Paper 2026/859 Original: eprint.iacr.org/2026/859 ↗
SoliloQuat: Throwing Caution to the Wind
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.
- History
- 2026-05-01: last updated
- 2026-05-01: published
- Short URL
- https://ia.cr/2026/859
- License
- https://creativecommons.org/licenses/by/4.0/
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}
}