Lecture: Modular Arithmetic

This lecture introduces the concept of modular arithmetic and presents a fast algorithm to compute the power of a number modulo another number. Constructive algorithms, based on the extended Euclidean algorithm, to compute modular inverses and solve the Chinese Remainder problem is presented. An algorithm to reconstruct a rational number from its modular image is presented. This algorithm also utilizes the extended Euclidean algorithm and the related concept of continued fraction approximation. Finally, a modular algorithm for integer multiplication is discussed.

Background Material