Blockchain-Assisted Robust Subgroup ECDSA Multisignature for Consensus

Abstract

The robust subgroup multisignature allows any subgroup of signers to generate a multisignature on behalf of the whole group, which can be flexibly applied in many blockchain consensus mechanisms. Unlike the security model of traditional subgroup multisignatures, robustness can prevent dishonest signers from joining a subgroup by checking each individual signature before combining. To enhance the robustness of subgroup multisignatures, we utilize an on-chain smart contract instead of an off-chain combiner to check each individual signature. We propose a blockchain-assisted robust subgroup elliptic curve digital signature (ECDSA) multisignature scheme and prove its robustness and unforgeability. Since the ECDSA signature is the most popular signature used for blockchains and some blockchain platforms, such as Ethereum, already have a precompiled contract for the verification of the ECDSA, the on-chain costs for each single ECDSA signature are very low. Experiments show that our blockchain-assisted subgroup ECDSA multisignature has efficient on-chain costs. On the other hand, multiplicative-to-additive (MtA) protocols are used in the construction of subgroup multisignatures, which results in increased communication and computational costs. We use two popular additive homomorphic encryption scheme (Paillier and Castagnos and Laguillaumie)-based MtA protocols to construct our scheme and test its performance. Finally, we apply our scheme in a consensus mechanism of a distributed blockchain interoperability oracle.