PEARL-SCALLOP: Parameter Extension Applicable in Real-Life SCALLOP

Bill Allombert; Jean-François Biasse; Jonathan Komada Eriksen; Péter Kutas; Chris Leonardi; Aurel Page; Renate Scheidler; Márton Tot Bagi

Paper 2024/1744

PEARL-SCALLOP: Parameter Extension Applicable in Real-Life SCALLOP

Bill Allombert, French National Centre for Scientific Research, University of Bordeaux

Jean-François Biasse, University of South Florida

Jonathan Komada Eriksen, KU Leuven

Péter Kutas, Eötvös Loránd University, University of Birmingham

Chris Leonardi, ISARA Corporation

Aurel Page, French Institute for Research in Computer Science and Automation, University of Bordeaux

Renate Scheidler, University of Calgary

Márton Tot Bagi, Eötvös Loránd University

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.

Note: Author affiliations added

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Isogeny Group Action Post-Quantum Cryptography
Contact author(s): Bill Allombert @ math u-bordeaux fr
biasse @ usf edu
jonathan eriksen97 @ gmail com
kutasp @ gmail com
chris leonardi @ isara com
aurel page @ inria fr
rscheidl @ ucalgary ca
mtotbagi @ gmail com
History: 2024-10-29: revised; 2024-10-25: received; See all versions
Short URL: https://ia.cr/2024/1744
License: CC BY

BibTeX

@misc{cryptoeprint:2024/1744,
      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},
      title = {{PEARL}-{SCALLOP}: Parameter Extension Applicable in Real-Life {SCALLOP}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/1744},
      year = {2024},
      url = {https://eprint.iacr.org/2024/1744}
}