Paper 2020/289
The security of Groups of Unknown Order based on Jacobians of Hyperelliptic Curves
Jonathan Lee
Abstract
Recent work using groups of unknown order to construct verifiable delay functions, polynomial commitment schemes and non interactive zero knowledge proofs have provoked fresh interest in the construction of efficient cryptographic groups of unknown order. It has been suggested that the Jacobian of hyperelliptic curves of genus 3 could be suitable for this purpose. Regrettably, efficient algorithms to compute the order of the Jacobian of a hyperelliptic curve are known. Concretely, it is unclear whether these groups are competitive with RSA groups or class groups at or above the 128 bit security level.
Metadata
- Available format(s)
-
PDF
- Category
- Cryptographic protocols
- Publication info
- Preprint. MINOR revision.
- Keywords
- hyperelliptic curvesaccumulatorsunknown order groupsverifiable delay functionzksnark
- Contact author(s)
- jonatlee @ microsoft com
- History
- 2020-03-06: received
- Short URL
- https://ia.cr/2020/289
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2020/289,
author = {Jonathan Lee},
title = {The security of Groups of Unknown Order based on Jacobians of Hyperelliptic Curves},
howpublished = {Cryptology ePrint Archive, Paper 2020/289},
year = {2020},
note = {\url{https://eprint.iacr.org/2020/289}},
url = {https://eprint.iacr.org/2020/289}
}
