Lattice Codes for Lattice-Based PKE

TL;DR

This paper demonstrates that lattice coding can replace naive modulation in lattice-based PKE, improving error correction and security parameters by modeling the protocol as a noisy channel and proposing an efficient lattice coding scheme.

Contribution

It introduces a lattice coding approach for lattice-based PKE, enhancing error correction and security, with a new labeling function for hypercube-shaped lattice codes.

Findings

Lattice coding improves correction performance over naive modulation.

Proposed Frodo-1344-E8 offers 10-bit security gain.

Parameter sets are optimized for higher security or smaller ciphertexts.

Abstract

Existing error correction mechanisms in lattice-based public key encryption (PKE) rely on either naive modulation or its concatenation with error correction codes (ECC). This paper shows that lattice coding, as a joint ECC and modulation technique, can substitute the naive modulation in existing lattice-based PKEs to enjoy better correction performance. We begin by modeling the FrodoPKE protocol as a noisy point-to-point communication system, where the communication channel is similar to the additive white Gaussian noise (AWGN) channel. To employ lattice codes for this special channel that hinges on hypercube shaping, we propose an efficient labeling function that converts between binary information bits and lattice codewords. The parameter sets of FrodoPKE are improved towards either higher security levels or smaller ciphertext sizes. For example, the proposed Frodo-1344-E$_\text{8}$ has a 10-bit classical security gain over Frodo-1344.