Add py_ecc tests to min-bindings
This commit is contained in:
Dankrad Feist
parent
67804099bc
commit
2e435a7e26
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@ -3,7 +3,7 @@ from fft import fft
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from multicombs import lincomb
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# Generatore for the field
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PRIMITIVE_ROOT = 5
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PRIMITIVE_ROOT = 7
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MODULUS = b.curve_order
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assert pow(PRIMITIVE_ROOT, (MODULUS - 1) // 2, MODULUS) != 1
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@ -0,0 +1,120 @@
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from py_ecc import optimized_bls12_381 as b
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def _simple_ft(vals, modulus, roots_of_unity):
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L = len(roots_of_unity)
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o = []
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for i in range(L):
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last = b.Z1 if type(vals[0]) == tuple else 0
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for j in range(L):
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if type(vals[0]) == tuple:
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last = b.add(last, b.multiply(vals[j], roots_of_unity[(i*j)%L]))
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else:
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last += vals[j] * roots_of_unity[(i*j)%L]
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o.append(last if type(last) == tuple else last % modulus)
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return o
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def _fft(vals, modulus, roots_of_unity):
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if len(vals) <= 4 and type(vals[0]) != tuple:
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#return vals
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return _simple_ft(vals, modulus, roots_of_unity)
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elif len(vals) == 1 and type(vals[0]) == tuple:
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return vals
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L = _fft(vals[::2], modulus, roots_of_unity[::2])
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R = _fft(vals[1::2], modulus, roots_of_unity[::2])
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o = [0 for i in vals]
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for i, (x, y) in enumerate(zip(L, R)):
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y_times_root = b.multiply(y, roots_of_unity[i]) if type(y) == tuple else y*roots_of_unity[i]
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o[i] = b.add(x, y_times_root) if type(x) == tuple else (x+y_times_root) % modulus
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o[i+len(L)] = b.add(x, b.neg(y_times_root)) if type(x) == tuple else (x-y_times_root) % modulus
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return o
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def expand_root_of_unity(root_of_unity, modulus):
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# Build up roots of unity
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rootz = [1, root_of_unity]
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while rootz[-1] != 1:
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rootz.append((rootz[-1] * root_of_unity) % modulus)
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return rootz
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def fft(vals, modulus, root_of_unity, inv=False):
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rootz = expand_root_of_unity(root_of_unity, modulus)
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# Fill in vals with zeroes if needed
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if len(rootz) > len(vals) + 1:
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vals = vals + [0] * (len(rootz) - len(vals) - 1)
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if inv:
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# Inverse FFT
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invlen = pow(len(vals), modulus-2, modulus)
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if type(vals[0]) == tuple:
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return [b.multiply(x, invlen) for x in
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_fft(vals, modulus, rootz[:0:-1])]
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else:
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return [(x*invlen) % modulus for x in
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_fft(vals, modulus, rootz[:0:-1])]
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else:
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# Regular FFT
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return _fft(vals, modulus, rootz[:-1])
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# Evaluates f(x) for f in evaluation form
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def inv_fft_at_point(vals, modulus, root_of_unity, x):
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if len(vals) == 1:
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return vals[0]
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# 1/2 in the field
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half = (modulus + 1)//2
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# 1/w
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inv_root = pow(root_of_unity, len(vals)-1, modulus)
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# f(-x) in evaluation form
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f_of_minus_x_vals = vals[len(vals)//2:] + vals[:len(vals)//2]
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# e(x) = (f(x) + f(-x)) / 2 in evaluation form
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evens = [(f+g) * half % modulus for f,g in zip(vals, f_of_minus_x_vals)]
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# o(x) = (f(x) - f(-x)) / 2 in evaluation form
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odds = [(f-g) * half % modulus for f,g in zip(vals, f_of_minus_x_vals)]
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# e(x^2) + coordinate * x * o(x^2) in evaluation form
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comb = [(o * x * inv_root**i + e) % modulus for i, (o, e) in enumerate(zip(odds, evens))]
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return inv_fft_at_point(comb[:len(comb)//2], modulus, root_of_unity ** 2 % modulus, x**2 % modulus)
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def shift_domain(vals, modulus, root_of_unity, factor):
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if len(vals) == 1:
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return vals
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# 1/2 in the field
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half = (modulus + 1)//2
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# 1/w
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inv_factor = pow(factor, modulus - 2, modulus)
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half_length = len(vals)//2
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# f(-x) in evaluation form
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f_of_minus_x_vals = vals[half_length:] + vals[:half_length]
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# e(x) = (f(x) + f(-x)) / 2 in evaluation form
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evens = [(f+g) * half % modulus for f,g in zip(vals, f_of_minus_x_vals)]
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print('e', evens)
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# o(x) = (f(x) - f(-x)) / 2 in evaluation form
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odds = [(f-g) * half % modulus for f,g in zip(vals, f_of_minus_x_vals)]
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print('o', odds)
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shifted_evens = shift_domain(evens[:half_length], modulus, root_of_unity ** 2 % modulus, factor ** 2 % modulus)
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print('se', shifted_evens)
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shifted_odds = shift_domain(odds[:half_length], modulus, root_of_unity ** 2 % modulus, factor ** 2 % modulus)
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print('so', shifted_odds)
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return (
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[(e + inv_factor * o) % modulus for e, o in zip(shifted_evens, shifted_odds)] +
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[(e - inv_factor * o) % modulus for e, o in zip(shifted_evens, shifted_odds)]
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)
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def shift_poly(poly, modulus, factor):
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factor_power = 1
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inv_factor = pow(factor, modulus - 2, modulus)
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o = []
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for p in poly:
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o.append(p * factor_power % modulus)
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factor_power = factor_power * inv_factor % modulus
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return o
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def mul_polys(a, b, modulus, root_of_unity):
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rootz = [1, root_of_unity]
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while rootz[-1] != 1:
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rootz.append((rootz[-1] * root_of_unity) % modulus)
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if len(rootz) > len(a) + 1:
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a = a + [0] * (len(rootz) - len(a) - 1)
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if len(rootz) > len(b) + 1:
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b = b + [0] * (len(rootz) - len(b) - 1)
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x1 = _fft(a, modulus, rootz[:-1])
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x2 = _fft(b, modulus, rootz[:-1])
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return _fft([(v1*v2)%modulus for v1,v2 in zip(x1,x2)],
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modulus, rootz[:0:-1])
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@ -0,0 +1,252 @@
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from py_ecc import optimized_bls12_381 as b
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from fft import fft
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from multicombs import lincomb
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# Generatore for the field
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PRIMITIVE_ROOT = 7
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MODULUS = b.curve_order
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assert pow(PRIMITIVE_ROOT, (MODULUS - 1) // 2, MODULUS) != 1
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assert pow(PRIMITIVE_ROOT, MODULUS - 1, MODULUS) == 1
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#########################################################################################
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#
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# Helpers
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#
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#########################################################################################
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def is_power_of_two(x):
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return x > 0 and x & (x-1) == 0
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def generate_setup(s, size):
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"""
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# Generate trusted setup, in coefficient form.
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# For data availability we always need to compute the polynomials anyway, so it makes little sense to do things in Lagrange space
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"""
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return (
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[b.multiply(b.G1, pow(s, i, MODULUS)) for i in range(size + 1)],
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[b.multiply(b.G2, pow(s, i, MODULUS)) for i in range(size + 1)],
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)
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#########################################################################################
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#
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# Field operations
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#
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#########################################################################################
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def get_root_of_unity(order):
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"""
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Returns a root of unity of order "order"
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"""
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assert (MODULUS - 1) % order == 0
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return pow(PRIMITIVE_ROOT, (MODULUS - 1) // order, MODULUS)
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def inv(a):
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"""
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Modular inverse using eGCD algorithm
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"""
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if a == 0:
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return 0
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lm, hm = 1, 0
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low, high = a % MODULUS, MODULUS
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while low > 1:
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r = high // low
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nm, new = hm - lm * r, high - low * r
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lm, low, hm, high = nm, new, lm, low
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return lm % MODULUS
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def div(x, y):
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return x * inv(y) % MODULUS
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#########################################################################################
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#
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# Polynomial operations
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#
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#########################################################################################
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def eval_poly_at(p, x):
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"""
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Evaluate polynomial p (coefficient form) at point x
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"""
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y = 0
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power_of_x = 1
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for i, p_coeff in enumerate(p):
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y += power_of_x * p_coeff
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power_of_x = (power_of_x * x) % MODULUS
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return y % MODULUS
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def div_polys(a, b):
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"""
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Long polynomial difivion for two polynomials in coefficient form
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"""
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a = [x for x in a]
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o = []
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apos = len(a) - 1
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bpos = len(b) - 1
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diff = apos - bpos
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while diff >= 0:
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quot = div(a[apos], b[bpos])
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o.insert(0, quot)
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for i in range(bpos, -1, -1):
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a[diff + i] -= b[i] * quot
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apos -= 1
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diff -= 1
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return [x % MODULUS for x in o]
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#########################################################################################
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#
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# Utils for reverse bit order
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#
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#########################################################################################
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def reverse_bit_order(n, order):
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"""
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Reverse the bit order of an integer n
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"""
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assert is_power_of_two(order)
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# Convert n to binary with the same number of bits as "order" - 1, then reverse its bit order
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return int(('{:0' + str(order.bit_length() - 1) + 'b}').format(n)[::-1], 2)
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def list_to_reverse_bit_order(l):
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"""
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Convert a list between normal and reverse bit order. This operation is idempotent.
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"""
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return [l[reverse_bit_order(i, len(l))] for i in range(len(l))]
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#########################################################################################
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#
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# Converting between polynomials (in coefficient form) and data (in reverse bit order)
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# and extending data
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#
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#########################################################################################
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def get_polynomial(data):
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"""
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Interpolate a polynomial (coefficients) from data in reverse bit order
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"""
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assert is_power_of_two(len(data))
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root_of_unity = get_root_of_unity(len(data))
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return fft(list_to_reverse_bit_order(data), MODULUS, root_of_unity, True)
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def get_data(polynomial):
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"""
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Get data (in reverse bit order) from polynomial in coefficient form
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"""
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assert is_power_of_two(len(polynomial))
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root_of_unity = get_root_of_unity(len(polynomial))
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return list_to_reverse_bit_order(fft(polynomial, MODULUS, root_of_unity, False))
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def get_extended_data(polynomial):
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"""
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Get extended data (expanded by 2x, reverse bit order) from polynomial in coefficient form
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"""
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assert is_power_of_two(len(polynomial))
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extended_polynomial = polynomial + [0] * len(polynomial)
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root_of_unity = get_root_of_unity(len(extended_polynomial))
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return list_to_reverse_bit_order(fft(extended_polynomial, MODULUS, root_of_unity, False))
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#########################################################################################
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#
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# Kate single proofs
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#
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#########################################################################################
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def commit_to_poly(polynomial, setup):
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"""
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Kate commitment to polynomial in coefficient form
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"""
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return lincomb(setup[0][:len(polynomial)], polynomial, b.add, b.Z1)
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def compute_proof_single(polynomial, x, setup):
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"""
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Compute Kate proof for polynomial in coefficient form at position x
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"""
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quotient_polynomial = div_polys(polynomial, [-x, 1])
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return lincomb(setup[0][:len(quotient_polynomial)], quotient_polynomial, b.add, b.Z1)
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def check_proof_single(commitment, proof, x, y, setup):
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"""
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Check a proof for a Kate commitment for an evaluation f(x) = y
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"""
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# Verify the pairing equation
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#
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# e([commitment - y], [1]) = e([proof], [s - x])
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# equivalent to
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# e([commitment - y]^(-1), [1]) * e([proof], [s - x]) = 1_T
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#
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s_minus_x = b.add(setup[1][1], b.multiply(b.neg(b.G2), x))
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commitment_minus_y = b.add(commitment, b.multiply(b.neg(b.G1), y))
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pairing_check = b.pairing(b.G2, b.neg(commitment_minus_y), False)
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pairing_check *= b.pairing(s_minus_x, proof, False)
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pairing = b.final_exponentiate(pairing_check)
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return pairing == b.FQ12.one()
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#########################################################################################
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#
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# Kate multiproofs on a coset
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#
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#########################################################################################
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def compute_proof_multi(polynomial, x, n, setup):
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"""
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Compute Kate proof for polynomial in coefficient form at positions x * w^y where w is
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an n-th root of unity (this is the proof for one data availability sample, which consists
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of several polynomial evaluations)
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"""
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quotient_polynomial = div_polys(polynomial, [-pow(x, n, MODULUS)] + [0] * (n - 1) + [1])
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return lincomb(setup[0][:len(quotient_polynomial)], quotient_polynomial, b.add, b.Z1)
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def check_proof_multi(commitment, proof, x, ys, setup):
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"""
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Check a proof for a Kate commitment for an evaluation f(x w^i) = y_i
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"""
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n = len(ys)
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root_of_unity = get_root_of_unity(n)
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# Interpolate at a coset. Note because it is a coset, not the subgroup, we have to multiply the
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# polynomial coefficients by x^i
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interpolation_polynomial = fft(ys, MODULUS, root_of_unity, True)
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interpolation_polynomial = [div(c, pow(x, i, MODULUS)) for i, c in enumerate(interpolation_polynomial)]
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# Verify the pairing equation
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#
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# e([commitment - interpolation_polynomial(s)], [1]) = e([proof], [s^n - x^n])
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# equivalent to
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# e([commitment - interpolation_polynomial]^(-1), [1]) * e([proof], [s^n - x^n]) = 1_T
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#
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xn_minus_yn = b.add(setup[1][n], b.multiply(b.neg(b.G2), pow(x, n, MODULUS)))
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commitment_minus_interpolation = b.add(commitment, b.neg(lincomb(
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setup[0][:len(interpolation_polynomial)], interpolation_polynomial, b.add, b.Z1)))
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pairing_check = b.pairing(b.G2, b.neg(commitment_minus_interpolation), False)
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pairing_check *= b.pairing(xn_minus_yn, proof, False)
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pairing = b.final_exponentiate(pairing_check)
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return pairing == b.FQ12.one()
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if __name__ == "__main__":
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polynomial = [1, 2, 3, 4, 7, 7, 7, 7, 13, 13, 13, 13, 13, 13, 13, 13]
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n = len(polynomial)
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setup = generate_setup(1927409816240961209460912649124, n)
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commitment = commit_to_poly(polynomial, setup)
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proof = compute_proof_single(polynomial, 17, setup)
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value = eval_poly_at(polynomial, 17)
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assert check_proof_single(commitment, proof, 17, value, setup)
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print("Single point check passed")
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root_of_unity = get_root_of_unity(8)
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x = 5431
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coset = [x * pow(root_of_unity, i, MODULUS) for i in range(8)]
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ys = [eval_poly_at(polynomial, z) for z in coset]
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proof = compute_proof_multi(polynomial, x, 8, setup)
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assert check_proof_multi(commitment, proof, x, ys, setup)
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print("Coset check passed")
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@ -0,0 +1,131 @@
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import random, time, sys, math
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# For each subset in `subsets` (provided as a list of indices into `numbers`),
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# compute the sum of that subset of `numbers`. More efficient than the naive method.
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def multisubset(numbers, subsets, adder=lambda x,y: x+y, zero=0):
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numbers = numbers[::]
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subsets = {i: {x for x in subset} for i, subset in enumerate(subsets)}
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output = [zero for _ in range(len(subsets))]
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for roundcount in range(9999999):
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# Compute counts of every pair of indices in the subset list
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pair_count = {}
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for index, subset in subsets.items():
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for x in subset:
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for y in subset:
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if y > x:
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pair_count[(x, y)] = pair_count.get((x, y), 0) + 1
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# Determine pairs with highest count. The cutoff parameter [:len(numbers)]
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# determines a tradeoff between group operation count and other forms of overhead
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pairs_by_count = sorted([el for el in pair_count.keys()], key=lambda el: pair_count[el], reverse=True)[:len(numbers)*int(math.log(len(numbers)))]
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# Exit condition: all subsets have size 1, no pairs
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if len(pairs_by_count) == 0:
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for key, subset in subsets.items():
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for index in subset:
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output[key] = adder(output[key], numbers[index])
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return output
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# In each of the highest-count pairs, take the sum of the numbers at those indices,
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# and add the result as a new value, and modify `subsets` to include the new value
|
||||
# wherever possible
|
||||
used = set()
|
||||
for maxx, maxy in pairs_by_count:
|
||||
if maxx in used or maxy in used:
|
||||
continue
|
||||
used.add(maxx)
|
||||
used.add(maxy)
|
||||
numbers.append(adder(numbers[maxx], numbers[maxy]))
|
||||
for key, subset in list(subsets.items()):
|
||||
if maxx in subset and maxy in subset:
|
||||
subset.remove(maxx)
|
||||
subset.remove(maxy)
|
||||
if not subset:
|
||||
output[key] = numbers[-1]
|
||||
del subsets[key]
|
||||
else:
|
||||
subset.add(len(numbers)-1)
|
||||
|
||||
# Alternative algorithm. Less optimal than the above, but much lower bit twiddling
|
||||
# overhead and much simpler.
|
||||
def multisubset2(numbers, subsets, adder=lambda x,y: x+y, zero=0):
|
||||
# Split up the numbers into partitions
|
||||
partition_size = 1 + int(math.log(len(subsets) + 1))
|
||||
# Align number count to partition size (for simplicity)
|
||||
numbers = numbers[::]
|
||||
while len(numbers) % partition_size != 0:
|
||||
numbers.append(zero)
|
||||
# Compute power set for each partition (eg. a, b, c -> {0, a, b, a+b, c, a+c, b+c, a+b+c})
|
||||
power_sets = []
|
||||
for i in range(0, len(numbers), partition_size):
|
||||
new_power_set = [zero]
|
||||
for dimension, value in enumerate(numbers[i:i+partition_size]):
|
||||
new_power_set += [adder(n, value) for n in new_power_set]
|
||||
power_sets.append(new_power_set)
|
||||
# Compute subset sums, using elements from power set for each range of values
|
||||
# ie. with a single power set lookup you can get the sum of _all_ elements in
|
||||
# the range partition_size*k...partition_size*(k+1) that are in that subset
|
||||
subset_sums = []
|
||||
for subset in subsets:
|
||||
o = zero
|
||||
for i in range(len(power_sets)):
|
||||
index_in_power_set = 0
|
||||
for j in range(partition_size):
|
||||
if i * partition_size + j in subset:
|
||||
index_in_power_set += 2 ** j
|
||||
o = adder(o, power_sets[i][index_in_power_set])
|
||||
subset_sums.append(o)
|
||||
return subset_sums
|
||||
|
||||
# Reduces a linear combination `numbers[0] * factors[0] + numbers[1] * factors[1] + ...`
|
||||
# into a multi-subset problem, and computes the result efficiently
|
||||
def lincomb(numbers, factors, adder=lambda x,y: x+y, zero=0):
|
||||
# Maximum bit length of a number; how many subsets we need to make
|
||||
maxbitlen = max((len(bin(f))-2 for f in factors), default=0)
|
||||
# Compute the subsets: the ith subset contains the numbers whose corresponding factor
|
||||
# has a 1 at the ith bit
|
||||
subsets = [{i for i in range(len(numbers)) if factors[i] & (1 << j)} for j in range(maxbitlen+1)]
|
||||
subset_sums = multisubset2(numbers, subsets, adder=adder, zero=zero)
|
||||
# For example, suppose a value V has factor 6 (011 in increasing-order binary). Subset 0
|
||||
# will not have V, subset 1 will, and subset 2 will. So if we multiply the output of adding
|
||||
# subset 0 with twice the output of adding subset 1, with four times the output of adding
|
||||
# subset 2, then V will be represented 0 + 2 + 4 = 6 times. This reasoning applies for every
|
||||
# value. So `subset_0_sum + 2 * subset_1_sum + 4 * subset_2_sum` gives us the result we want.
|
||||
# Here, we compute this as `((subset_2_sum * 2) + subset_1_sum) * 2 + subset_0_sum` for
|
||||
# efficiency: an extra `maxbitlen * 2` group operations.
|
||||
o = zero
|
||||
for i in range(len(subsets)-1, -1, -1):
|
||||
o = adder(adder(o, o), subset_sums[i])
|
||||
return o
|
||||
|
||||
# Tests go here
|
||||
def make_mock_adder():
|
||||
counter = [0]
|
||||
def adder(x, y):
|
||||
if x and y:
|
||||
counter[0] += 1
|
||||
return x+y
|
||||
return adder, counter
|
||||
|
||||
def test_multisubset(numcount, setcount):
|
||||
numbers = [random.randrange(10**20) for _ in range(numcount)]
|
||||
subsets = [{i for i in range(numcount) if random.randrange(2)} for i in range(setcount)]
|
||||
adder, counter = make_mock_adder()
|
||||
o = multisubset(numbers, subsets, adder=adder)
|
||||
for output, subset in zip(o, subsets):
|
||||
assert output == sum([numbers[x] for x in subset])
|
||||
|
||||
def test_lincomb(numcount, bitlength=256):
|
||||
numbers = [random.randrange(10**20) for _ in range(numcount)]
|
||||
factors = [random.randrange(2**bitlength) for _ in range(numcount)]
|
||||
adder, counter = make_mock_adder()
|
||||
o = lincomb(numbers, factors, adder=adder)
|
||||
assert o == sum([n*f for n,f in zip(numbers, factors)])
|
||||
total_ones = sum(bin(f).count('1') for f in factors)
|
||||
print("Naive operation count: %d" % (bitlength * numcount + total_ones))
|
||||
print("Optimized operation count: %d" % (bitlength * 2 + counter[0]))
|
||||
print("Optimization factor: %.2f" % ((bitlength * numcount + total_ones) / (bitlength * 2 + counter[0])))
|
||||
|
||||
if __name__ == '__main__':
|
||||
test_lincomb(int(sys.argv[1]) if len(sys.argv) >= 2 else 80)
|
||||
|
|
@ -0,0 +1,71 @@
|
|||
import atexit
|
||||
import ckzg
|
||||
import kzg_proofs
|
||||
import random
|
||||
from py_ecc import optimized_bls12_381 as b
|
||||
from py_ecc.bls.point_compression import compress_G1, decompress_G1, decompress_G2
|
||||
|
||||
|
||||
polynomial = [random.randint(0, kzg_proofs.MODULUS) for i in range(4096)]
|
||||
n = len(polynomial)
|
||||
|
||||
x = 9283547894352
|
||||
|
||||
y = kzg_proofs.eval_poly_at(polynomial, x)
|
||||
|
||||
root_of_unity = kzg_proofs.get_root_of_unity(n)
|
||||
roots_of_unity = [pow(root_of_unity, i, kzg_proofs.MODULUS) for i in range(n)]
|
||||
|
||||
polynomial_l = [kzg_proofs.eval_poly_at(polynomial, w) for w in roots_of_unity]
|
||||
|
||||
def evaluate_polynomial_in_evaluation_form(polynomial, z, roots_of_unity):
|
||||
|
||||
width = len(polynomial)
|
||||
inverse_width =kzg_proofs.inv(width)
|
||||
|
||||
# Make sure we won't divide by zero during division
|
||||
assert z not in roots_of_unity
|
||||
|
||||
result = 0
|
||||
for i in range(width):
|
||||
result += kzg_proofs.div(polynomial[i] * roots_of_unity[i], (z - roots_of_unity[i]))
|
||||
result = result * (pow(z, width, kzg_proofs.MODULUS) - 1) * inverse_width % kzg_proofs.MODULUS
|
||||
return result
|
||||
|
||||
y2 = evaluate_polynomial_in_evaluation_form(polynomial_l, x, roots_of_unity)
|
||||
|
||||
assert y == y2
|
||||
|
||||
polynomial_l_rbo = kzg_proofs.list_to_reverse_bit_order(polynomial_l)
|
||||
roots_of_unity_rbo = kzg_proofs.list_to_reverse_bit_order(roots_of_unity)
|
||||
|
||||
y3 = evaluate_polynomial_in_evaluation_form(polynomial_l_rbo, x, roots_of_unity_rbo)
|
||||
|
||||
assert y == y3
|
||||
|
||||
ts = ckzg.load_trusted_setup("../../src/trusted_setup.txt")
|
||||
ckzg_poly = ckzg.alloc_polynomial([ckzg.bytes_to_bls_field(r.to_bytes(32, "little")) for r in polynomial_l_rbo])
|
||||
ckzg_y4 = ckzg.evaluate_polynomial_in_evaluation_form(ckzg_poly, ckzg.bytes_to_bls_field(x.to_bytes(32, "little")), ts)
|
||||
y4 = ckzg.int_from_bls_field(ckzg_y4)
|
||||
|
||||
assert y == y4
|
||||
|
||||
def load_trusted_setup(filename):
|
||||
with open(filename, "r") as f:
|
||||
g1_length = int(f.readline())
|
||||
g2_length = int(f.readline())
|
||||
g1_setup = []
|
||||
g2_setup = []
|
||||
for i in range(g1_length):
|
||||
g1_setup.append(decompress_G1(int(f.readline(), 16)))
|
||||
#for i in range(g2_length):
|
||||
# l = f.readline()
|
||||
# g2_setup.append(decompress_G2((int(l[:48], 16), int(l[48:], 16))))
|
||||
return [g1_setup, g2_setup]
|
||||
|
||||
ts_pyecc = load_trusted_setup("../../src/trusted_setup.txt")
|
||||
|
||||
commitment_pyecc = kzg_proofs.commit_to_poly(polynomial, ts_pyecc)
|
||||
commitment_ckzg = ckzg.blob_to_kzg_commitment([ckzg.bytes_to_bls_field(r.to_bytes(32, "little")) for r in polynomial_l_rbo], ts)
|
||||
|
||||
assert compress_G1(commitment_pyecc).to_bytes(48, "big") == ckzg.bytes_from_g1(commitment_ckzg)
|
||||
Loading…
Reference in New Issue