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