A novel fast hybrid GCD computation algorithm

Abstract

We propose a novel algorithm for integer’s greatest common divisor (GCD) computation that hybridises both Euclidian and binary algorithms according to a new schema, in order to accelerate the GCD computation especially in the case of large bit difference between the two inputs. The proposed algorithm run slightly faster than existing algorithms and is very much easier to implement. We provide a simple proof of correctness for the algorithm, and we show that best performances can be achieved for large integers when subtraction operator complexity is relatively low with respect to the division one.