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 ...
In 1971, German mathematicians Schönhage and Strassen predicted a faster algorithm for multiplying large numbers, but it ...
Inspired by Rearick's work on logarithm and exponential functions of arithmetic functions, we introduce two new operators, LOG and EXP. The LOG operates on generalized Fibonacci polynomials giving ...
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 ...
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