Security analysis of cryptographic Boolean functions using a discrete mathematical model and machine learning
Priya Mathurdrpriyamathur21@gmail.comDepartment of MathematicsPoornima Institute of Engineering & TechnologyJaipur, Rajasthan, 302022, IndiaView full profile → , *Kusum Lata JainCorresponding authorkusmlata.jain@jaipur.manipal.eduDepartment of Computer and Communication EngineeringManipal University JaipurJaipur, Rajasthan, 303007, IndiaView full profile → , Meenakshi Nawalmeenakshi.nawal.02@gmail.comDepartment of Computer Science & EngineeringSwami Keshavanand Institute of Technology, Management & GramothanJaipur, Rajasthan, 302017, IndiaView full profile → , Neerajneeraj.bhardwaj@chitkarauniversity.edu.inDepartment of Computer ApplicationChitkara School of Engineering & TechnologyChitkara UniversityBaddi, Himachal Pradesh, 174103, IndiaView full profile → , Amit Kumar Guptaamit.gupta@jaipur.manipal.eduDepartment of Computer Science & EngineeringFaculty of Science, Technology and Architecture (FoSTA)Manipal University JaipurJaipur, Rajasthan, 303007, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Jan 2026
- Published Online:
- 14 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2748
- Pages:
- 3219–3227
Abstract
Cryptographic security of symmetric primitives relies on the discrete mathematical properties of Boolean functions and S-boxes. While machine learning (ML) has shown effectiveness in cryptanalysis, many approaches lack theoretical grounding. This paper proposes an ML-based cryptanalysis framework rooted in Boolean function theory, integrating Walsh–Hadamard analysis, nonlinearity computation, and algebraic characterization. Boolean functions and S-boxes are modeled for precise evaluation of cryptographic strength. The study establishes theoretical links between nonlinearity and ML learnability, validated using neural classifiers. The framework is further extended to side-channel analysis under the Hamming weight model, enabling reliable key recovery. Results show that higher nonlinearity reduces ML learnability, though S-boxes may still exhibit vulnerabilities. Overall, ML-based cryptanalysis is shown to exploit inherent Boolean structural weaknesses, emphasizing the importance of discrete mathematical analysis in security evaluation.
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References
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