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May
8
comment What does $(\mathbb{Z}_n^*)^2$ mean?
@HenrickHellström: I have looked a little bit around. The theorem was copied from another paper. In the original paper they have never used quadratic residues but Cartesian products. It makes all sense now! Thanks a lot for your help!
May
8
comment What does $(\mathbb{Z}_n^*)^2$ mean?
Thanks for your answer. I have inserted the theorem which contains $\mathbb{Z}_n^*$. I think what they really mean is $(g, h) \in (\mathbb{Z}_n^∗)^2$, or?
Apr
28
comment Question about proof of knowledge defintion?
thanks for your answer, but I don't get why the number of trials is important. The term says that $K$ returns the secret in polynomial time ($|x|^c$), right? Do you know, why the factor $1/..$ is important (why not write just $|x|^c$)?
Apr
14
comment Comprehension question on a signature protocol based on the RSA assumption
your answer really, really helps! Thanks a lot!!! The paper is about the CL-protocol (tor-svn.freehaven.net/anonbib/cache/camenisch2002ssep.pdf). They choose $n$ as a safe prime product, so you are right in general. What I still don't get is why they say, that the exponent (in the paper they call it $e$ instead of $x$) must be prime.
Mar
8
comment Zero-knowledge proof that a group element is a quadratic residue?
A signature of knowledge means to use the Fiat-Shamir heuristic to make a ZK proof protocol non-interactive. It uses the output of a hash function as the challenge. Security is then also based on the random oracle model.
Mar
8
comment How difficult is it to check if a group element is in a sub group?
Thanks, this helps!
Mar
8
comment How difficult is it to check if a group element is in a sub group?
It was just a general question. I didn't have a specific group in my mind.
Mar
8
comment Is it possible to determine the group order by knowing the “public” and “private” key exponents in an RSA group?
cool, this helps... Thanks!
Jan
24
comment How to find an element of high-order in an RSA group?
Thanks for your answer. Maybe I am thinking to complicated but how can I find such elements and how can I be sure that they have maximum order?
Jan
21
comment Why work in a subgroup QR(n) of an RSA group $Z^*_n$?
thanks a lot, this helps...