Conceptual Review on Number Theoretic Transform and Comprehensive Review on Its Implementations

The Number Theoretic Transform (NTT) is a powerful mathematical tool that has become increasingly important in developing Post Quantum Cryptography (PQC) and Homomorphic Encryption (HE). Its ability to efficiently calculate polynomial multiplication using the convolution theorem with quasi-linear complexity O ( xmlns:xlink="http://www.w3.org/1999/xlink">n log ) made it key component modern cryptography. NTT particularly useful lattice-based cryptography, which relies on hardness of certain problems ensure security. importance these fields continues grow as quantum computing technology advances traditional encryption methods vulnerable. In this report, we discuss concepts multiplications provide comprehensive review latest implementation state-of-the-art both PQC HE schemes.