Ramified Well-Rounded Lattice Codes: Bridging Number Fields and PQC Efficiency

Bastos et al. (2025) construct well-rounded lattices from ramified number fields, but their cryptographic potential is unexplored. This idea leverages their geometric density and error-correction properties to design lattice codes where error patterns align with cryptographic noise distributions. Unlike Wang et al.’s (2021) generic lattice-code hybrids, this uses ramified fields to optimize sphere-packing efficiency, potentially shrinking ciphertexts. The HNF-based key compression from Hooshmand (2024) could further reduce key sizes. By analyzing decoding complexity via Craps et al.’s (2022) CVP bounds, security-performance tradeoffs can be quantified. Impact: A new lattice family for PQC with provable geometric advantages, ideal for bandwidth-constrained IoT (Akçay & Yalçin, 2024).

References:

1. A Key Encapsulation Mechanism from Low Density Lattice Codes. Reza Hooshmand (2024). arXiv.org.
2. Lightweight ASIP Design for Lattice-Based Post-quantum Cryptography Algorithms. Latif Akçay, B. Yalçin (2024). The Arabian journal for science and engineering.
3. Bounds on quantum evolution complexity via lattice cryptography. B. Craps, Marine De Clerck, O. Evnin, Philip Hacker, M. Pavlov (2022). SciPost Physics.
4. Quantum-safe cryptography: crossroads of coding theory and cryptography. Jiabo Wang, Ling Liu, Shanxiang Lyu, Zheng Wang, Mengfan Zheng, Fuchun Lin, Zhao Chen, L. Yin, Xiaofu Wu, Cong Ling (2021). Science China Information Sciences.
5. Well-rounded lattices from odd prime degree number fields in the ramified case. Jefferson Luiz Rocha Bastos, Robson Ricardo de Araujo, Trajano Pires da N'obrega Neto, Antonio Aparecido de Andrade (2025). Advances in Geometry.