From 91f8558c13299bc987878ee024d72042cd8c8de4 Mon Sep 17 00:00:00 2001 From: Yoichi Hirai Date: Mon, 5 Mar 2018 15:14:47 +0100 Subject: [PATCH 1/2] Fix the curve equation of G2 It is different from that of G1. See https://github.com/ethereum/yellowpaper/pull/659 --- EIPS/eip-197.md | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/EIPS/eip-197.md b/EIPS/eip-197.md index 0f553472..7abcc842 100644 --- a/EIPS/eip-197.md +++ b/EIPS/eip-197.md @@ -53,12 +53,11 @@ In order to check that an input is an element of `G_1`, verifying the encoding o ### Definition of the groups -The groups `G_1` and `G_2` are cyclic groups of prime order `q = 21888242871839275222246405745257275088548364400416034343698204186575808495617` on the elliptic curve `alt_bn128` defined by the curve equation -`Y^2 = X^3 + 3`. +The groups `G_1` and `G_2` are cyclic groups of prime order `q = 21888242871839275222246405745257275088548364400416034343698204186575808495617`. -The group `G_1` is a cyclic group on the above curve over the field `F_p` with `p = 21888242871839275222246405745257275088696311157297823662689037894645226208583` with generator `P1 = (1, 2)`. +The group `G_1` is defined on the curve `Y^2 = X^3 + 3` over the field `F_p` with `p = 21888242871839275222246405745257275088696311157297823662689037894645226208583` with generator `P1 = (1, 2)`. -The group `G_2` is a cyclic group on the same elliptic curve over a different field `F_p^2 = F_p[i] / (i^2 + 1)` (p is the same as above) with generator +The group `G_2` is defined on the curve `Y^2 = X^3 + 3 ((i+9)^(-1))` over a different field `F_p^2 = F_p[i] / (i^2 + 1)` (p is the same as above) with generator ``` P2 = ( 11559732032986387107991004021392285783925812861821192530917403151452391805634 * i + From 698d42f5321f84d0b2bfdc593a2cfadc712bc727 Mon Sep 17 00:00:00 2001 From: Yoichi Hirai Date: Fri, 9 Mar 2018 10:45:07 +0100 Subject: [PATCH 2/2] Simpler notation A division `/` is simpler than multiplying the inverse `^(-1)` --- EIPS/eip-197.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/EIPS/eip-197.md b/EIPS/eip-197.md index 7abcc842..e4bab91e 100644 --- a/EIPS/eip-197.md +++ b/EIPS/eip-197.md @@ -57,7 +57,7 @@ The groups `G_1` and `G_2` are cyclic groups of prime order `q = 218882428718392 The group `G_1` is defined on the curve `Y^2 = X^3 + 3` over the field `F_p` with `p = 21888242871839275222246405745257275088696311157297823662689037894645226208583` with generator `P1 = (1, 2)`. -The group `G_2` is defined on the curve `Y^2 = X^3 + 3 ((i+9)^(-1))` over a different field `F_p^2 = F_p[i] / (i^2 + 1)` (p is the same as above) with generator +The group `G_2` is defined on the curve `Y^2 = X^3 + 3/(i+9)` over a different field `F_p^2 = F_p[i] / (i^2 + 1)` (p is the same as above) with generator ``` P2 = ( 11559732032986387107991004021392285783925812861821192530917403151452391805634 * i +