# Is there a signature scheme for the Cramer-Shoup cryptosystem?

I have a project that I have to use cryptosystem and signature scheme for it.

I've read about Cramer-Shoup cryptosystem and I want to use it since it is more secure the ElGamal cryptosystem, but, I need a signature scheme based on it which I did not find. Is there such a signature scheme?

If it does not exist I thought of two solutions:

1. I can use DSA for it but since there is one generator $g$ in DSA and two generators $g_1$,$g_2$ in Cramer-Shoup cryptosystem. So I think I may not be able to use it.
2. I can generate a separate DH key and use it as a signature public key for the user. Then I could use this key for DSA. But I am not sure if this is considered secure.

Are these options valid?

• @Sebi Easy there, cowboy. It's OK to ask for accepting an answer after a day or so, if there is no peep from the poster in the mean time. Jul 26 '15 at 21:58
• @Maarten Bodewes :P This question was migrated from security.stackexchange.com. People seem rather shy on accepting answers there :))
– Sebi
Jul 26 '15 at 22:02
• @Sebi Trust me if I say that it is the same on SO. Not so much here. But you do have to give people some time. Last time I asked a question - not something that occurs often - I was asked out to dinner right after... Anyway, welcome to crypto :) Jul 26 '15 at 22:07