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Clarify further "choose the greater" mechanism

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vbuterin 2019-01-29 07:52:42 -06:00 committed by GitHub
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specs/bls_signature.md
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@ -88,7 +88,7 @@ def hash_to_G2(message: bytes32, domain: uint64) -> [uint384]:
`modular_squareroot(x)` returns a solution `y` to `y**2 % q == x`, and `None` if none exists. If there are two solutions the one with higher imaginary component is favored; if both solutions have equal imaginary component the one with higher real component is favored (note that this is equivalent to saying that the single solution with either imaginary component > p/2 or imaginary component zero and real component > p/2 is favored).
The following is a sample implementation; implementers are free to implement modular square roots as they wish. Note that `x2 = -x1` is an _additive modular inverse_ so real and imaginary coefficients remain in `[0 .. q-1]`
The following is a sample implementation; implementers are free to implement modular square roots as they wish. Note that `x2 = -x1` is an _additive modular inverse_ so real and imaginary coefficients remain in `[0 .. q-1]`. `coerce_to_int` is a function that takes Fq elements (ie. integers mod q) and converts them to regular integers.
```python
Fq2_order = q ** 2 - 1
@ -100,7 +100,9 @@ def modular_squareroot(value: Fq2) -> Fq2:
if check in eighth_roots_of_unity[::2]:
x1 = candidate_squareroot / eighth_roots_of_unity[eighth_roots_of_unity.index(check) // 2]
x2 = -x1
return x1 if (x1.coeffs[1].n, x1.coeffs[0].n) > (x2.coeffs[1].n, x2.coeffs[0].n) else x2
x1_re, x1_im = coerce_to_int(x1.coeffs[0]), coerce_to_int(x1.coeffs[1])
x2_re, x2_im = coerce_to_int(x2.coeffs[0]), coerce_to_int(x2.coeffs[1])
return x1 if (x1_im > x2_im or (x1_im == x2_im and x1_re > x2_re)) else x2
return None
```