A Truly Dynamic Substitution Box Generator for Block Ciphers Based on Elliptic Curves Over Finite Rings

Hayat, Umar; Azam, Naveed Ahmed; Gallegos-Ruiz, Homero R.; Naz, Sadia; Batool, Lubna

doi:10.1007/s13369-021-05666-9

Cited by 28 publications

(35 citation statements)

References 63 publications

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“…The AC of the presented S-box is greater than the AC of the S-boxes proposed in [51,58,64,65] and equal to that of the S-boxes [37,62,63,66]. From the above discussion, it is obvious that the proposed S-box is highly secure against linear attacks, compared to the S-boxes in [37,51,58,[62][63][64][65][66], while the security of the proposed S-box against linear attacks is comparable with the S-boxes in [8,12,48].…”

Section: Linear Attacksmentioning

confidence: 76%

“…The values of the NL, LAP, and AC for the S-box shown in Table 1 are 106, 0.0156, and 254, respectively. Moreover, from Table 2, it follows that the NL of the proposed S-box is greater than those of [51,[62][63][64][65][66] and equal to NL of the S-boxes in [8,12,37,48,58]. Similarly, the LAP of the new S-box is less than the LAP of the S-boxes in [8,12,37,48,51,58,[62][63][64][65][66].…”

Section: Linear Attacksmentioning

confidence: 92%

“…Moreover, from Table 2, it follows that the NL of the proposed S-box is greater than those of [51,[62][63][64][65][66] and equal to NL of the S-boxes in [8,12,37,48,58]. Similarly, the LAP of the new S-box is less than the LAP of the S-boxes in [8,12,37,48,51,58,[62][63][64][65][66]. The AC of the presented S-box is greater than the AC of the S-boxes proposed in [51,58,64,65] and equal to that of the S-boxes [37,62,63,66].…”

Section: Linear Attacksmentioning

confidence: 95%

“…Cheon et al [10] used hyperelliptic curves to obtain a lower bound on the nonlinearity of Boolean functions. Hayat et al [11,12] employed ECs over finite fields and rings to design secure S-boxes. It is analyzed that the S-box generators over finite rings generate dynamic S-boxes with reasonable time complexity.…”

Section: Introductionmentioning

confidence: 99%

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A Novel Image Encryption Scheme Based on Elliptic Curves over Finite Rings

Azam

2022

Entropy

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Image encryption based on elliptic curves (ECs) is emerging as a new trend in cryptography because it provides high security with a relatively smaller key size when compared with well-known cryptosystems. Recently, it has been shown that the cryptosystems based on ECs over finite rings may provide better security because they require the computational cost for solving the factorization problem and the discrete logarithm problem. Motivated by this fact, we proposed a novel image encryption scheme based on ECs over finite rings. There are three main steps in our scheme, where, in the first step, we mask the plain image using points of an EC over a finite ring. In step two, we create diffusion in the masked image with a mapping from the EC over the finite ring to the EC over the finite field. To create high confusion in the plain text, we generated a substitution box (S-box) based on the ordered EC, which is then used to permute the pixels of the diffused image to obtain a cipher image. With computational experiments, we showed that the proposed cryptosystem has higher security against linear, differential, and statistical attacks than the existing cryptosystems. Furthermore, the average encryption time for color images is lower than other existing schemes.

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Section: Linear Attacksmentioning

confidence: 76%

Section: Linear Attacksmentioning

confidence: 92%

Section: Linear Attacksmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

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A Novel Image Encryption Scheme Based on Elliptic Curves over Finite Rings

Azam

2022

Entropy

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“…A dynamic S-Box depends on the key and is stronger and more effective in terms of confusion as compared to a static S-Box [6], [7]. Over the years, cryptography researchers developed many S-Boxes which have used different models like dynamic random growth technique [8], DNA computing [9], [10], optimization techniques [11]- [14], linear fractional transformation (LFT) [15]- [17], cellular automata [18], elliptic curve [19]- [22], etc. Recently, chaotic maps have become extensively pragmatic in the design of novel S-boxes for secure communication [23]- [25].…”

Section: Introductionmentioning

confidence: 99%

A New Dynamic Substitution Box for Data Security Using an Innovative Chaotic Map

2022

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As the motivations and capabilities of threat actors continue to evolve, providing data security has become more important than ever. For this purpose, different ciphers using various techniques are being developed. Currently, chaotic maps are designed and applied in the development of these ciphers. Modern ciphers utilize a substitution box (S-Box) as a core module to provide data security. In this article, an innovative chaotic map is suggested for the design of new and dynamic S-Box. Criteria like Bijectiveness, Nonlinearity (NL), Strict Avalanche Criterion (SAC), Bit Independence Criterion (BIC), Linear Approximation Probability (LP), and Differential Approximation Probability (DP) are used to critically analyze and evaluate the proposed S-Box performance against various attacks. The cryptanalytic strength of the proposed S-Box is equated with freshly designed S-Boxes for its customization in real-life security applications. The comparative analysis gratifies the true potential of the proposed S-Box for its solicitation in data security domain.

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