Algebraic construction and security evaluation of substitution boxes using finite field and permutation group techniques
M. Manideepikamanideepika@outlook.comDepartment of CSE (Artificial Intelligence & Machine Learning)Pragati Engineering CollegeSurampalem, Kakinada District, Andhra Pradesh, 533437, IndiaView full profile → , *Dinesh Baban KuteCorresponding authordineshkute90@gmail.comDepartment of Applied Sciences and HumanitiesPimpri Chinchwad College of EngineeringPune, Maharashtra, 411044, India0000-0002-7285-0165View full profile → , Amruta Tejaskumar Mokashiamruta.mokashi2@vit.eduDepartment of Chemical EngineeringVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Padmavati Shrivastavadr.padmavati.shrivastava@rungta.orgDepartment of Computer Science and EngineeringRungta College of Engineering and TechnologyRungta International Skills UniversityBhilai, Chhattisgarh, 490024, IndiaView full profile → , Dipak Sethidir.son@niu.edu.inSchool of NursingNoida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , Pooja Pathakpooja.pathak@gla.ac.inDepartment of Computer Engineering & ApplicationsGLA UniversityMathura, Uttar Pradesh, 281406, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 31 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-3072
- Pages:
- 4547–4556
Abstract
S-boxes (substitution boxes) are essential nonlinear elements that guarantee confusion in symmetric cryptosystems, but it is still difficult to come up with structures that have a good algebraic and cryptographic structure. This paper is an attempt to suggest a hybrid construction approach characterized by a combination of finite field GF(2n) transformations and permutation group techniques to create secure and efficient S-boxes. The method is a combination of algebraic inversion, affine mapping and permutation cycles to maximize nonlinearity, objectivity and resistance to differential and linear cryptanalysis. The proposed construction of hybrid S-box uses finite-field inversion, affine transformations and permutation-group operations to enhance the cryptographic substitution properties. The results reported here show a nonlinearity of 114, while AES S-box and traditional S-box have values of 112 and 96, respectively, which represent 1.79% and 18.75% improvement, respectively. The proposed construction meets the AES baseline by +1.4 and +2.4 percentage points on both the Strict Avalanche Criterion (SAC) and Bit Independence Criterion (BIC) respectively. The reported computational time is 11.1 ms which is 11.90% faster than traditional S-box but 7.77% slower than AES. These comparisons suggest that these characteristics are reported to be better with little to be gained in terms of computation.
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References
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