Trapdoor function based on the Ring-LWE and applications in communications

The strong trapdoor function for lattice has been constructed by Daniele Micciancio and Chris Peikert in EUROCRYPT 2012, which is simple, efficient, and easy to implement. In this paper, we present a new trapdoor function based on ring learning with errors problem (Ring-LWE) on lattice, and simultaneously the corresponding efficient inverse algorithm is given which involves two sub-algorithms: the trapdoor inverse algorithm and the iterative inverse algorithm. Our trapdoor function for lattice based on Ring-LWE is simultaneously more simple and efficient because of the ring structure. In addition to these advantages, our algorithm extends the parameters, and this can make our trapdoor function have a wider choice of applications.