A novel systematic byte substitution method to design strong bijective substitution box (S-box) using piece-wise-linear chaotic map
Cryptography deals with designing practical mathematical algorithms having the two primitive elements of confusion and diffusion. The security of encrypted data is highly dependent on these two primitive elements and a key. S-box is the nonlinear component present in a symmetric encryption algorithm...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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PeerJ Inc.
2022-05-01
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| Series: | PeerJ Computer Science |
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| Online Access: | https://peerj.com/articles/cs-940.pdf |
| _version_ | 1811255341314211840 |
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| author | Asim Ali Muhammad Asif Khan Ramesh Kumar Ayyasamy Muhammad Wasif |
| author_facet | Asim Ali Muhammad Asif Khan Ramesh Kumar Ayyasamy Muhammad Wasif |
| author_sort | Asim Ali |
| collection | DOAJ |
| description | Cryptography deals with designing practical mathematical algorithms having the two primitive elements of confusion and diffusion. The security of encrypted data is highly dependent on these two primitive elements and a key. S-box is the nonlinear component present in a symmetric encryption algorithm that provides confusion. A cryptographically strong bijective S-box structure in cryptosystem ensures near-optimal resistance against cryptanalytic attacks. It provides uncertainty and nonlinearity that ensures high confidentiality and security against cryptanalysis attacks. The nonlinearity of an S-box is highly dependent on the dispersal of input data using an S-box. Cryptographic performance criteria of chaos-based S-boxes are worse than algebraic S-box design methods, especially differential probability. This article reports a novel approach to design an 8 × 8 S-box using chaos and randomization using dispersion property to S-box cryptographic properties, especially differential probability. The randomization using dispersion property is introduced within the design loop to achieve low differential uniformity possibly. Two steps are involved in generating the proposed S-box. In the first step, a piecewise linear chaotic map (PWLCM) is utilized to generate initial S-box positions. Generally, the dispersion property is a post-processing technique that measures maximum nonlinearity in a given random sequence. However, in the second step, the concept is carefully reverse engineered, and the dispersion property is used within the design loop for systematic dispersal of input substituting sequence. The proposed controlled randomization changes the probability distribution statistics of S-box’s differentials. The proposed methodology systematically substitutes the S-box positions that cause output differences to recur for a given input difference. The proposed S-box is analyzed using well-established and well-known statistical cryptographic criteria of nonlinearity, strict avalanche criteria (SAC), bit independence criteria (BIC), differential probability, and linear probability. Further, the S-box’s boomerang connectivity table (BCT) is generated to analyze its strength against boomerang attack. Boomerang is a relatively new attacking framework for cryptosystem. The proposed S-box is compared with the state-of-the-art latest related publications. Results show that the proposed S-box achieves an upper bound of cryptographic properties, especially differential probability. This work hypothesizes that highly dispersive hamming distances at output difference, generated a systematic S-box. The mixing property of chaos generated trajectories utilized for decimal mapping. To test the randomness of generated chaotic trajectories, a cryptographically secure pseudo-random sequence was generated using a chaotic map that was tested using the National Institute of Standards and Technology (NIST) NIST-800-22 test suit. |
| first_indexed | 2024-04-12T17:22:22Z |
| format | Article |
| id | doaj.art-3f16b7f159114594aea930859b5f319f |
| institution | Directory Open Access Journal |
| issn | 2376-5992 |
| language | English |
| last_indexed | 2024-04-12T17:22:22Z |
| publishDate | 2022-05-01 |
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| spelling | doaj.art-3f16b7f159114594aea930859b5f319f2022-12-22T03:23:26ZengPeerJ Inc.PeerJ Computer Science2376-59922022-05-018e94010.7717/peerj-cs.940A novel systematic byte substitution method to design strong bijective substitution box (S-box) using piece-wise-linear chaotic mapAsim Ali0Muhammad Asif Khan1Ramesh Kumar Ayyasamy2Muhammad Wasif3Computer Science, Comsats University Islamabad, Wah Cantt Campus, Punjab, PakistanComputer Engineering Department, University of Engineering and Technology Taxila, Taxila, Punjab, PakistanDepartment of Information Systems, Faculty of Information and Communication Technology, Universiti Tunku Abdul Rahman (UTAR), Kampar, Perak, MalaysiaDepartment of Computer Science, Comsats University Islamabad, Wah Cantt Campus, Punjab, PakistanCryptography deals with designing practical mathematical algorithms having the two primitive elements of confusion and diffusion. The security of encrypted data is highly dependent on these two primitive elements and a key. S-box is the nonlinear component present in a symmetric encryption algorithm that provides confusion. A cryptographically strong bijective S-box structure in cryptosystem ensures near-optimal resistance against cryptanalytic attacks. It provides uncertainty and nonlinearity that ensures high confidentiality and security against cryptanalysis attacks. The nonlinearity of an S-box is highly dependent on the dispersal of input data using an S-box. Cryptographic performance criteria of chaos-based S-boxes are worse than algebraic S-box design methods, especially differential probability. This article reports a novel approach to design an 8 × 8 S-box using chaos and randomization using dispersion property to S-box cryptographic properties, especially differential probability. The randomization using dispersion property is introduced within the design loop to achieve low differential uniformity possibly. Two steps are involved in generating the proposed S-box. In the first step, a piecewise linear chaotic map (PWLCM) is utilized to generate initial S-box positions. Generally, the dispersion property is a post-processing technique that measures maximum nonlinearity in a given random sequence. However, in the second step, the concept is carefully reverse engineered, and the dispersion property is used within the design loop for systematic dispersal of input substituting sequence. The proposed controlled randomization changes the probability distribution statistics of S-box’s differentials. The proposed methodology systematically substitutes the S-box positions that cause output differences to recur for a given input difference. The proposed S-box is analyzed using well-established and well-known statistical cryptographic criteria of nonlinearity, strict avalanche criteria (SAC), bit independence criteria (BIC), differential probability, and linear probability. Further, the S-box’s boomerang connectivity table (BCT) is generated to analyze its strength against boomerang attack. Boomerang is a relatively new attacking framework for cryptosystem. The proposed S-box is compared with the state-of-the-art latest related publications. Results show that the proposed S-box achieves an upper bound of cryptographic properties, especially differential probability. This work hypothesizes that highly dispersive hamming distances at output difference, generated a systematic S-box. The mixing property of chaos generated trajectories utilized for decimal mapping. To test the randomness of generated chaotic trajectories, a cryptographically secure pseudo-random sequence was generated using a chaotic map that was tested using the National Institute of Standards and Technology (NIST) NIST-800-22 test suit.https://peerj.com/articles/cs-940.pdfChaosCryptographyDifferential probabilitySubstitution-box |
| spellingShingle | Asim Ali Muhammad Asif Khan Ramesh Kumar Ayyasamy Muhammad Wasif A novel systematic byte substitution method to design strong bijective substitution box (S-box) using piece-wise-linear chaotic map PeerJ Computer Science Chaos Cryptography Differential probability Substitution-box |
| title | A novel systematic byte substitution method to design strong bijective substitution box (S-box) using piece-wise-linear chaotic map |
| title_full | A novel systematic byte substitution method to design strong bijective substitution box (S-box) using piece-wise-linear chaotic map |
| title_fullStr | A novel systematic byte substitution method to design strong bijective substitution box (S-box) using piece-wise-linear chaotic map |
| title_full_unstemmed | A novel systematic byte substitution method to design strong bijective substitution box (S-box) using piece-wise-linear chaotic map |
| title_short | A novel systematic byte substitution method to design strong bijective substitution box (S-box) using piece-wise-linear chaotic map |
| title_sort | novel systematic byte substitution method to design strong bijective substitution box s box using piece wise linear chaotic map |
| topic | Chaos Cryptography Differential probability Substitution-box |
| url | https://peerj.com/articles/cs-940.pdf |
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