For any monotone function in a complete lattice, one can obtain its least fixed-point by finding the limit of the approximation sequence obtained by starting with the minimal element and iteratively substituting the result of the function to be its input. However if we start with an arbitrary element, or the function is not monotone, then the approximation sequence sometimes oscillates instead of converging. We study the (iterative) substitution over basic modal logic, characterizing its power and applying it to analyze oscillations.
We propose a new PRG-based function secret sharing scheme to succinctly and additively share multi-point functions. It appears to be the practically fastest solution in most application scenarios (e.g. when used to derive pseudorandom correlation generator for OLEs).
Attempts to solve standard lattice problems via qunatum algorithms
We attempted to solve standard lattice problems via quantum algorithms by first reducing it to a quantum analog of LWE (learning with errors) with special error distribution, and then solving the quantum LWE problem. We closed the first step, leaving the second step open.
We discuss a simple logic to describe the hide-and-seek game, and show that adding an equality constant to describe the winning condition of the seeker makes our logic undecidable.
