Mathematicians have proven the existence of a faster algorithm for multiplying large numbers, making multiplication and other ...

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 ...

This monthly journal, published since 1900, is devoted entirely to research in pure and applied mathematics, and, in general, includes longer papers than those in the Proceedings of the American ...

An algorithm for realizing finite field arithmetic is presented. The relationship between linear recursions and polynomial arithmetic (modulo a fixed polynomial) over ...

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 ...

The FACTEX procedure constructs a fractional design for q-level factors using the Galois field (or finite field) of size q. This is a system with q elements and two operations + and ×, which satisfy ...