Detailed Proposed Algorithm: Symmetric Encryption and Decryption Using Eulerian Circuits in Simple Graphs

<jats:p>This paper proposes a novel symmetric-key encryption scheme using simple weighted graphs and Eulerian circuits. Unlike NP-complete Hamiltonian cycle methods, it employs polynomial-time Eulerian circuits via Hierholzer‘s algorithm. Plaintext is mapped to a weighted graph using a secret key. An Eulerian circuit generates a dynamic key and Euler Tour Matrix. Encryption uses matrix multiplications with a shared upper triangular key and modular reduction. Decryption reverses the operations using matrix inverses. Statistical tests confirm strong diffusion and randomness. The scheme provides better efficiency and scalability than traditional Hamiltonian-based approaches.</jats:p>