# Information Set Decoding in the Lee Metric with Applications to Cryptography

## TL;DR

This paper adapts an information set decoding algorithm to the Lee metric over the ring Z/4Z, demonstrating its potential to significantly reduce key sizes in cryptographic systems like McEliece and Niederreiter.

## Contribution

It introduces a novel ISD algorithm in the Lee metric and establishes a framework for cryptosystems over Z/4Z, highlighting advantages over traditional Hamming metric codes.

## Key findings

- Lee metric codes can drastically reduce key sizes.
- The framework applies to McEliece and Niederreiter cryptosystems.
- Results can be extended to other Galois rings.

## Abstract

We convert Stern's information set decoding (ISD) algorithm to the ring $\mathbb{Z}/4 \mathbb{Z}$ equipped with the Lee metric. Moreover, we set up the general framework for a McEliece and a Niederreiter cryptosystem over this ring. The complexity of the ISD algorithm determines the minimum key size in these cryptosystems for a given security level. We show that using Lee metric codes can drastically decrease the key size, compared to Hamming metric codes. In the end we explain how our results can be generalized to other Galois rings $\mathbb{Z}/p^s\mathbb{Z}$.