journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2817 A discrete graph-theoretic spectral framework for analyzing classical cipher security Mathur Priya Department of Mathematics, Poornima Institute of Engineering & Technology, Jaipur, Rajasthan, 302022, India 29 8 3305 3313 14 08 2026

This paper proposes a spectral graph-theoretic framework for cryptanalysis using Cipher Transition Graphs (CTGs) and metrics such as eigenvalues, spectral gap, entropy, clustering, and path length. Results show that plaintext and Caesar cipher share identical properties (spectral gap 1.2056, entropy 12.6732), indicating weak transformation; Vigenère shows slight variation (gap 1.2652, clustering 0.1545); while Playfair exhibits higher clustering (0.1824) but lower entropy (11.4216). Overall, all ciphers retain structural patterns, confirming their moderate security and limitations.

 Spectral graph theory Cryptanalysis Classical ciphers Cipher transition graph Eigenvalue analysis Graph entropy Network metrics Discrete mathematics access open retracted no