Thresholdizing HashEdDSA: MPC to the Rescue

Abstract

Following recent comments in a NIST document related to threshold cryptographic standards, we examine the case of thresholdizing the HashEdDSA signature scheme. This is a deterministic signature scheme based on Edwards elliptic curves. Unlike DSA, it has a Schnorr-like signature equation, which is an advantage for threshold implementations, but it has the disadvantage of having the ephemeral secret obtained by hashing the secret key and the message. We show that one can obtain relatively efficient implementations of threshold HashEdDSA with no modifications to the behaviour of the signing algorithm; we achieve this using a doubly authenticated bit (daBit) generation protocol tailored for Q(2) access structures that is more efficient than prior work. However, if one was to modify the standard algorithm to use an MPC-friendly hash function, such as Rescue, the performance becomes very fast indeed.