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The genus of lattice forms and algebraic-arithmetic-geometric invariants

June 28, 2023


Daniel Apon - MITRE


Abstract: In this talk, I will define the genus of lattice forms, discuss invariants of such genera, and identify if-and-when such invariants are efficiently computable. This talk is motivated by a pursuit of the origin of fundamental connections between lattice cryptography and code cryptography. I hope for (but do not expect) applications both to future lattice-based cryptosystems as well as potentially to advanced cryptanalyses of current lattice cryptography. This is a "math talk," intended to provide new tools and a framework to analyze lattice cryptography, aimed to encourage further research in pursuit of applicability to standards.

Suggested readings:,, arXiv:1501.00178, arXiv:1706.07373, arXiv:1910.03838, doi:10.1016/j.laa.2021.03.028, doi:10.1016/0024-3795(91)90183-W

Presented at

Crypto Reading Club talk on 2023-Jun-28

Parent Project

See: Crypto Reading Club

Related Topics

Security and Privacy: cryptography

Created May 24, 2023, Updated June 05, 2023