extended Euclidean algorithmk-ary GCD algorithmcalculation of inverse elements by moduleBezout's equation is a representation of the greatest common divisor d of integers A and B as a linear combination Ax + By
We can find the GCD of any pair of numbers using a basic algorithm called theEuclidean algorithm. Euclidean algorithm is a method to find the largest number that can divide two other numbers without leaving a remainder. Think of two numbers, say21and49. Now, find the largest number that ca...
Euclidean algorithm yields in tegers � 1 , � 2 , � 3 , and � with d := gcd(t 1 ; t 2 ) = � 2 t 1 � � 1 t 2 ; (1) 1 = gcd (d; t 3 ) = � 3 d � �t 3 : (2) W e set � 3 = 0, � 1 = t 1 =d � �, and � 2...
holdsforeverybwithgcd(n,b)=1.If(1.2)holdsthenwesaythatnpassesthe Miller(strong pseudoprime) test [12] to base b; if, in addition, n is composite, then we say n is a strong pseudoprime to base b, or spsp(b) for short. Monier [13] and ...
extended Euclidean algorithmk-ary GCD algorithmcalculation of inverse elements by moduleAbstractBezout's equation is a representation of the greatest common divisordof integersAandBas a linear combinationAx+By=d, wherexandyare integers called Bezout's coefficients. The task of finding Bezout's ...
The asymptotically fasted GCD algorithm is based on FFT methods and is due to Schonhage [16]. It has a running time of O(n log 2 n log log n) bit operations on inputs of n bits in length, but this a...G. B. Purdy "A carry-free algorithm for finding the greatest common ...