A hybrid lattice-based commitment scheme for anonymous proof of linear relations between hidden values is proposed. The proposed approach is based on a modification of the BDLOP zero-knowledge scheme, where Learning with Errors problem was replaced with Learning with Rounding problem, which reduced the parameter sizes and complexity of parameter sampling process. The proposed scheme retains its mathematical properties, including additive homomorphism, enabling it use for proving linear relations. The results obtained can be applied to the design of protocol of electronic voting and anonymous transactions.