Lecture

Algorithms for Big Numbers: Z_n and Orders

Description

This lecture covers algorithms for big numbers, focusing on Z_n, the ring of residues modulo n, and orders in a group. It explains the multiplication algorithm, double-and-add method, and square-and-multiply technique. The instructor discusses the definition of a ring, group of units, and group and ring constructors. Examples of Z, Z[X], and modulo 9 reduction are provided. The lecture also delves into the Diffie-Hellman cryptography, modular arithmetic, and modular inversion. Various arithmetic operations with big numbers are explained, including addition, multiplication, Euclidean division, and the Euclid algorithm. The importance of structure property of Z, element order, group exponent, and orders in Zm are highlighted.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.