Using Learning with Rounding to Instantiate Post-Quantum Cryptographic Algorithms

Andrea Basso; Joppe W. Bos; Jan-Pieter D'Anvers; Angshuman Karmakar; Jose Maria Bermudo Mera; Joost Renes; Sujoy Sinha Roy; Frederik Vercauteren; Peng Wang; Yuewu Wang; Shicong Zhang; Chenxin Zhong

Paper 2025/1382

Using Learning with Rounding to Instantiate Post-Quantum Cryptographic Algorithms

Andrea Basso

, IBM Zurich

Joppe W. Bos

, NXP Semiconductors

Jan-Pieter D'Anvers

, KU Leuven

Angshuman Karmakar

, Indian Institute of Technology Kanpur

Jose Maria Bermudo Mera

, PQShield

Joost Renes

, NXP Semiconductors

Sujoy Sinha Roy

, Graz University of Technology

Frederik Vercauteren

, KU Leuven

Peng Wang, University of Chinese Academy of Sciences

Yuewu Wang, University of Chinese Academy of Sciences

Shicong Zhang, University of Chinese Academy of Sciences

Chenxin Zhong, University of Chinese Academy of Sciences

Abstract

The Learning with Rounding (LWR) problem, introduced as a deterministic variant of Learning with Errors (LWE), has become a promising foundation for post-quantum cryptography. This Systematization of Knowledge (SoK) paper presents a comprehensive survey of the theoretical foundations, algorithmic developments, and practical implementations of LWR-based cryptographic schemes. We introduce LWR within the broader landscape of lattice-based cryptography and post-quantum security, highlighting its advantages such as reduced randomness, improved efficiency, and enhanced side-channel resistance. We explore the evolution of security reductions from LWR to LWE, including recent advances that support practical parameter regimes and address challenges in both bounded and unbounded sample settings. This paper systematically reviews existing LWR-based schemes --- including Saber, Lizard, Florete, Espada, Sable, and SMAUG --- analyzing their design choices, parameter sets, and performance trade-offs. Furthermore, we examine the impact of LWR on side-channel resistance, failure probabilities, and masking efficiency, demonstrating its suitability for secure and efficient implementations. By consolidating the research spanning theory and practice, this SoK aims to guide future cryptographic design and standardization efforts leveraging LWR.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Post-Quantum Cryptography Learning with Rounding Lattice-Based Cryptography Cryptographic Survey
Contact author(s): joppe bos @ nxp com
History: 2025-07-31: approved; 2025-07-29: received; See all versions
Short URL: https://ia.cr/2025/1382
License: CC BY

BibTeX

@misc{cryptoeprint:2025/1382,
      author = {Andrea Basso and Joppe W. Bos and Jan-Pieter D'Anvers and Angshuman Karmakar and Jose Maria Bermudo Mera and Joost Renes and Sujoy Sinha Roy and Frederik Vercauteren and Peng Wang and Yuewu Wang and Shicong Zhang and Chenxin Zhong},
      title = {Using Learning with Rounding to Instantiate Post-Quantum Cryptographic Algorithms},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/1382},
      year = {2025},
      url = {https://eprint.iacr.org/2025/1382}
}