A graph-theoretic discrete mathematical model for cryptanalysis of classical ciphers using spectral transition network analysis
Priya Mathurdrpriyamathur21@gmail.comDepartment of MathematicsPoornima Institute of Engineering & TechnologyJaipur, Rajasthan, 302022, IndiaView full profile → , *Amit Kumar GuptaCorresponding authoramit.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-2815
- Pages:
- 3279–3294
Abstract
Cryptanalysis plays an essential role in evaluating the robustness and reliability of cryptographic systems used for secure communication. Traditional cryptanalysis methods primarily rely on statistical and algebraic techniques to analyze encryption algorithms; however, recent advancements in data science and network analysis have introduced new mathematical approaches for studying encrypted data. This paper proposes a graphtheoretic cryptanalysis framework based on transition network analysis for detecting structural differences between plaintext and classical cipher texts. In the proposed approach, textual sequences are modeled as directed weighted -graphs, where nodes represent alphabet characters and edges represent transitions between consecutive symbols. Spectral and structural properties of the resulting graphs are extracted using matrix representations such as adjacency and Laplacian matrices. These features, including spectral radius, algebraic connectivity, spectral entropy, graph energy, density, clustering coefficient, and centrality measures, are used to construct a feature vector representing the structural characteristics of the text network. An ensemble machine learning classifier combining Random Forest and Gradient Boosting algorithms is employed to classify plaintext and ciphertext samples. Experimental results obtained from a dataset of 6000 text samples with a 15-dimensional feature vector demonstrate that the proposed method achieves a classification accuracy of 74.72% with a recall of 1.0 and an F1-score of 0.8553. The findings indicate that transition network analysis provides a promising mathematical framework for detecting encryption patterns and analyzing cryptographic structures using graph theory and machine learning techniques.
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References
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