26 lines
851 B
Python
26 lines
851 B
Python
|
from typing import Tuple
|
||
|
|
|
||
|
|
|
||
|
|
def compute_root_of_unity(primitive_root: int, order: int, modulus: int) -> int:
|
||
|
|
"""
|
||
|
|
Generate a w such that ``w**length = 1``.
|
||
|
|
"""
|
||
|
|
assert (modulus - 1) % order == 0
|
||
|
|
return pow(primitive_root, (modulus - 1) // order, modulus)
|
||
|
|
|
||
|
|
|
||
|
|
def compute_roots_of_unity(primitive_root: int, order: int, modulus: int) -> Tuple[int]:
|
||
|
|
"""
|
||
|
|
Compute a list of roots of unity for a given order.
|
||
|
|
The order must divide the BLS multiplicative group order, i.e. BLS_MODULUS - 1
|
||
|
|
"""
|
||
|
|
assert (modulus - 1) % order == 0
|
||
|
|
root_of_unity = compute_root_of_unity(primitive_root, order, modulus)
|
||
|
|
|
||
|
|
roots = []
|
||
|
|
current_root_of_unity = 1
|
||
|
|
for _ in range(order):
|
||
|
|
roots.append(current_root_of_unity)
|
||
|
|
current_root_of_unity = current_root_of_unity * root_of_unity % modulus
|
||
|
|
return tuple(roots)
|