In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that This is a certifying algorithm, because the gcd is the only number that can simultaneously satisfy this equation and divide the inputs.It allows one to compute also, with almost no extra cost, the quotients of a and b by their greatest common divisor. Extended Euclidean algorithm also refers to a very similar algorithm for computing the polynomial greatest common divisor and the coefficients of Bézout's identity of two univariate polynomials. The extended Euclidean algorithm is particularly useful when a and b are coprime. With that provision, x is the modular multiplicative inverse of a modulo b, and y is the modular multiplicative inverse of b modulo a. Similarly, the polynomial extended Euclidean algorithm allows one to compute the multiplicative inverse in algebraic field extensions and, in particular in finite fields of non prime order. It follows that both extended Euclidean algorithms are widely used in cryptography. In particular, the computation of the modular multiplicative inverse is an essential step in the derivation of key-pairs in the RSA public-key encryption method. (Wikipedia).
The extended Euclidean algorithm in one simple idea
An intuitive explanation of the extended Euclidean algorithm as a simple modification of the Euclidean algorithm. This video is part of playlist on GCDs and the Euclidean algorithm: https://www.youtube.com/playlist?list=PLrm9Y---qlNxXccpwYQfllCrHRJWwMky-
From playlist GCDs and Euclidean algorithm
Compute E Solution - Applied Cryptography
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
From playlist Applied Cryptography
Extended Fundamental Theorem of Calculus
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Extended Fundamental Theorem of Calculus. You can use this instead of the First Fundamental Theorem of Calculus and the Second Fundamental Theorem of Calculus. - Formula - Proof sketch of the formula - Six Examples
From playlist Calculus
Extended Euclidean Algorithm to Solve Linear Diophantine Equation
#shorts #mathonshorts Check out the videos on the GCD, Euclidean algorithms here Two Basic Theorems on gcd (Greatest Common Divisors) of Two Integers (Bezout's Identity) https://youtu.be/mQMksLNscY4 An Example of GCD, and Extended Euclidean Algorithm In Finding the Bezout Coefficients h
From playlist Elementary Number Theory
12_1_1 Introduction to Taylor Polynomials
An introduction to expand a function into a Taylor polynomial.
From playlist Advanced Calculus / Multivariable Calculus
This video walks through the technique for finding the GCD of two integers (not both zero), d = gcd(m,n), and then finding coefficients a and b for which d = am + bn.
From playlist Math
12_2_1 Taylor Polynomials of Multivariable Functions
Now we expand the creation of a Taylor Polynomial to multivariable functions.
From playlist Advanced Calculus / Multivariable Calculus
Gary Rubinstein teaches how to do the substitution method of the extended euclidean algorithm.
From playlist Cryptography, Security
Number Theory | Extended Euclidean Algorithm Example 2
We use the extended Euclidean algorithm to write the greatest common divisor of two natural numbers as a linear combination of them.
From playlist Divisibility and the Euclidean Algorithm
Introduction to Public-Key Cryptography
From playlist Cryptography Lectures
A Short Course in Algebra and Number Theory - Elementary Number Theory
To supplement a course taught at The University of Queensland's School of Mathematics and Physics I present a very brief summary of algebra and number theory for those students who need to quickly refresh that material or fill in some gaps in their understanding. This is the fourth lectu
From playlist A Short Course in Algebra and Number Theory
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
Math Major Examples — Number Theory #3
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From playlist Number Theory
Number Theory | Extended Euclidean Algorithm Example #1
We use the extended Euclidean algorithm to write the greatest common divisor of two natural numbers as a linear combination of them.
From playlist Divisibility and the Euclidean Algorithm