If GCD(Q-1,m) ≠1, then the mth look-up table actually consists of (GCD(Q-1,m)) sub-tables storing GF element α-(mi+j), where j=0, 1, ..., GCD(Q-1,m)-1.

Remark $\ $ The penultimate equivalence in the proof uses said (universal) definition of gcd, followed by the gcd distributive law.

So the two pairs (a, b) and (b, c) have the same common divisors, and thus gcd(a,b) = gcd(b,c).

An alternative method of computing the gcd is the binary GCD algorithm which uses only subtraction and division by 2.

5.28.7 GCD of two polynomials with the Euclidean algorithm: gcd

An alternative method of computing the gcd is the binary gcd method which uses only subtraction and division by 2.

The present invention relates to a method to protect a binary GCD computation against SPA attacks.

If r is an integral domain then any two gcd's of a and b must be associate elements, since by definition either one must divide the other; indeed if a gcd exists, any one of its associates is a gcd as well.

gcd: function() { // method that calculates the greatest common divisor

gcd: function { // method that calculates the greatest common divisor

If R is an integral domain then any two gcd's of a and b must be associate elements, since by definition either one must divide the other; indeed if a gcd exists, any one of its associates is a gcd as well.

gcd: function () { // method that calculates the greatest common divisor

// Only need to calculate GCD once, so "redefine" this method.

This is an important feature of GCD which we'll discuss shortly.

A few more abilities are coming off the GCD in the next beta build.