I'm trying to test the ring signature scheme proposed by Rivest Shamir and Tauman in the famous paper "How to leak a secret".
One of the step consist in
4) the signer solves the following ring equation for y1: Ck,v(y1,y2,y3)=v"
I have everything except $y_1$.
It's defined that
$C_k,v(y_1,y_2,y_3) = E_k(y_1 \oplus E_k(y_2 \oplus E_k(y_3 XOR v)))$
where $E_k$ means symmetric encryption with the key $k$.
So what I have to solve is something like:
$y_1 = ? \\ y_2 = 1010 \\ y_3 = 1011 \\ v = 0011$
I have no idea whatsoever on how to solve this. Can you at least tell me if this is possible?
I know that I should provide k and other things but the only thing i need to know if it is possible to actually solve that thing above and how. In reality I'm using 64 bits binary numbers, not 4 bits.
The main question is: can I solve this for $x$, knowing the key $k$?
$$E_k( BinaryNumber \oplus x ) = BinaryNumber$$