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

TL;DR

This paper introduces a novel, simple, and efficient post-quantum cryptosystem based on the knapsack problem that achieves CCA2 security in the standard model, addressing active attack scenarios.

Contribution

It presents the first construction of a CCA2-secure post-quantum cryptosystem using the NP-hard knapsack problem in the standard model.

Findings

Achieves CCA2 security in the standard model

Uses a precoding-based encryption with knapsack problem

More efficient and simpler than existing approaches

Abstract

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.