+ HomElG Zero-knowledge Proof Protocol for Privacy Protection of Consortium Blockchain Transfer

Abstract

In order to solve the problems of imperfect transaction legitimacy verification strategies for protecting account balances and transaction amounts in privacy protection of consortium blockchain, and the low efficiency of the basic encryption algorithm Paillier, a ⁺HomElG zero-knowledge proof protocol for consortium blockchain transfer privacy protection was proposed. A consortium blockchain transfer privacy protection application was constructed based on PBFT, which expounded the consensus interaction scenario of zero-knowledge proof of homomorphic encryption. The transaction amount and balance of account were encrypted by the ⁺HomElG algorithm, and the zero-knowledge proof of the ciphertext was designed with the Σ protocol. The non-interactive zero-knowledge was designed through the idea of the Fiat-Shamir algorithm processes such as the proof of equality, the amount of the transaction greater than zero and the balance of the transfer party not less than zero in the proof of range. The protocol was proved to be correct, complete and zero-knowledge under the DDH. A consortium blockchain transfer privacy protection prototype system based on Hyperledger Fabric was constructed. The results verified that the protocol can realize ciphertext transactions to protect balance of account and transaction amount under the condition of non-interactive zero-knowledge proof. When the key length is 3072 bit and the data length is a 12-bit decimal integer, the efficiency of the ⁺HomElG algorithm is 150.3 ms, and the efficiency of the proof of equality, the amount of the transaction greater than zero and the balance of the transfer party not less than zero in the proof of range are 482.3 ms, 209.3 ms and 261.3 ms respectively. Compared with the existing protocols, the proposed ⁺HomElG algorithm is more efficient, and its transaction legitimacy verification strategies such as equality proof and range proof are more perfect and efficient. The proposed protocol can meet the privacy protection requirements of consortium blockchain transfer transactions.