Expand Alogrithm in paper

[czh-rot]

I am confused about the pseudocode described in the paper. Take the Figure 3 and Figure 4.
(1) query = Enc(x^2);
(2) First Outer loop: C0=Enc(x^2), C1=Enc(x^1), C0'=C0+sub(C0,5), C1'=C1+sub(C1,5);
In this step, sub(C1, 5) = Enc(x^5) mod x^4+1 = Enc(-x^1), so C1= Enc(0);
But, sub(C0, 5) = Enc(x^10) mod x^4+1, I do not know if my solution is right, but x^10 = x^4+1 * (x^6-x^2) + x^2, so sub(C0,5) = Enc(x^2) ? If it is true, C0' = Enc(2x^2), why the result in Figure 4 is [0,2,0,0], i.e., Enc(2x^1)?

I would appreciate it if you could point out my mistake.

[sga001]

Are you looking at the latest version of the paper? https://www.cis.upenn.edu/~sga001/papers/pbc-sp18.pdf

It seems I forgot to update the eprint version a while back. I have updated the eprint version as well.

[czh-rot]

So, the 1st outer loop finish, ciphertext[k] = {Enc(2x^2), Enc(0)};
for the 2nd outer loop & 1st inner loop:
(1) C0 =ciphertext[0] [0,0,2,0], i.e., Enc(2x^2);
(2) C1 = C0 * x^-2 = [2,0,0,0], i.e., Enc(2);
(3) C0' = C0 + sub(C0, 3) = Enc(2x^2) + Enc(2x^6) mod (x^4+1) = Enc(2x^2) + Enc(-2x^2) = Enc(0);
(4) C2' = C1 + sub(C1, 3) = Enc(2) + Enc(2)mod (x^4+1) = Enc(4);
and the 2nd inner loop generate C1' & C3';

Nice job! I haven't found the pattern yet, but thank you very much for your reply