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 defacto 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 some random fogged data to the message bits. Compared to other approaches were introduced today, our approach is very simple and more efficient. 
Roohallah Rastaghi
cs.CR cs.IT math.IT