Paper 2025/521 Original: eprint.iacr.org/2025/521 ↗
Division polynomials for arbitrary isogenies
Abstract
Following work of Mazur-Tate and Satoh, we extend the definition of division polynomials to arbitrary isogenies of elliptic curves, including those whose kernels do not sum to the identity. In analogy to the classical case of division polynomials for multiplication-by-n, we demonstrate recurrence relations, identities relating to classical elliptic functions, the chain rule describing relationships between division polynomials on source and target curve, and generalizations to higher dimension (i.e., elliptic nets).
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2025-03-19: last updated
- 2025-03-19: published
- Short URL
- https://ia.cr/2025/521
- License
- https://creativecommons.org/licenses/by-nc-nd/4.0/
BibTeX
@misc{cryptoeprint:2025/521,
author = {Katherine E. Stange},
title = {Division polynomials for arbitrary isogenies},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/521},
year = {2025},
url = {https://eprint.iacr.org/2025/521}
}