Public-key encryption from high-rate, low-noise sLSN or via improved reductions

Develop either (i) an improved quantum reduction that extends the current sLSN[k,n,p] to sympLPN reduction beyond k = O(log n), or (ii) a direct construction of public-key encryption based on the high-rate, low-noise state Learning Stabilizers with Noise (sLSN) problem, thereby avoiding reliance on classical sympLPN in the public-key setting.

Background

The paper’s public-key encryption and OT rely on reducing sLSN with k = O(log n) to a classical sympLPN instance and then building from sympLPN. The authors note that sLSN hardness appears not to scale with k in the same way as LPN, suggesting potential for direct or stronger constructions if k could be larger.

Achieving either an improved reduction or a direct construction would tighten the connection between quantum-native hardness (sLSN) and classical public-key primitives.