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

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