Lattice-Based Commitment Scheme for Proving Linear Relations between Hidden Values

A hybrid lattice-based commitment scheme is proposed for anonymous proofs between hidden values. The method is based on a modification of the BDLOP zero-knowledge proof (ZKP) scheme by replacing the learning with errors (LWE) problem with a learning with rounding (LWR) problem, which theoretically makes it possible to reduce the size of the parameters and reduce the complexity of parameter selection. It is shown that the proposed scheme preserves the property of additive homomorphism, which makes it possible to apply it to prove linear relations. The obtained results can be applied to construct electronic voting protocols or conduct anonymous transactions.