To Study the Effect of the Generating Polynomial on the Quality of Nonlinear Components in Block Ciphers

Mahmood, Shahid; Farwa, Shabieh; Rafiq, Muhammad; Riaz, Sadia; Shah, Tariq; Jamal, Sajjad Shaukat

doi:10.1155/2018/5823230

Cited by 19 publications

(9 citation statements)

References 21 publications

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“…Enhancement in nonlinearity (NL) value of initial S-box using dynamic permutation approach with respect to computation time is depicted in Figure 3. Although many authors suggested new methods to construct S-Box having nonlinearity>=112 like AES, these approaches lack one or more security criteria like non-bijectiveness [77], the existence of fixed points [45,78,79,80,81], high value of differential probability [82], static permutation [83], usage of fixed irreducible polynomial by [80,83] and AES, complex construction process [82], etc. Our proposed scheme for construction of S-box uses simple and novel dynamic transformation being the first one of its nature, employs dynamic affine transformation using modular multiplicative inversion as compared to the static affine transformation used in many of the above mentioned techniques employing complex GF inversion process, and a new dynamic permutation procedure in comparison to the static permutation utilized in these methods.…”

Section: G Fixed Points Analysis (Fpa)mentioning

confidence: 99%

Dynamic S-Box Design Using a Novel Square Polynomial Transformation and Permutation

et al. 2021

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New era ciphers employ substitution boxes (S-boxes) which assist in the provision of security for the plaintext in the encryption phase and transforming the ciphertext on the receiver side into original plaintext in the decryption phase. The overall security of a given cipher engaging an S-box greatly depends on the cryptographic forte of the respective S-box. Consequently, many researchers have used different innovative approaches to construct robust S-Boxes. In this article, an innovative and modest square polynomial transformation, the very first time, along with a novel affine transformation and a pioneering permutation approach to construct dynamic S-boxes is proposed. The proposed method has the capability to erect a huge number of robust S-boxes by applying minute changes in the parameters of transformation and permutation processes. An example S-Box is generated, and its recital analysis has been done using typical criteria including bijectivity, strict avalanche criterion, nonlinearity, bit independence criterion, linear probability, differential probability, and fixed-point analysis to check its cryptographic forte. This performance of the proposed S-box is placed side by side against state-of-the-art S-boxes to prove its strength. The performance and comparative analyses authenticate that the projected S-box possesses the true competence for its application in modern-day ciphers.

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Section: G Fixed Points Analysis (Fpa)mentioning

confidence: 99%

Dynamic S-Box Design Using a Novel Square Polynomial Transformation and Permutation

et al. 2021

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“…In [ 17 ], the authors proposed two different S-boxes for AES by modifying the affine transformation matrices. In [ 18 , 19 ], the authors proposed a variable and dynamic S-box mapping for AES using different irreducible polynomials. Thus, a different S-box is generated in each round of AES, which enhances the security of AES but only generates a limited number of S-boxes.…”

Section: Introductionmentioning

confidence: 99%

A highly nonlinear substitution-box (S-box) design using action of modular group on a projective line over a finite field

Siddiqui

Yousaf

Murtaza³

et al. 2020

PLoS ONE

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Cryptography is commonly used to secure communication and data transmission over insecure networks through the use of cryptosystems. A cryptosystem is a set of cryptographic algorithms offering security facilities for maintaining more cover-ups. A substitution-box (S-box) is the lone component in a cryptosystem that gives rise to a nonlinear mapping between inputs and outputs, thus providing confusion in data. An S-box that possesses high nonlinearity and low linear and differential probability is considered cryptographically secure. In this study, a new technique is presented to construct cryptographically strong 8×8 S-boxes by applying an adjacency matrix on the Galois field GF(28). The adjacency matrix is obtained corresponding to the coset diagram for the action of modular group PSL(2,Z) on a projective line PL(F7) over a finite field F7. The strength of the proposed S-boxes is examined by common S-box tests, which validate their cryptographic strength. Moreover, we use the majority logic criterion to establish an image encryption application for the proposed S-boxes. The encryption results reveal the robustness and effectiveness of the proposed S-box design in image encryption applications.

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“…The authors in [46] proposed two different S-boxes instead of one AES S-box by modifying the affine transformation matrices that are used alternatively in the algorithm. In [47], [48] the authors proposed a variable mapping S-boxes for AES. Using secret key as well as using different irreducible polynomials produce dynamic S-boxes.…”

Section: Introductionmentioning

confidence: 99%

Generation of Highly Nonlinear and Dynamic AES Substitution-Boxes (S-Boxes) Using Chaos-Based Rotational Matrices

et al. 2020

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This work reports a novel chaos-based affine transformation generation method, which is based on rotational matrices to design strong key-based S-boxes. Chaotic logistic map's nonlinear trajectories are used to generate rotational matrices under given design conditions. Thus, the inherent logic is to generate key-based S-boxes, as strong as AES S-box, in terms of cryptographic properties using chaos in affine transformation. The randomness of chaotic sequences is tested using the National Institute of Standard and Technology (NIST) Statistical Test Suit (STS) 800-22 that validates the generated sequences for S-box design. The results show that methodology adapted to design proposed key-based dynamic S-boxes entails near-optimal cryptographic properties so that proposed S-boxes are as stronger as AES S-box. INDEX TERMS Affine transformation, chaotic logistic map, S-box, NIST test.

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To Study the Effect of the Generating Polynomial on the Quality of Nonlinear Components in Block Ciphers

Cited by 19 publications

References 21 publications

Dynamic S-Box Design Using a Novel Square Polynomial Transformation and Permutation

Dynamic S-Box Design Using a Novel Square Polynomial Transformation and Permutation

A highly nonlinear substitution-box (S-box) design using action of modular group on a projective line over a finite field

Generation of Highly Nonlinear and Dynamic AES Substitution-Boxes (S-Boxes) Using Chaos-Based Rotational Matrices

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