This article explores the Schönhage-Strassen algorithm and Number Theoretic Transform (NTT) for multiplying very large integers, moving beyond Toom-Cook methods. It explains how convolution and FFT enable efficient computation of all cross terms simultaneously, a key technique in cryptography and high-performance computing. The content is technically rigorous and serves as a valuable reference for algorithm engineers. The article details the transition from polynomial evaluation and interpolation in Toom-Cook to using convolution and FFT to handle all cross terms in one go. It covers the mathematical foundations of NTT, including modular arithmetic and primitive roots, and explains how Schönhage-Strassen achieves near-linear time complexity for extremely large integers. This is essential reading for anyone working on cryptographic algorithms, numerical libraries, or high-performance computing.
This article explores the Schönhage-Strassen algorithm and Number Theoretic Transform (NTT) for multiplying very large integers, moving beyond Toom-Cook methods. It explains how convolution and FFT enable efficient computation of all cross terms simultaneously, a key technique in cryptography and high-performance computing. The content is technically rigorous and serves as a valuable reference for algorithm engineers.