SoliloQuat: Throwing Caution to the Wind
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 underlyin