qap¶
Module Contents¶
Classes¶
Given $n$ equations we pick arbitrary distinct $r_1,cdots,r_n in mathbb{F}$ and define |
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class
qap.QAP(A=Iterable, B=Iterable, C=Iterable)¶ Given $n$ equations we pick arbitrary distinct $r_1,cdots,r_n in mathbb{F}$ and define $$ t(x) = prod_{q=1}^n (x - r_q) $$ Since $t(X)$ is the lowest degreee monomial with $t(r_q) = 0 $ in each point, we can refomulate as: $$ sum_{i=0}^m a_i u_i(X) circ sum_{i=0}^m a_i v_i(X) = sum_{i=0}^m a_i w_i(X) mod t(X) $$ we will be working with quadratic arithmetic programsRthat have thefollowing description
$$ R = (mathbb{F}, aux, l, {u_i(X), v_i(X), w_i(X)}_{i=0}^n, t(X)) $$
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O(self, ws)¶
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H(self, ws)¶
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property
qap(self)¶
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proof(self, x: FiniteField, s: Iterable[FiniteField], start=0, end=None)¶ c: Callange s: witness vertex
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verify(s, A, B, C, Z, H)¶
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