# How to sign comitted group elements?

I'm actually searching some particular primitive compatible with Groth Sahai commitment.

I would like to know a signature scheme (on group elements), such that there exists an algorithm $$\mathtt{SigCom}$$ such that it takes as input the commitment key $$\mathtt{ck}$$ , the signing key $$\mathtt{sk}$$ and a commitment $$\mathtt{c}$$ and outputs a committed signature $$\mathtt{c}_\sigma$$ with a (Groth-Sahai) proof $$\pi$$ that certifies the signature committed is the signature of the value (in the commitment of the input).

I found this article : https://eprint.iacr.org/2002/014.pdf It does exactly what I want except that the value are on a precise type $$\left(G^m, H^m\right)$$, and it's too restrictive for me.

If you know a more general result (or something that fit with two group elements without any relation between them), it would be amazing.