From 8ea07dabdc798a37296877ede4a4a244559cfd70 Mon Sep 17 00:00:00 2001 From: Olga Kunyavskaya Date: Tue, 12 Dec 2023 10:52:50 +0200 Subject: [PATCH] fix style --- neps/nep-0488.md | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/neps/nep-0488.md b/neps/nep-0488.md index d26b85132..b359a68d7 100644 --- a/neps/nep-0488.md +++ b/neps/nep-0488.md @@ -87,9 +87,9 @@ $$ y^2 \equiv x^3 + Ax + B \mod p $$ -together with an imaginary point at infinity $\mathcal{O}$, where: $A, B \in F_p$, p is prime > 3, and $4A^3 + 27B^2 \not \equiv 0 \mod p$ +together with an imaginary point at infinity $\mathcal{O}$, where: $A, B \in F_p$, $p$ is a prime $> 3$, and $4A^3 + 27B^2 \not \equiv 0 \mod p$ -In the case of BLS12-381 equation is $y^2 \equiv x^3 + 4 \mod p$[^15],[^51],[^14],[^11] +In the case of BLS12-381 the equation is $y^2 \equiv x^3 + 4 \mod p$[^15],[^51],[^14],[^11] **Parameters for our case:** @@ -97,16 +97,16 @@ In the case of BLS12-381 equation is $y^2 \equiv x^3 + 4 \mod p$[^15],[^51],[^14 - $B = 4$ - $p = \mathtt{0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab}$ -Let $P \in E(F_q)$ have coordinates (x, y), define **$-P$** as a point on a curve with coordinates (x, -y). +Let $P \in E(F_q)$ have coordinates $(x, y)$, define **$-P$** as a point on a curve with coordinates $(x, -y)$. -**The addition operation for Elliptic Curve** is a function $+\colon E(F_p) \times E(F_p) \rightarrow E(F_p)$ defined with following rules: let P and Q $\in E(F_p)$ +**The addition operation for Elliptic Curve** is a function $+\colon E(F_p) \times E(F_p) \rightarrow E(F_p)$ defined with following rules: let $P$ and $Q \in E(F_p)$ - if $P \ne Q$ and $P \ne -Q$ - - draw a line passing through P and Q. This line intersects the curve at a third point R - - reflect the point R across the x-axis by changing the sign of the y-coordinate. The resulting point is P+Q. + - draw a line passing through $P$ and $Q$. This line intersects the curve at a third point $R$. + - reflect the point $R$ across the $x$-axis by changing the sign of the $y$-coordinate. The resulting point is $P+Q$. - if $P=Q$ - - draw a tangent line throw P for an elliptic curve. The line will intersect the curve at the second point R. - - reflect the point R across the x-axis the same way to get point 2P + - draw a tangent line through $P$ for an elliptic curve. The line will intersect the curve at the second point $R$. + - reflect the point $R$ across the $x$-axis the same way to get point $2P$ - $P = -Q$ - $P + Q = P + (-P) = \mathcal{O}$ — the point on infinity - $Q = \mathcal{O}$ @@ -552,7 +552,7 @@ This section aims to validate the correctness of point inversion: Edge cases: - Point not from $G_1$ -- -$\mathcal{O}$ +- $-\mathcal{O}$ Tests for incorrect data