Secure Code-Based Key Encapsulation Mechanism with Short Ciphertext and Secret Key

Abstract

Code-based public key cryptosystems are one of the main techniques available in the area of Post-Quantum Cryptography. This work aims to propose a key encapsulation mechanism (KEM) with short ciphertext and secret key. Our goal is achieved in two steps. We first present a public key encryption (PKE) scheme, basicPKE, using a parity check matrix of Maximum Distance Separable (MDS) code as the public key matrix. In our construction, we exploit the structure of a companion matrix to obtain an MDS code which significantly reduces the storage of the secret key. The scheme basicPKE provides security against Indistinguishability under Chosen Plaintext Attacks (IND-CPA). Secondly, following the design framework of basicPKE, we construct another PKE scheme, fullPKE, that leads us to design our KEM scheme, fullKEM. We have shown that the scheme fullPKE is secure against One-Wayness under Plaintext and Validity Checking Attacks (OW-PCVA) and the scheme fullKEM achieves security against Indistinguishability under Chosen Ciphertext Attacks (IND-CCA) in the random oracle model. Moreover, our KEM can be shown to accomplish post-quantum security in the quantum random oracle model