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Update bls_verify.md

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Justin 2018-12-10 14:30:36 +00:00 committed by GitHub
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@ -67,17 +67,18 @@ G2_cofactor = 305502333931268344200999753193121504214466019254188142667664032982
q = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab
def hash_to_G2(message, domain):
x1 = int.from_bytes(hash(bytes8(domain) + b'\x01' + message), 'big')
x2 = int.from_bytes(hash(bytes8(domain) + b'\x02' + message), 'big')
x_coordinate = FQ2([x1, x2]) # x1 + x2 * i
# Initial candidate x coordinate
x_re = int.from_bytes(hash(bytes8(domain) + b'\x01' + message), 'big')
x_im = int.from_bytes(hash(bytes8(domain) + b'\x02' + message), 'big')
x_coordinate = FQ2([x_re, x_im]) # x = x_re + i * x_im
# Test candidate y coordinates until a one is found
while 1:
x_cubed_plus_b2 = x_coordinate ** 3 + FQ2([4, 4])
y_coordinate = modular_squareroot(x_cubed_plus_b2)
if y_coordinate is not None:
break
x_coordinate += FQ2([1, 0]) # Add one until we get a quadratic residue
assert is_on_G2((x_coordinate, y_coordinate))
y_coordinate_squared = x_coordinate ** 3 + FQ2([4, 4]) # The curve is y^2 = x^3 + 4(i + 1)
y_coordinate = modular_squareroot(y_coordinate_squared)
if y_coordinate is not None: # Check if quadratic residue found
return multiply_in_G2((x_coordinate, y_coordinate), G2_cofactor)
x_coordinate += FQ2([1, 0]) # Add 1 and try again
```
### `modular_squareroot`