Paper 2022/874

Lattice Codes for Lattice-Based PKE

Shanxiang Lyu, Jinan University, State Key Laboratory of Cryptology
Ling Liu, Shenzhen University
Cong Ling, Imperial College London
Junzuo Lai, Jinan University
Hao Chen, Jinan University

Existing error correction mechanisms in lattice-based public key encryption (PKE) rely on either trivial modulation or its concatenation with error correction codes (ECC). This paper demonstrates that lattice coding, as a combined ECC and modulation technique, can replace trivial modulation in current lattice-based PKEs, resulting in improved error correction performance. We model the FrodoPKE protocol as a noisy point-to-point communication system, where the communication channel resembles an additive white Gaussian noise (AWGN) channel. To utilize lattice codes for this specific channel with hypercube shaping, we propose an efficient labeling function that converts binary information bits to lattice codewords and vice versa. The parameter sets of FrodoPKE are enhanced to achieve higher security levels or smaller ciphertext sizes. For instance, the proposed Frodo-1344-E$_\text{8}$ offers a 10-bit classical security improvement over Frodo-1344. The code for reproducing our main experiments is available at

Note: the paper has been accepted by Designs, Codes and Cryptography.

Available format(s)
Public-key cryptography
Publication info
public key encryption (PKE)lattice-based cryptography (LBC)lattice codescoded modulation
Contact author(s)
lsx07 @ jnu edu cn
liulingcs @ szu edu cn
c ling @ imperial ac uk
laijunzuo @ gmail com
chenhao @ fudan edu cn
2023-10-10: last of 5 revisions
2022-07-04: received
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      author = {Shanxiang Lyu and Ling Liu and Cong Ling and Junzuo Lai and Hao Chen},
      title = {Lattice Codes for Lattice-Based PKE},
      howpublished = {Cryptology ePrint Archive, Paper 2022/874},
      year = {2022},
      note = {\url{}},
      url = {}
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