81 lines
2.4 KiB
Python
81 lines
2.4 KiB
Python
# Ref:
|
|
# - https://github.com/ethereum/research/blob/8f084630528ba33d92b2bc05edf5338dd193c6f1/trusted_setup/trusted_setup.py
|
|
# - https://github.com/asn-d6/kzgverify
|
|
from py_ecc.optimized_bls12_381 import ( # noqa: F401
|
|
G1,
|
|
G2,
|
|
Z1,
|
|
Z2,
|
|
curve_order as BLS_MODULUS,
|
|
add,
|
|
multiply,
|
|
neg,
|
|
)
|
|
from eth2spec.utils import bls
|
|
|
|
|
|
PRIMITIVE_ROOT_OF_UNITY = 7
|
|
|
|
|
|
def generate_setup(generator, secret, length):
|
|
"""
|
|
Generate trusted setup of ``generator`` in ``length``.
|
|
"""
|
|
result = [generator]
|
|
for _ in range(1, length):
|
|
result.append(multiply(result[-1], secret))
|
|
return tuple(result)
|
|
|
|
|
|
def fft(vals, modulus, domain):
|
|
"""
|
|
FFT for group elements
|
|
"""
|
|
if len(vals) == 1:
|
|
return vals
|
|
L = fft(vals[::2], modulus, domain[::2])
|
|
R = fft(vals[1::2], modulus, domain[::2])
|
|
o = [0] * len(vals)
|
|
for i, (x, y) in enumerate(zip(L, R)):
|
|
y_times_root = multiply(y, domain[i])
|
|
o[i] = add(x, y_times_root)
|
|
o[i + len(L)] = add(x, neg(y_times_root))
|
|
return o
|
|
|
|
|
|
def compute_root_of_unity(length) -> int:
|
|
"""
|
|
Generate a w such that ``w**length = 1``.
|
|
"""
|
|
assert (BLS_MODULUS - 1) % length == 0
|
|
return pow(PRIMITIVE_ROOT_OF_UNITY, (BLS_MODULUS - 1) // length, BLS_MODULUS)
|
|
|
|
|
|
def compute_roots_of_unity(field_elements_per_blob):
|
|
"""
|
|
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 (BLS_MODULUS - 1) % field_elements_per_blob == 0
|
|
root_of_unity = compute_root_of_unity(length=field_elements_per_blob)
|
|
|
|
roots = []
|
|
current_root_of_unity = 1
|
|
for _ in range(field_elements_per_blob):
|
|
roots.append(current_root_of_unity)
|
|
current_root_of_unity = current_root_of_unity * root_of_unity % BLS_MODULUS
|
|
return roots
|
|
|
|
|
|
def get_lagrange(setup):
|
|
"""
|
|
Convert a G1 or G2 portion of a setup into the Lagrange basis.
|
|
"""
|
|
root_of_unity = compute_root_of_unity(len(setup))
|
|
assert pow(root_of_unity, len(setup), BLS_MODULUS) == 1
|
|
domain = [pow(root_of_unity, i, BLS_MODULUS) for i in range(len(setup))]
|
|
# TODO: introduce an IFFT function for simplicity
|
|
fft_output = fft(setup, BLS_MODULUS, domain)
|
|
inv_length = pow(len(setup), BLS_MODULUS - 2, BLS_MODULUS)
|
|
return [bls.G1_to_bytes48(multiply(fft_output[-i], inv_length)) for i in range(len(fft_output))]
|