On the Closest Vector Problem for Lattices Constructed from Polynomials and Their Cryptographic Applications

TL;DR

This paper introduces new polynomial-based lattice constructions with trapdoor functions, enabling quantum-safe encryption schemes that balance security and efficiency, and analyzing their resistance to lattice attacks.

Contribution

It presents novel polynomial-based lattices with trapdoors for the closest vector problem, advancing quantum-safe cryptographic constructions.

Findings

Achieves approximately 106 bits of security.

Public key size around 6.4 KB.

Efficient key generation, encryption, and decryption.

Abstract

In this paper, we propose new classes of trapdoor functions to solve the closest vector problem in lattices. Specifically, we construct lattices based on properties of polynomials for which the closest vector problem is hard to solve unless some trapdoor information is revealed. We thoroughly analyze the security of our proposed functions using state-of-the-art attacks and results on lattice reductions. Finally, we describe how our functions can be used to design quantum-safe encryption schemes with reasonable public key sizes. In particular, our scheme can offer around $106$ bits of security with a public key size of around $6.4$ $\texttt{KB}$. Our encryption schemes are efficient with respect to key generation, encryption and decryption.