{
  "annotation_id": "72bc0c46-81f1-4330-a184-8b3f0cd4fad6",
  "date_created": "2026-02-17T05:53:16.237000Z",
  "date_modified": "2026-02-17T05:53:16.237000Z",
  "file_hash": "f18cb6fba9cbd19c33bfbd2916f50f6adc66ad90a00210ac25aa7fa05148f5d5",
  "private": false,
  "record": {
    "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 $\\ell \u003e 2$, while matching Minal code performance for $\\ell = 2$.",
    "arxiv_id": "2601.08452",
    "authors": [
      "Shuiyin Liu",
      "Amin Sakzad"
    ],
    "categories": [
      "cs.CR",
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "On the Maximum Toroidal Distance Code for Lattice-Based Public-Key Cryptography",
    "url": "https://arxiv.org/abs/2601.08452",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ebefdcfb-dfc0-4c18-ac85-0145db3a7d44",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}