Lets assume we have a group $G$ with unknown order. And we have a pair $(A_1,K_1), (A_2,K_2)$ in which all $A_1,K_1,A_2,K_2$ are group elements. The claim is $A_1= K_1 ^ x$ and $A_2 = K_2 ^ x$. or informally we want to show they both have the same exponent. ($x$ is prime)
We do not want to share both $K_1,K_2$. We want to share a single element as a proof for this fact. It is ok if someone can extract $K_1,K_2$ from the single element provided.
Is there any protocol for this?