Lattice-Based versus Group-Theoretic Cryptography: A Comparative Study with Example
Varsha J. Patil, Mayuri B. Babar, Gitanjali N. Pawar
The evolution of quantum computing poses a profound challenge to traditional cryptographic systems based on number-theoretic assumptions such as integer factorization and discrete logarithms. This paper presents a comparative analysis between lattice-based and group-theoretic cryptographic schemes, two promising post-quantum approaches. The study highlights their mathematical foundations, underlying hardness assumptions, and operational principles. Furthermore, practical examples such as NewHope and Ko–Lee key exchange protocols are examined to illustrate the working mechanisms of both paradigms. The findings indicate that lattice-based cryptography demonstrates superior quantum resistance, efficiency, and standardization potential, whereas group-theoretic cryptography remains primarily theoretical but offers fertile ground for future innovations.
International Journal of Computer Sciences and Engineering•Apr 30, 2026•0 citations