Abstract: We propose a new number representation and arithmetic for the elements of the ring of integers modulo p. The so-called polynomial modular number system (PMNS) allows for fast polynomial ...

Abstract: Finite field arithmetic has advantageous space and time complexity when the field is constructed with a sparse polynomial. Katti and Brennan in (May, 20023) introduced a new type of ...

This project implements polynomial arithmetic in Galois Fields (GF(2^m)) with a focus on mathematical rigor, computational accuracy, and user-centered design. It provides a robust backend and an ...

Arithmetic circuit complexity investigates the computational resources required to evaluate polynomial functions via networks of arithmetic operations. At its core, this field seeks to classify ...

We introduce a large polynomial arithmetic library optimized for Nvidia GPUs to support fully homomorphic encryption schemes. To realize the large polynomial arithmetic library we convert polynomials ...

A comprehensive cryptographic education platform that visualizes modular arithmetic through interactive clock systems. This project implements classical ciphers, RSA encryption, and number theory ...

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 ...