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Update bls_verify.md

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Justin 2018-12-09 14:30:48 +00:00 committed by GitHub
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specs/bls_verify.md
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@ -66,7 +66,7 @@ def hash_to_G2(message, domain):
x2 = hash(bytes8(domain) + b'\x02' + message)
x_coordinate = FQ2([x1, x2]) # x1 + x2 * i
while 1:
x_cubed_plus_b2 = x_coordinate ** 3 + FQ2([4,4])
x_cubed_plus_b2 = x_coordinate ** 3 + FQ2([4, 4])
y_coordinate = modular_square_root(x_cubed_plus_b2)
if y_coordinate is not None:
break
@ -91,7 +91,7 @@ def modular_square_root(value):
## Signature verification
In the following `e` is the pairing function and `id_G1` the identity in G1.
In the following `e` is the pairing function and `g` is the generator in G1.
### `bls_verify`
@ -99,7 +99,7 @@ In the following `e` is the pairing function and `id_G1` the identity in G1.
* Verify that `pubkey` is a valid G1 point.
* Verify that `signature` is a valid G2 point.
* Verify `e(pubkey, hash_to_G2(message, domain)) == e(id_G1, sig)`.
* Verify `e(pubkey, hash_to_G2(message, domain)) == e(g, sig)`.
### `bls_verify_multiple`
@ -108,4 +108,4 @@ In the following `e` is the pairing function and `id_G1` the identity in G1.
* Verify that each `pubkey` in `pubkeys` is a valid G1 point.
* Verify that `signature` is a valid G2 point.
* Verify that `len(pubkeys)` equals `len(messages)` and denote the length `L`.
* Verify that `e(pubkeys[0], hash_to_G2(messages[0], domain)) * ... * e(pubkeys[L-1], hash_to_G2(messages[L-1], domain)) == e(id_G1, sig)`.
* Verify that `e(pubkeys[0], hash_to_G2(messages[0], domain)) * ... * e(pubkeys[L-1], hash_to_G2(messages[L-1], domain)) == e(g, sig)`.