# Interleaving Loidreau's Rank-Metric Cryptosystem

## TL;DR

This paper introduces an interleaved version of Loidreau's rank-metric cryptosystem, analyzing its security, proposing design guidelines, and suggesting a new code construction to improve key size and security.

## Contribution

It presents a novel interleaved cryptosystem variant, analyzes attack resilience, and proposes a probabilistic code construction for secure, efficient implementation.

## Key findings

- Secure instances require near-MRD codes not previously studied.
- A new random code construction increases the probability of MRD codes over large fields.
- An upper bound on decryption failure rate is derived, enabling parameter optimization.

## Abstract

We propose and analyze an interleaved variant of Loidreau's rank-metric cryptosystem based on rank multipliers. We analyze and adapt several attacks on the system, propose design rules, and study weak keys. Finding secure instances requires near-MRD rank-metric codes which are not investigated in the literature. Thus, we propose a random code construction that makes use of the fact that short random codes over large fields are MRD with high probability. We derive an upper bound on the decryption failure rate and give example parameters for potential key size reduction.