UMass Lowell Computer Science Analysis of Algorithms Prof. Karen Daniels Fall, 2001 Lecture 7 Tuesday, 11/6/01 Number-Theoretic Algorithms Chapter 33
Chapter Dependencies Ch 33 Number-Theoretic Algorithms RSA Math: Number Theory You’re responsible for material in this chapter that we discussed in lecture. (Note that this does not include sections 33.8 or 33.9.)
Overview ä Motivation: RSA ä Basics ä Euclid’s GCD Algorithm ä Chinese Remainder Theorem ä Powers of an Element ä RSA Details
Motivation: RSA
RSA Encryption source: textbook Cormen et al.
RSA Digital Signature source: textbook Cormen et al.
RSA Cryptosystem source: textbook Cormen et al.
Basic Concepts
Division & Remainders source: textbook Cormen et al.
Equivalence Class Modulo n source: textbook Cormen et al.
Common Divisors source: textbook Cormen et al.
Greatest Common Divisor source: textbook Cormen et al.
Greatest Common Divisor source: textbook Cormen et al.
Relatively Prime Integers source: textbook Cormen et al.
Relatively Prime Integers source: textbook Cormen et al.
Greatest Common Divisor source: textbook Cormen et al.
Euclid’s GCD Algorithm
source: textbook Cormen et al.
Extended Euclid source: textbook Cormen et al.
Chinese Remainder Theorem
Modular Arithmetic source: textbook Cormen et al.
Finite Groups source: textbook Cormen et al.
Finite Groups source: textbook Cormen et al.
Finite Groups source: textbook Cormen et al.
Euler’s Phi Function source: textbook Cormen et al.
Lagrange’s Theorem source: textbook Cormen et al.
Finite Groups source: textbook Cormen et al.
Solving Modular Linear Eq source: textbook Cormen et al.
Solving Modular Linear Eq source: textbook Cormen et al.
Solving Modular Linear Eq source: textbook Cormen et al.
Chinese Remainder Theorem source: textbook Cormen et al.
Chinese Remainder Theorem source: textbook Cormen et al.
Powers of an Element
Theorems of Euler & Fermat source: textbook Cormen et al.
Modular Exponentiation source: textbook Cormen et al.
RSA Details
RSA Correctness source: textbook Cormen et al.