Promise $$\varSigma $$-Protocol: How to Construct Efficient Threshold ECDSA from Encryptions Based on Class Groups

Threshold Signatures allow n parties to share the ability of issuing digital signatures so that any coalition of size at least \(t+1\) can sign, whereas groups of t or fewer players cannot. The currently known class-group-based threshold ECDSA constructions are either inefficient (requiring parallel-repetition of the underlying zero knowledge proof with small challenge space) or requiring rather non-standard low order assumption. In this paper, we present efficient threshold ECDSA protocols from encryption schemes based on class groups with neither assuming the low order assumption nor parallel repeating the underlying zero knowledge proof, yielding a significant efficiency improvement in the key generation over previous constructions.