Paper 2026/1369
Algebraic Modelings of the Supersingular Isogeny Problem
, University of Genoa, University of Genoa, University of ZurichAbstract
We present a new algebraic modeling of the Supersingular Isogeny Problem as a system of multivariate polynomial equations, in the case where the elliptic curves are connected by an isogeny whose degree is a power of $2$ or $3$. This modeling relies on Renes formulas for elliptic curves in Montgomery form (degree $2$) or triangular form (degree $3$). We investigate several algebraic properties of these systems: we prove that they are zero-dimensional, compute the dimension of their highest degree part, and show that they are not in generic coordinates. Experimental results show that solving these systems via Gröbner basis techniques is significantly faster than solving the algebraic modeling with modular polynomials.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- Supersingular Isogeny ProblemGröbner basessolving degreealgebraic modeling
- Contact author(s)
-
alessio caminata @ unige it
andrea o sanguineti @ gmail com
silvia sconza @ math uzh ch - History
- 2026-07-06: approved
- 2026-07-03: received
- See all versions
- Short URL
- https://ia.cr/2026/1369
- License
-
CC BY-SA
BibTeX
@misc{cryptoeprint:2026/1369,
author = {Alessio Caminata and Andrea Sanguineti and Silvia Sconza},
title = {Algebraic Modelings of the Supersingular Isogeny Problem},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/1369},
year = {2026},
url = {https://eprint.iacr.org/2026/1369}
}
