From 62757bfa614c9653a09586327d9651df57cd28ce Mon Sep 17 00:00:00 2001 From: therealyingtong Date: Wed, 24 May 2023 02:02:22 +0800 Subject: [PATCH] Fix step 14; fix v in step 18 Co-authored-by: Daira Hopwood Co-authored-by: str4d --- book/src/design/protocol.md | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/book/src/design/protocol.md b/book/src/design/protocol.md index 89319e4b..539e41ab 100644 --- a/book/src/design/protocol.md +++ b/book/src/design/protocol.md @@ -353,7 +353,7 @@ In the following protocol, we take it for granted that each polynomial $a_i(X, \ 14. $\prover$ sends $Q' = \innerprod{\mathbf{q'}}{\mathbf{G}} + [\cdot] W$ where $\mathbf{q'}$ defines the coefficients of the polynomial $$q'(X) = \sum\limits_{i=0}^{n_q - 1} -x_2^i +x_2^{n_q - 1 - i} \left( \frac {q_i(X) - r_i(X)} @@ -371,9 +371,10 @@ $$ 17. $\verifier$ responds with challenge $x_4$. 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 = $ $$ +x_4^{n_q} \cdot \sum\limits_{i=0}^{n_q - 1} \left( -x_2^i +x_2^{n_q - 1 - i} \left( \frac { \mathbf{u}_i - r_i(x_3) } @@ -387,7 +388,7 @@ x_2^i \right) \right) + -x_4 \sum\limits_{i=0}^{n_q - 1} x_4 \mathbf{u}_i +\sum\limits_{i=0}^{n_q - 1} x_4^{n_q - 1 - i} \mathbf{u}_i $$ 19. $\prover$ sets $p(X) = x_4^{n_q} \cdot q'(x) + \sum\limits_{i=0}^{n_q - 1} x_4^{n_q - 1 - i} \cdot q_i(X)$. 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 $s(X)$.