  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.
