SoliloQuat: Throwing Caution to the Wind

Andrew Mendelsohn; Ben Nelson

Paper 2026/859

SoliloQuat: Throwing Caution to the Wind

Andrew Mendelsohn

, Imperial College London

Ben Nelson

Abstract

We propose a plausibly post-quantum additively homomorphic PKE scheme, SoliloQuat, based on the short generator principal ideal problem (SG-PIP) in orders of quaternion algebras. SoliloQuat is inspired by Soliloquy, a KEM that was both introduced and broken by Campbell-Groves-Shepherd in 2014. However, it is not known if their attack can be generalised to the non-commutative setting, despite having received cryptanalytic attention due to a reduction from the rank 2 module-LIP instances underlying HAWK to nrd-PIP (Eurocrypt `25). Demonstrating the correctness of our scheme requires novel results on the eigenvalues of the left regular representation of quaternions, which may be of independent interest. We prove IND-CPA security of our scheme, assuming the hardness both of SG-PIP in orders of quaternion algebras, and some less-exotic lattice-based assumptions.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: post-quantum cryptography principal ideal problem quaternions lattices
Contact author(s): andrew mendelsohn18 @ imperial ac uk
bennelson3141 @ gmail com
History: 2026-05-05: approved; 2026-05-01: received; See all versions
Short URL: https://ia.cr/2026/859
License: CC BY

BibTeX

@misc{cryptoeprint:2026/859,
      author = {Andrew Mendelsohn and Ben Nelson},
      title = {{SoliloQuat}: Throwing Caution to the Wind},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/859},
      year = {2026},
      url = {https://eprint.iacr.org/2026/859}
}