January 15, 2002
Practical Aspects of Modern
Cryptography
Extended Euclidean Algorithm
Given A,B > 0, set
x1=1, x2=0, y1=0, y2=1, a1=A, b1=B, i=1.
Repeat while bi>0: {i = i + 1;
q = ai-1 div bi-1; bi = ai-1-qbi-1; ai = bi-1;
xi+1=xi-1-qxi; yi+1=yi-1-qyi}.
Axi + Byi = ai = gcd(A,B).