Ben Nelson
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.
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}
}
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