Paper 2026/191

On the Active Security of the PEARL-SCALLOP Group Action

Marc Houben, Inria Bordeaux - Sud-Ouest Research Centre, Institut de Mathématiques de Bordeaux

Gioella Lorenzon, KU Leuven

Ryan Rueger, IBM Research - Zurich, Technical University of Munich

Parsa Tasbihgou, École Polytechnique Fédérale de Lausanne

Abstract

We present an active attack against the PEARL-SCALLOP group action. Modelling Alice as an oracle that outputs the action by a secret ideal class on suitably chosen oriented elliptic curves, we show how to recover the secret using a handful of oracle calls (four for the parameter set targeting a security level equivalent to CSIDH-1024), by reducing to the computation of moderately-sized group action discrete logarithms. The key ingredient to the attack is to employ curves with non-primitive orientations inherent to the PEARL-SCALLOP construction. We provide methods for public-key validation — that is, for deciding whether a given orientation is primitive — and discuss their practicality.

Note: Revision 2026/04/13: corrections in Section 4 and typos.

@misc{cryptoeprint:2026/191,
      author = {Tako Boris Fouotsa and Marc Houben and Gioella Lorenzon and Ryan Rueger and Parsa Tasbihgou},
      title = {On the Active Security of the {PEARL}-{SCALLOP} Group Action},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/191},
      year = {2026},
      url = {https://eprint.iacr.org/2026/191}
}