RAMESSES, a Rank Metric Encryption Scheme with Short Keys

TL;DR

This paper introduces RAMESSES, a rank metric encryption scheme with short keys, efficient algorithms, and quantum-resistant security based on rank decoding problems, suitable for practical cryptographic applications.

Contribution

The paper presents a novel rank metric encryption scheme with short keys, efficient operations, and security relying solely on rank decoding problems, without structural hiding.

Findings

Comparable key and ciphertext sizes to isogeny-based cryptography

Efficient encryption and decryption using linear algebra over finite fields

Quantum-resistant security based on rank decoding problems

Abstract

We present a rank metric code-based encryption scheme with key and ciphertext sizes comparable to that of isogeny-based cryptography for an equivalent security level. The system also benefits from efficient encryption and decryption algorithms, which rely on linear algebra operations over finite fields of moderate sizes. The security only relies on rank metric decoding problems, and does not require to hide the structure of a code. Based on the current knowledge, those problems cannot be efficiently solved by a quantum computer. Finally, the proposed scheme admits a failure probability that can be precisely controlled and made as low as possible.