5
$\begingroup$

I am going through the Pinocchio protocol paper and I need 2 clarifications in the section Protocol 1 (Verifiable Computation from strong QAP). The part that explains the Verify process, which contains this expression: $$e(g^{v_0}.g^{v_{io}}.g^{v(s)}, g^{w_0}.g^{w(s)})/e(g^{y_0}.g^{y(s)},g) = e(g^{h(s)},g^{t(s)})$$.

  1. since $e:G \times G \to G_T$, what is the definition of the division operation as shown in the expression above, wrt $G_T$?

  2. If my understanding is correct, the first term in the first pairing should be $g^{v_0}.g^{v_{io}}.g^{v_{mid}(s)}$ instead of $g^{v_0}.g^{v_{io}}.g^{v(s)}$

$\endgroup$
  • 1
    $\begingroup$ $G_T$ is the multiplicative group of a finite field, so the division is division in that field. I'll look into 2 (and post an answer) later, if no one does it before. $\endgroup$ – fkraiem Mar 7 at 8:03
  • $\begingroup$ OK the division is the multiplicative inverse in that group. Now it seems obvious. Thanks. Any update on 2? $\endgroup$ – Abhijit Mar 8 at 7:22
3
$\begingroup$

The first part of the question is answered in the comments. Regarding the second part, yes, indeed, you are right! It's a typo in the Pinocchio paper, Section 2.3. Protocol 1., you also linked. The problem is that the left hand side of the verification equation enumaretes the I/O related coefficients twice in the left wire polynomial, V, therefore $g^{v_0}.g^{v_{io}}.g^{v_{mid}(s)}$ should be instead of $g^{v_0}.g^{v_{io}}.g^{v(s)}$ in the first argument of the first pairing.

However, in the original version of the protocol, see the end of Section 3.1., this typo error is not present.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.