Post-Quantum Module Learning with Rounding-Based Public Key Encryption Using Incomplete Number Theoretic Transform

Abstract: Post Quantum Cryptographic (PQC) techniques are widely used in encryption standards and digital signatures. Lattice-based post-quantum cryptographic techniques have been reported in the last decades. The present work proposes an optimized quantum-safe lattice public key encryption (PKE) scheme based on the Module Learning with Rounding (MLWR) problem, enhanced by the use of Incomplete Number Theoretic Transform (NTT). The objective of the proposed scheme is to achieve efficient encryption and decryption while maintaining robust security in accordance with the National Institute of Standards and Technology (NIST) recommendations. The incomplete NTT relaxes the modulus q requirement, enables a smaller modulus for efficient arithmetic, and reduces computational complexity. This approach results in significant improvements in the speed of key generation, encryption, and decryption with a marked reduction in rejection probability, compared to schemes utilizing complete NTT. The proposed scheme demonstrates competitive performance against other lattice-based encryption schemes such as Kyber and Frodo. It shows lower encryption and decryption times while offering comparable security levels. Proposed scheme is at least a hundred times faster than Frodo lattice-based public-key encryption schemes. For NIST-recommended security level, in proposed scheme, each encryption needs an average of 300K CPU cycles, and each decryption needs 120K CPU cycles. Additionally, modulus 7937 enables a reduction in key and ciphertext sizes, optimizing the scheme for practical deployment in resource-constrained environments. Performance evaluations confirm the practicality of the scheme with substantial reductions in computational overhead, making it a highly efficient and secure candidate for post-quantum encryption.

Anupama Arjun Pandit and Arun Mishra. “Post-Quantum Module Learning with Rounding-Based Public Key Encryption Using Incomplete Number Theoretic Transform”. International Journal of Advanced Computer Science and Applications (IJACSA) 17.2 (2026). http://dx.doi.org/10.14569/IJACSA.2026.0170296

@article{Pandit2026,
title = {Post-Quantum Module Learning with Rounding-Based Public Key Encryption Using Incomplete Number Theoretic Transform},
journal = {International Journal of Advanced Computer Science and Applications},
doi = {10.14569/IJACSA.2026.0170296},
url = {http://dx.doi.org/10.14569/IJACSA.2026.0170296},
year = {2026},
publisher = {The Science and Information Organization},
volume = {17},
number = {2},
author = {Anupama Arjun Pandit and Arun Mishra}
}