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Trying to explain why a generator appears

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Yoichi Hirai 2017-12-04 21:53:01 +01:00 committed by GitHub
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EIPS/eip-197.md
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@ -34,7 +34,7 @@ Address: 0x8
For a cyclic group `G` (written additively) of prime order `q` let `log_P: G -> F_q` be the discrete logarithm on this group with respect to a generator `P`, i.e. `log_P(x)` is the smallest non-negative integer `n` such that `n * P = x`. For a cyclic group `G` (written additively) of prime order `q` let `log_P: G -> F_q` be the discrete logarithm on this group with respect to a generator `P`, i.e. `log_P(x)` is the smallest non-negative integer `n` such that `n * P = x`.
The precompiled contract is defined as follows, where the two groups `G_1` and `G_2` and their generators `P_1` and `P_2` are defined below. Both generators have the same prime order `q` and the actual choice of the generators does not matter, as long as they have order `q`. The precompiled contract is defined as follows, where the two groups `G_1` and `G_2` are defined by their generators `P_1` and `P_2` below. Both generators have the same prime order `q`.
``` ```
Input: (a1, b1, a2, b2, ..., ak, bk) from (G_1 x G_2)^k Input: (a1, b1, a2, b2, ..., ak, bk) from (G_1 x G_2)^k
@ -68,7 +68,7 @@ P2 = (
) )
``` ```
Note that `G_2` is the only group of order `q` of that elliptic curve over the field `F_p^2`. Note that `G_2` is the only group of order `q` of that elliptic curve over the field `F_p^2`. Any other generator of order `q` instead of `P2` would define the same `G_2`. However, a skeptical reader can compare `q * P2` and `P2` to check the existence of a group of order `q` on `G_2`.
### Encoding ### Encoding