This project implements both the Euclidean Algorithm to compute the Greatest Common Divisor (GCD) of two integers and the Extended Euclidean Algorithm, which finds integer coefficients for Bézout's ...

Abstract: This paper presents a dual-field modular division (inversion) algorithm and its hardware design. The algorithm is based on the Extended Euclidean and the Binary GCD algorithms. The use of ...

Montgomery algorithms represent a transformative advancement in the computation of modular arithmetic, specifically designed to bypass the costly division steps inherent in traditional methods. By ...

The Crandall reduction algorithm provides an efficient way to compute modular reduction for numbers of the special form p = 2^k + c. This is particularly useful in cryptographic applications, such as ...

You may never have heard of modular arithmetic, but you use it every day without the slightest difficulty. In this system, numbers wrap around when they reach a certain size called the modulus; it is ...