On the Maximum Toroidal Distance Code for Lattice-Based Public-Key Cryptography

• URL: http://arxiv.org/abs/2601.08452v1
• Date: Tue, 13 Jan 2026 11:27:15 GMT
• Title: On the Maximum Toroidal Distance Code for Lattice-Based Public-Key Cryptography
• Authors: Shuiyin Liu, Amin Sakzad,
• Abstract summary: We propose a maximum toroidal distance (MTD) code for lattice-based public-key encryption (PKE)<n>We show that the MTD code is essentially a variant of the Minal code recently introduced at IACR CHES 2025.
• Score: 3.8559042217241566
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a maximum toroidal distance (MTD) code for lattice-based public-key encryption (PKE). By formulating the encryption encoding problem as the selection of $2^\ell$ points in the discrete $\ell$-dimensional torus $\mathbb{Z}_q^\ell$, the proposed construction maximizes the minimum $L_2$-norm toroidal distance to reduce the decryption failure rate (DFR) in post-quantum schemes such as the NIST ML-KEM (Crystals-Kyber). For $\ell = 2$, we show that the MTD code is essentially a variant of the Minal code recently introduced at IACR CHES 2025. For $\ell = 4$, we present a construction based on the $D_4$ lattice that achieves the largest known toroidal distance, while for $\ell = 8$, the MTD code corresponds to $2E_8$ lattice points in $\mathbb{Z}_4^8$. Numerical evaluations under the Kyber setting show that the proposed codes outperform both Minal and maximum Lee-distance ($L_1$-norm) codes in DFR for $\ell > 2$, while matching Minal code performance for $\ell = 2$.

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