CryptoDB
Faster SCALLOP from Non-Prime Conductor Suborders in Medium Sized Quadratic Fields
| Authors: |
|
|---|---|
| Download: | |
| Conference: | PKC 2025 |
| Abstract: | A crucial ingredient for many cryptographic primitives such as key exchange protocols and advanced signature schemes is a commutative group action where the structure of the underlying group can be computed efficiently. SCALLOP provides such a group action, based on oriented supersingular elliptic curves. We present PEARL-SCALLOP, a variant of SCALLOP that changes several parameter and design choices, thereby improving on both efficiency and security and enabling feasible parameter generation for larger security levels. Within the SCALLOP framework, our parameters are essentially optimal; the orientation is provided by a $2^e$-isogeny, where $2^e$ is roughly equal to the discriminant of the acting class group. As an important subroutine we present a practical algorithm for generating oriented supersingular elliptic curves. To demonstrate our improvements, we provide a proof-of-concept implementation which instantiates PEARL-SCALLOP at all relevant security levels. Our timings are more than an order of magnitude faster than any previous implementation. |
BibTeX
@inproceedings{pkc-2025-35169,
title={Faster SCALLOP from Non-Prime Conductor Suborders in Medium Sized Quadratic Fields},
publisher={Springer-Verlag},
author={Bill Allombert and Jean-François Biasse and Jonathan Komada Eriksen and Péter Kutas and Chris Leonardi and Aurel Page and Renate Scheidler and Márton Tot Bagi},
year=2025
}