# Binary equation with encryption

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 $k$?

$$E_k( BinaryNumber \oplus x ) = BinaryNumber$$

• Decrypt and then XOR. – SEJPM Oct 7 '15 at 20:22
• Are you telling me that Ek(Binary number) XOR Ek (unknown) is the same as Ek(Binary number XOR unknown) ? – user3753342 Oct 8 '15 at 13:24
• And of course this is not working... for example using E(f999 XOR a123) = ad8b4583635c2f1b), whereas doing E(f999)XOR E(a123) gives e87a515b1c28eba2. Both time with the same key 63 using DES in ECB. every number is hexadecimal, including the key. – user3753342 Oct 8 '15 at 13:55
• I'm telling you that x=Dk(BinaryNumber)XOR BinaryNumber. – SEJPM Oct 8 '15 at 15:30