I have read the paper "Threshold Cryptosystems from Threshold Fully Homomorphic Encryption" [BGG+17] and would like to ask about the threshold signature scheme construction in Section 8.2.
Question.
I have one question about the threshold signature construction in Section 8.2 in [BGG+17]. The construction requires modeling the signature scheme as a circuit (see picture below).
However, all existing signature schemes I know are only proven secure in random oracle model, and you cannot model a random oracle as circuit. Therefore, I would like to ask if there is any existing signature scheme that is proven to be secure in the standard model. So far, I know that the paper [PS19] provides a NIZK for all NP relations in the crs model, but I do not know if the NIZK is sufficient for a signature, since it is not a PoK (Proof of Knowledge), while all existing signature schemes I know use a PoK to extract the secret key by rewinding.
Reference.
[BGG+17] Threshold Cryptosystems from Threshold Fully Homomorphic Encryption (https://eprint.iacr.org/2017/956.pdf).
[PS19] Non-Interactive Zero-Knowledge for all NP from Plain Learning with Error (https://web.eecs.umich.edu/~cpeikert/pubs/nizk-lwe.pdf).
