New Approach for CCA2-Secure Post-Quantum Cryptosystem Using Knapsack Problem

— Chosen-ciphertext security, which guarantees confidentiality of encrypted messages even in the presence of a decryption oracle, has become the de facto notion of security for public-key encryption under active attack. In this manuscript, for the first time, we propose a new approach for constructing post-quantum cryptosystems secure against adaptive chosen ciphertext attack (CCA2-secure) in the standard model using the knapsack problem. The computational version of the knapsack problem is NP-hard. Thus, this problem is expected to be difficult to solve using quantum computers. Our construction is a precoding-based encryption algorithm and uses the knapsack problem to perform a permutation and pad random fogged data to the message bits. Compared to other approaches in use today, our approach is more efficient and its CCA2 security in quantum environment can be reduced in the standard model to the assumption that the knapsack problem is intractable. Furthermore, we show that our approach is a general paradigm and can be applying to any (post-quantum) trapdoor one-way function candidate.