Take the 2-minute tour ×  Let $P_i(x)$ be polynomials
$i=1,...,n$, $s$ some value, and $g$ a generator of a group $G$
where the discrete logarithm is hard.  Assume a prover wants to
convince a verifier having access to the values $g^{P_i(s)}$
that it knows polynomials $q_i(x)$ such that the following
equation holds:
$q_1(s)*P_1(s)+q_2(s)*P_2(s)+\ldots+q_n(s)*P_n(s) = 1.$  The
prover thus sends the verifier the values $g^{q_i(s)}$ and uses
bilinear maps to verify the correctness of the answer.  Can the
following equation tell me whether it has correctly computed the
$q_i(s)$: $$e(g^{q_i(s)},g^{P_i(s)}) = e (g,g)$$ where $e$ is a
bilinear map $G\times G\rightarrow G_1$.  So basically I want my
bilinear map to verify on the exponents while hiding them. Is
the second part of the equation correct? Or should it be 1, or
$e(g,g)^{ord(G)}=1$?  share|improve this question There seems to
be a typo or grammatical error in the question, which has me
lost. "...for some secret s that the prover which is...": is
there some