Spectral security analysis of cryptographic Boolean functions using discrete mathematical modelling and machine learning
Priya Mathurdrpriyamathur21@gmail.comDepartment of MathematicsPoornima Institute of Engineering & TechnologyJaipur, Rajasthan, 302022, IndiaView full profile → , Pradeep Guptagupta.pradeep85@gmail.comDepartment of Computer Science and EngineeringAjay Kumar Garg Engineering CollegeGhaziabad, Uttar Pradesh, 201015, IndiaView full profile → , K. Nandhininandhukk28@gmail.comDepartment of Computer Science and Engineering (AIML)Sridevi Women’s Engineering CollegeHyderabad, Telangana, 500075, IndiaView full profile → , Lipika Goellipika.bose@gmail.comDepartment of Computer Science and Engineering (AIML)Sridevi Women’s Engineering CollegeHyderabad, Telangana, 500075, IndiaView full profile → , *Satpal Singh KushwahaCorresponding authorsatpal.singh@jaipur.manipal.eduDepartment of Computer Science & EngineeringManipal University JaipurJaipur, Rajasthan, 303007, IndiaView full profile → , Amit Kumar Guptaamit.gupta@jaipur.manipal.eduDepartment of Computer Science & EngineeringManipal University JaipurJaipur, Rajasthan, 303007, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Mar 2026
- Published Online:
- 14 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2812
- Pages:
- 3249–3257
Abstract
This study investigates how the structural and spectral properties of Boolean functions influence their susceptibility to machine learning–based cryptanalysis. A comprehensive framework is proposed, combining Boolean function generation, truth table representation, Walsh–Hadamard spectral analysis, and machine learning evaluation. Using a dataset of 2000 functions (linear, balanced, bent-like, and random), results show that higher nonlinearity reduces learnability, while linear functions remain predictable. A strong negative correlation (−0.6499) between nonlinearity and learning accuracy is observed. Functions with large Walsh coefficients are more easily approximated. The findings confirm that machine learning exploits inherent structural weaknesses, aiding the design of more secure, learning-resistant cryptographic primitives.
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References
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