mirror of https://github.com/zcash/halo2.git
Fix step 14; fix v in step 18
Co-authored-by: Daira Hopwood <daira@jacaranda.org> Co-authored-by: str4d <jack@electriccoin.co>
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@ -353,7 +353,7 @@ In the following protocol, we take it for granted that each polynomial $a_i(X, \
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14. $\prover$ sends $Q' = \innerprod{\mathbf{q'}}{\mathbf{G}} + [\cdot] W$ where $\mathbf{q'}$ defines the coefficients of the polynomial
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14. $\prover$ sends $Q' = \innerprod{\mathbf{q'}}{\mathbf{G}} + [\cdot] W$ where $\mathbf{q'}$ defines the coefficients of the polynomial
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$$q'(X) = \sum\limits_{i=0}^{n_q - 1}
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$$q'(X) = \sum\limits_{i=0}^{n_q - 1}
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x_2^i
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x_2^{n_q - 1 - i}
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\left(
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\left(
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\frac
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\frac
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{q_i(X) - r_i(X)}
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{q_i(X) - r_i(X)}
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@ -371,9 +371,10 @@ $$
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17. $\verifier$ responds with challenge $x_4$.
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17. $\verifier$ responds with challenge $x_4$.
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18. $\verifier$ sets $P = [x_4^{n_q}]Q' + \sum\limits_{i=0}^{n_q - 1} [x_4^{n_q - 1 - i}] Q_i$ and $v = $
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18. $\verifier$ sets $P = [x_4^{n_q}]Q' + \sum\limits_{i=0}^{n_q - 1} [x_4^{n_q - 1 - i}] Q_i$ and $v = $
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$$
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$$
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x_4^{n_q} \cdot
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\sum\limits_{i=0}^{n_q - 1}
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\sum\limits_{i=0}^{n_q - 1}
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\left(
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\left(
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x_2^i
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x_2^{n_q - 1 - i}
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\left(
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\left(
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\frac
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\frac
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{ \mathbf{u}_i - r_i(x_3) }
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{ \mathbf{u}_i - r_i(x_3) }
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@ -387,7 +388,7 @@ x_2^i
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\right)
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\right)
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\right)
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\right)
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+
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+
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x_4 \sum\limits_{i=0}^{n_q - 1} x_4 \mathbf{u}_i
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\sum\limits_{i=0}^{n_q - 1} x_4^{n_q - 1 - i} \mathbf{u}_i
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$$
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$$
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19. $\prover$ sets $p(X) = x_4^{n_q} \cdot q'(x) + \sum\limits_{i=0}^{n_q - 1} x_4^{n_q - 1 - i} \cdot q_i(X)$.
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19. $\prover$ sets $p(X) = x_4^{n_q} \cdot q'(x) + \sum\limits_{i=0}^{n_q - 1} x_4^{n_q - 1 - i} \cdot q_i(X)$.
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20. $\prover$ samples a random polynomial $s(X)$ of degree $n - 1$ with a root at $x_3$ and sends a commitment $S = \innerprod{\mathbf{s}}{\mathbf{G}} + [\cdot] W$ where $\mathbf{s}$ defines the coefficients of $s(X)$.
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20. $\prover$ samples a random polynomial $s(X)$ of degree $n - 1$ with a root at $x_3$ and sends a commitment $S = \innerprod{\mathbf{s}}{\mathbf{G}} + [\cdot] W$ where $\mathbf{s}$ defines the coefficients of $s(X)$.
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