From ec76fd36cc6b9e9d0f7a9495094e76b86e53dab4 Mon Sep 17 00:00:00 2001 From: Tengfei Niu Date: Sun, 4 Sep 2022 12:41:47 +0800 Subject: [PATCH] Fix book error (#162) * Fix book error * fix typos in book --- plonk-book/src/chapter_1.md | 2 +- plonk-book/src/chapter_2.md | 4 ++-- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/plonk-book/src/chapter_1.md b/plonk-book/src/chapter_1.md index e7e6fbfd..0d89d64d 100644 --- a/plonk-book/src/chapter_1.md +++ b/plonk-book/src/chapter_1.md @@ -76,7 +76,7 @@ We will first compute $P+Q$ in the affine form and then projective form. 1. We have two points $P=(x_p,y_p)$ and $Q=(x_q,y_q)$ where $P\neq Q$. If $P=O$ then $P$ is the identity point which means $P+Q=Q$. Likewise if $Q=O$, then $P+Q=P$ \ Else, $P+Q=S$ for $S=(x_s,y_s)$ where $S=-R$ (the point represented in the graph) such that: $$x_s=\lambda^2-x_p-x_q$$ and $$y_s=\lambda(x_p-x_s)-y_p$$ where $\lambda=\dfrac{y_q-y_p}{x_q-x_p}$ -2. In the projective form, each elliptic curve point has 3 coordinates instead of 2 $(x,y,z)$ for $z\neq 0$ (for all points except the point at infinity). Using the projective form allows us to give coordinates to the point at infinity. It also speeds up some of the most used arithmetic operations in the curve. The forward mapping is given by $(x,y)\rightarrow (xz,yz,z)$ and reverse mapping is giving by $(x,y,z)(\dfrac{x}{z},\dfrac{y}{z})$. Let $P=(x_p,y_p,z_p)$ and $Q=(x_q,y_q,z_q)$ and $\dfrac{x_p}{z_q}\neq\dfrac{x_q}{z_p}$. +2. In the projective form, each elliptic curve point has 3 coordinates instead of 2 $(x,y,z)$ for $z\neq 0$ (for all points except the point at infinity). Using the projective form allows us to give coordinates to the point at infinity. It also speeds up some of the most used arithmetic operations in the curve. The forward mapping is given by $(x,y)\rightarrow (xz,yz,z)$ and reverse mapping is giving by $(x,y,z)(\dfrac{x}{z},\dfrac{y}{z})$. Let $P=(x_p,y_p,z_p)$ and $Q=(x_q,y_q,z_q)$ and $\dfrac{x_p}{z_p}\neq\dfrac{x_q}{z_q}$.
diff --git a/plonk-book/src/chapter_2.md b/plonk-book/src/chapter_2.md index e4595757..63633701 100644 --- a/plonk-book/src/chapter_2.md +++ b/plonk-book/src/chapter_2.md @@ -179,7 +179,7 @@ will add blinders to add the zero-knowledge property to the Plonk protocol. e(W + r'\cdot W', [x]_2) $$ -Extending the right side of the check we get +Extending the left side of the check we get $$ e(F +z \cdot W + r'z'\cdot W', [1]_2) =\\ e( \left( \sum_{i=1}^{t_1} \gamma^{i-1} \cdot cm_i - @@ -214,7 +214,7 @@ Extending the right side of the check we get [1]_2) $$ -From the left side we get +From the right side we get $$ e(W + r' \cdot W', [x]_2) =\\ e( \sum_{i=1}^{t_1} \gamma^{i-1}