An IND-CCA Rank Metric Encryption Scheme Implementation

Abstract

The advances in the field of quantum computation impose a severe threat to the cryptographic primitives used nowadays. In particular, the community predicts public-key cryptography will be turned completely obsolete if these computers are ever produced. In the light of these facts, researchers are contributing in a great effort to preserve current information systems against quantum attacks. Post-quantum cryptography is the area of research that aims to develop cryptographic systems to resist against both quantum and classical computers while assuring interoperability with existing networks and protocols. This work considers the use of Gabidulin codes—a class of error-correcting codes using rank metric—in the construction of encryption schemes. We first introduce error-correcting codes in general and Gabidulin codes in particular. Then, we present the use of these codes in the context of public-key encryption schemes and show that, while providing the possibility of smaller key sizes, they are especially challenging in terms of security. We present the scheme proposed in Loidreau in 2017, showing that although correcting the main weakness in previous propositions, it is still insecure related to chosen-ciphertext attacks. Then, we present a modification to the scheme, proposed by Shehhi et al. to achieve CCA security, and provide an implementation. We also analyze the theoretical complexity of recent attacks to rank-based cryptography and propose a set of parameters for the scheme.