MaTRU-KE revisited: CCA2-secure key establishment protocol based on MaTRU

Quantum attack-resistant cryptosystems are required for secure communication since there is a big demand to have quantum computers. Lattice-based cryptography is one of the quantum-secure families due to its key/ciphertext sizes and performance. NTRU-based cryptosystems, a member of lattice-based cryptosystems, have received much more attention. MaTRU, a noncommutative version of NTRU with some matrix properties, is used to obtain a key exchange protocol in 2018. In this paper, we focus on MaTRU-based key exchange protocols having CCA2 properties. We propose CCA2-secure versions of MaTRU-KE and then provide a security analysis of CCA2-secure key establishment protocols. We also provide a comparison with the previous ones.