Paper 2019/1278

An IND-CCA-Secure Code-Based EncryptionScheme Using Rank Metric

Hamad Al Shehhi and Emanuele Bellini and Filipe Borba and Florian Caullery and Marc Manzano and Victor Mateu

Abstract

The use of rank instead of Hamming metric has been proposed to address the main drawback of code-based cryptography: large key sizes. There exist several Key Encapsulation Mechanisms (KEM) and Public Key Encryption (PKE) schemes using rank metric including some submissions to the NIST call for standardization of Post-Quantum Cryptography. In this work, we present an IND-CCA PKE scheme based on the McEliece adaptation to rank metric proposed by Loidreau at PQC 2017. This IND-CCA PKE scheme based on rank metric does not use a hybrid construction KEM + symmetric encryption. Instead, we take advantage of the bigger message space obtained by the different parameters chosen in rank metric, being able to exchange multiple keys in one ciphertext. Our proposal is designed considering some specific properties of the random error generated during the encryption. We prove our proposal IND-CCA-secure in the QROM by using a security notion called disjoint simulatability introduced by Saito et al. in Eurocrypt 2018. Moreover, we provide security bounds by using the semi-oracles introduced by Ambainis et al.