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Fix the curve equation of G2 

It is different from that of G1.  See https://github.com/ethereum/yellowpaper/pull/659
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Yoichi Hirai 2018-03-05 15:14:47 +01:00
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@ -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 +