A new approach to efficient verifiable secret sharing for threshold KCDSA signature

Abstract

This paper is to propose a threshold KCDSA (Korean Certificationbased Digital Signature Algorithm) signature scheme. For this goal we present some new secret sharing schemes and a robust multiplication protocol based on the non-interactive ZK proof. The secret sharing scheme using a hash function can verify the validity of the received data easily, therefore we can reduce the complexity of the protocol. Also we present a robust multiplication protocol of two shared secrets based on non-interactive ZK proof scheme. Players check the validity of the broadcasted shares by using a non-interactive ZK proof, and accept only the correct shares, and then interpolate the polynomial by using the accepted shares. Finally we propose a threshold KCDSA signature, which is composed of key-sharing protocol and signature generation protocol. We prove that the proposed KCDSA signature is a (t, n)-robust threshold protocol, which tolerates up to t eavesdropping and halting faults if the number of players is n ≥ 2t +1.