# Fast Xor-based Erasure Coding based on Polynomial Ring Transforms

## TL;DR

This paper introduces a novel method for reducing the complexity of finite field multiplication in erasure codes by leveraging polynomial ring transforms, leading to more efficient software implementations.

## Contribution

It proposes a new approach using polynomial ring transforms to simplify finite field operations, improving the efficiency of erasure coding implementations.

## Key findings

- Reduced finite field multiplication complexity
- Efficient scheduling decreases operation count
- Potential for faster erasure coding algorithms

## Abstract

The complexity of software implementations of MDS erasure codes mainly depends on the efficiency of the finite field operations implementation. In this paper, we propose a method to reduce the complexity of the finite field multiplication by using fast transforms between a field and a ring to perform the multiplication in a ring. We show that moving to a ring reduces the complexity of the operations. Then, we show that this construction allows the use of simple scheduling to reduce the number of operations.