Welcome to the resource topic for 2024/585
Title:
A Complete Beginner Guide to the Number Theoretic Transform (NTT)
Authors: Ardianto Satriawan, Rella Mareta
Abstract: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 a quasi-linear complexity O(n \log{n}) instead of O(n^2) when implemented with Fast Fourier Transform-style algorithms has made it a key component in modern cryptography. FFT-style NTT algorithm or fast-NTT is particularly useful in lattice-based cryptography. In this short note, we briefly introduce the basic concepts of linear, cyclic, and negacyclic convolutions via traditional schoolbook algorithms, traditional NTT, its inverse (INTT), and FFT-like versions of NTT/INTT. We then provide consistent toy examples through different concepts and algorithms to understand the basics of NTT concepts.
ePrint: https://eprint.iacr.org/2024/585
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