2 research outputs found
Construction of generalized-involutory MDS matrices
Maximum Distance Separable (MDS) matrices are usually used to be diffusion
layers in cryptographic designs. The main advantage of involutory MDS matrices lies in
that both encryption and decryption share the same matrix-vector product. In this paper,
we present a new type of MDS matrices called generalized-involutory MDS matrices, implementation
of whose inverse matrix-vector products in decryption is the combination of the
matrix-vector products in encryption plus a few extra XOR gates. For the purpose of verifying
the existence of such matrices, we found 4 × 4 Hadamard generalized-involutory MDS
matrix over GF(24) consuming as little as 38 XOR gates with 4 additional XOR gates for
inverse matrix, while the best previous single-clock implementation in IWSEC 2019 needs
46 XOR gates with 51 XOR gates for inverse matrix. For GF(28), our results also beat the
best previous records in ToSC 2017
Secure Code-Based Key Encapsulation Mechanism with Short Ciphertext and Secret Key
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