New Results for Rank-Based Cryptography

Abstract

In this paper we survey new results for rank-based cryptography: cryptosystems which are based on error-correcting codes embedded with the rank metric. These new results results first concern the LRPC cryptosystem, a cryptosystem based on a new class of decodable rank codes: the LRPC codes (for Low Rank Parity Check codes) which can be seen as an analog of the classical LDPC codes but for rank metric. The LRPC cryptosystem can benefit from very small public keys of less than 2,000 bits and is moreover very fast. We also present new optimized attacks for solving the general case of the rank syndrome decoding problem, together with a zero-knowledge authentication scheme and a new signature scheme based on a mixed errors-erasures decoding of LRPC codes, both these systems having public keys of a few thousand bits. These new recent results highlight that rank-based cryptography has many good features that can be used for practical cryptosystems.