# Encryption Scheme Based on Expanded Reed-Solomon Codes

## TL;DR

This paper introduces a new code-based public-key cryptosystem utilizing expanded Reed-Solomon codes, offering enhanced security against certain attacks and significantly reducing key size compared to traditional systems.

## Contribution

It proposes a novel encryption scheme based on shortened expanded Reed-Solomon codes that improves security and reduces key size without relying on cyclic structures.

## Key findings

- Provides security against Schur product-based distinguishers
- Achieves approximately 45% key size reduction
- Demonstrates practical viability of the scheme

## Abstract

We present a code-based public-key cryptosystem, in which we use Reed-Solomon codes over an extension field as secret codes and disguise it by considering its shortened expanded code over the base field. Considering shortened expanded codes provides a safeguard against distinguisher attacks based on the Schur product. Moreover, without using a cyclic or a quasi-cyclic structure we obtain a key size reduction of nearly $45 \%$ compared to the classic McEliece cryptosystem proposed by Bernstein et al.