On the Closest Vector Problem for Lattices Constructed from Polynomials and Their Cryptographic Applications
This work addresses the problem of designing efficient and secure quantum-resistant encryption for cryptography applications, representing a strong specific gain rather than a foundational breakthrough.
The paper tackles the closest vector problem in lattices by constructing new trapdoor functions based on polynomial properties, achieving around 106 bits of security with a public key size of approximately 6.4 KB for quantum-safe encryption schemes.
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.