 )( 𝜉 35 𝜉 92 )(𝜉 36 , 𝜉 91 )(𝜉 37 , 𝜉 90 ) (𝜉 38 , 𝜉 89 )(𝜉 39 , 𝜉 88 )(𝜉 40 , 𝜉 87 )(𝜉 41 , 𝜉 86 )(𝜉 42 , 𝜉 85 )(𝜉 43 , 𝜉 84 )(𝜉 44 64 ). 𝑦 = (0 , ∞, 1)(𝜉 1 , 𝜉 96 , 𝜉 30 ) (𝜉 2 , 𝜉 65 , 𝜉 60 )(𝜉 3 , 𝜉 120 , 𝜉 4 )(𝜉 5 , 𝜉 45 , 𝜉 77 )(𝜉 6 , 𝜉 113 , 𝜉 8 )(𝜉 7 , 𝜉 124 , 𝜉 123 ) (𝜉 , 𝜉 83 , 𝜉 35 )(𝜉 10 , 𝜉 90 , 𝜉 27 )(𝜉 11 , 𝜉 93 , 𝜉 <...…”

Section: Coset Graphs Ofmentioning

confidence: 99%

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Enhancing the Robustness of Block Ciphers through a Graphical S-Box Evolution Scheme for Secure Multimedia Applications

Razaq

Ahsan

Alolaiyan

et al. 2023

Preprint

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Block ciphers, which serve as primary components of network security systems, play a crucial role in securely exchanging and communicating confidential information. Substitution boxes (S-boxes) are the most significant components of contemporary block ciphers. Inherently, the security strength of such cryptosystems relies on the quality of the S-box employed. The cryptographically strong S-boxes provide robustness and assurance of the security competency to block ciphers. To generate the strong S-boxes, a number of chaos-based methods have been investigated in the past decade. However, chaos-based methods are random approaches which are computationally intensive and don’t guarantee the generation of strong S-boxes. To meet the challenges of strong and fast S-box generation, a novel coset graphs based algebraic method is proposed to evolve robust and efficient S-box. Firstly, an initial S-box of decent cryptographic strength is generated by using the vertices of coset graphs for two Galois fields and a bijective function. After that, the initial S-box's robustness is improved by rearranging its columns in a particular manner, which yields the strong proposed S-box. The effectiveness of the proposed method is validated by comparing various attributes of our S-box against some recently investigated S-boxes. Additionally, the generated S-box is applied for image encryption and analyzed using the MLC criterions. The results show the suitability of the proposed S-box for secure multimedia applications.

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Section: Coset Graphs Ofmentioning

confidence: 99%

“…For the construction of S-boxes, [11] presents a method that relies on elliptic curves over finite rings. In order to attain high nonlinearity in the construction of S-boxes, a new strategy was presented in [12]. This method combined finite graphs for (2,3,8) with a permutation group of high order.…”

mentioning

confidence: 99%

Enhancing the Robustness of Block Ciphers through a Graphical S-Box Evolution Scheme for Secure Multimedia Applications

Razaq

Ahsan

Alolaiyan

et al. 2023

Preprint

Self Cite

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“…The study of the action of the modular group PSL(2, Z) and its subgroups on various commutative algebraic structures has been common since the works of Graham Higman and his collaborators in the 1980s ( [8], [11], [12]). Moreover, various tracks of applications of the action of the modular group (especially in multimedia security) have been appearing recently, see for instance [1], [14], [16], [17], and [18]. This indeed suggests a promising future for the applications of this seemingly purely mathematical topic.…”

Section: Introductionmentioning

confidence: 97%

Revisiting the action of a subgroup of the modular group on imaginary quadratic number fields

Deajim¹

2022

Preprint

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Consider the modular group PSL(2, Z) = x, y | x 2 = y 3 = 1 generated by the transformations x : z → −1/z and y : z → (z − 1)/z. Let H be the proper subgroup y, v | y 3 = v 3 = 1 of PSL(2, Z), where v = xyx. The reference (M. Ashiq and Q. Mushtaq, Actions of a subgroup of the modular group on an imaginary quadratic field, Quasigropus and Related Systems 14 (2006), 133-146) proposed results concerning the action of H on the subset { a+ √ −n c | a, b = a 2 +n c , c ∈ Z, c = 0} of the imaginary quadratic number field Q( √ −n) for a positive square-free integer n.In the current article, the author points out and corrects errors appearing in the aforementioned reference. Most importantly, the corrected estimate for the number of orbits arising from this action is given.

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“…Razzaq et al in [5] used the concept of coset graph and symmetric group by the action on modular group for the construction of S-box and resultant S-box has optimal features. Newly published work on S-box construction by using the concept of coset graph and symmetric group ∆ (2,3,8) is present in [6]. Linear transformation (LT) is another area of research to construct the S-boxes.…”

Section: Introductionmentioning

confidence: 99%

A Novel Construction of Substitution Box Based on Polynomial Mapped and Finite Field With Image Encryption Application

et al. 2022

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In the modern block cipher, the substitution box (S-box) is a nonlinear constituent that plays a substantial role to create the confusion in ciphertext. S-boxes with low value of differential uniformity and high value of nonlinearity are considered more secure against cryptanalysis attacks. For the construction of 8×8 S-boxes, an efficient and novel scheme is presented in this paper. This scheme based on polynomial mapped and finite field which work only for even integers without multiple of 4 in the range (2-254). Firstly, we take a quadratic polynomial mapped for the construction of S-box from the newly designed map. To keep the S-box bijective, swap each missing entries with repeating entries after that we acquire the initial box. Secondly, to increase the randomness of initial S-box special permutations of symmetric group S256 used and generated the proposed S-box. Lastly, to examine the validity of the suggested S-box we used various tests such as nonlinearity (NL), bit independence criteria (BIC), strict avalanche criteria (SAC), differential uniformity (DU) and linear approximation probability (LAP) which all certify algebraic properties of S-box. Moreover, the features of newly constructed S-box compared with recent S-boxes from literature which show superior performance against intruders' attacks. Further, S-box is utilized in image encryption scheme and apply MLC (majority logic criterion) and histogram analysis to examined the encryption quality. Our results shows that proposed S-box based encryption scheme is very good as compared to other encryption methods.

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A group theoretic construction of highly nonlinear substitution box and its applications in image encryption

Cited by 18 publications

References 53 publications

Enhancing the Robustness of Block Ciphers through a Graphical S-Box Evolution Scheme for Secure Multimedia Applications

Enhancing the Robustness of Block Ciphers through a Graphical S-Box Evolution Scheme for Secure Multimedia Applications

Revisiting the action of a subgroup of the modular group on imaginary quadratic number fields

A Novel Construction of Substitution Box Based on Polynomial Mapped and Finite Field With Image Encryption Application

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