Abstract: The decentralization of blockchain can easily lead to the leakage of users’ private data at the transaction layer,which in turn leads to information security issues.The zero-knowledge range proof is designed to confidentially verify that the transaction data belongs to a legal positive integer range without revealing the transaction data.It effectively solves the problem of blockchain privacy leakage.The existing blockchain range proof scheme can still be further optimized in terms of proof speed,verification speed and calculation cost.In addition,the existing solutions cannot handle the floating-point number problem,thus limiting the application fields of range proofs.This paper proposes an efficient range proof scheme with constant computational cost and universal for floating-point numbers and integers,ZKFERP.It improves the zero-knowledge protocol based on Bulletproofs to optimize the proof structure,and a Lagrangian inner product vector generation method is designed to make the witness generation time constant and the commitment is constructed according to the floating-point number range relationship to implement floating-point range proof.ZKFERP only relies on the discrete logarithm assumption,and third-party credibility is not required.The communication cost and time complexity of ZKFERP are constant.Experimental results show that,compared with the most advanced known range proof scheme,ZKFERP’s proof speed is increased by 40.0%,and the verification speed is increased by 29.8%.

Key words: Blockchain, Privacy protection, Zero-knowledge proof, Range proof, Vector inner product commitment