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Extended euclid - PowerPoint PPT Presentation

Outline

Outline

Outline. greatest common divisors and Euclid’s algorithm applications of large primes: public-key cryptosystems (RSA) primality testing integer factorization. GCD and Euclid’s algorithm. gcd(a,b) - the greatest common divisor of integers a and b. Euclid ( a , b )

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1.04k views • 85 slides
CS 312: Algorithm Design & Analysis

CS 312: Algorithm Design & Analysis

This work is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License. CS 312: Algorithm Design & Analysis. Lecture #4: Primality Testing, GCD. Slides by: Eric Ringger, with contributions from Mike Jones, Eric Mercer, Sean Warnick. Announcements.

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491 views • 32 slides
CS 312: Algorithm Analysis

CS 312: Algorithm Analysis

This work is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License. CS 312: Algorithm Analysis. Lecture #4: Primality Testing, GCD. Slides by: Eric Ringger, with contributions from Mike Jones, Eric Mercer, Sean Warnick. Objectives. Part 1:

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421 views • 32 slides
第十四讲 有关数论算法

第十四讲 有关数论算法

第十四讲 有关数论算法. 内容提要： 初等数论概念 最大公约数 模运算和模线性方程 中国余数定理. 初等数论概念. 整除性和约数 1 ） d | a ，读作 ”d 整除 a” ，表示 a 是 d 的倍数； 2 ） 约数 ： d | a 且 d>0 ，则 d 是 a 的约数；（即定义约数为非负整数） 3 ）对整数 a 最小约数为 1 ，最大为 |a| 。其中， 1 和 |a| 为整数的平凡约数 , 而 a 的非平凡约数称为 a 的因子； 素数和合数 1) 素数 ( 质数 ) ：对于整数 a > 1 ，如果它仅有平凡约数 1 和 a ，则 a 为素数；

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CSC2110 Discrete Mathematics Tutorial 6 Chinese Remainder Theorem, RSA and Primality Test

CSC2110 Discrete Mathematics Tutorial 6 Chinese Remainder Theorem, RSA and Primality Test

CSC2110 Discrete Mathematics Tutorial 6 Chinese Remainder Theorem, RSA and Primality Test. Hackson Leung. Announcement. Homework Set 2 is released! Deadline 30 Oct 17:00 Sharp No late submission is accepted Submit at the drop box near SHB 924 Project

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1.54k views • 21 slides
RSA Public Key Encryption

RSA Public Key Encryption

RSA Public Key Encryption. To do RSA we need fast Modular Exponentiation and Primality generation which we have shown We also need Modular Division To do Modular Division we use the extended Euclid Algorithm which we will now build towards. Euclid’s Rule for GCD.

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281 views • 18 slides

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