Quantum-resistant public-key encryption and signature schemes with smaller key sizes

The emergence of new complex technologies, such as cloud and quantum computing, has a complicated computational structure, which can compromise the security of traditional cryptographic protocols. It has been noted that traditional security systems utilize non-quantum resistance factorization and Diffie–Hellman (DH) hard problems for their protection. Lattice-based cryptography appears to be a potential post-quantum substitute for the presently employed public-key cryptography. As a result, we have been motivated to focus on increasingly sophisticated and challenging lattice hard assumptions capable of withstanding new modern technologies with quantum resistance properties. In this paper, we devise a new lattice-based public-key encryption and signature schemes with smaller key sizes. The proposed scheme also resists the quantum attack because of the lattice small integer solution problem and its variant. The security claim has also been proved in a well-suited model for quantum attacks. The performance analysis shows that the presented schemes outperform the DH-type schemes and compete with similar lattice-based schemes in terms of storage, communication, key sizes, and computational overheads.