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:
- 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.
- 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?