New trend for LWE application in different computer science fields.

Problems of large keys in the on-lattice ring signature link due to reduce to the lattice, based on the problem of fault-tolerant learning on the ring (RLWE), according to "Homomorphic Commitment→Σ-Protocol→Fiat-Shamir Transformation" reconstructs a linkable ring signature scheme on a lattice. First construct a base “Homomorphic commitment scheme” on polynomial ring of RLWE difficult, and use the Fiat-Shamir transformation method. The method converts the Σ-protocol into a linkable ring signature scheme, and suggests linkable ring signature scheme model. It is resistant to quantum computer attacks. compared with the previous linkable ring signature schemes on lattices, proposed methods with high computational, simple and less time frame because the ring elements in the scheme are taken from small polynomials which represents as case of application in computer science. [ABSTRACT FROM AUTHOR]