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: ia.cr/2021/154, ia.cr/2022/861, 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
Security and Privacy: cryptography