KEA assumption details
I think why this assumption is hard is that in the prime field $F_p$, you can't find directly $a$ from $g^a \bmod p$ , where $g$ is generator.
So if prime is too large it takes a lot of time to find $a$, because you need to try all the elements in $1..p$.

that is based on DLP(Discrete Logarithm Problem).