Determine what parts of "A Tool for Fast and Secure LWE Parameter Selection: the FHE case" can be integrated in HEIR

https://github.com/Crypto-TII/fastparameterselection

https://eprint.iacr.org/2024/1895

Beatrice Biasioli, Technology Innovation Institute
Elena Kirshanova, Technology Innovation Institute
Chiara Marcolla, Technology Innovation Institute
Sergi Rovira, Pompeu Fabra University

Abstract
The field of fully homomorphic encryption (FHE) has seen many theoretical and computational advances in recent years, bringing the technology closer to practicality than ever before. For this reason, practitioners in related fields, such as machine learning, are increasingly interested in using FHE to provide privacy to their applications.

Despite this progress, selecting secure and efficient parameters for FHE remains a complex and challenging task due to the intricate interdependencies between parameters. In this work, we address this issue by providing a rigorous theoretical foundation for parameter selection for any LWE-based schemes, with a specific focus on FHE. Our approach starts with an in-depth analysis of lattice attacks on the LWE problem, deriving precise expressions for the most effective ones. Building on this, we introduce closed-form formulas that establish the relationships among the LWE parameters.

In addition, we introduce a numerical method to enable the accurate selection of any configurable parameter to meet a desired security level.
Finally, we use our results to build a practical and efficient tool for researchers and practitioners deploying FHE in real-world applications, ensuring that our approach is both rigorous and accessible.