Finish implementing fk20

da/kzg_rs/fk20.py

@@ -23,25 +23,41 @@ def toeplitz1(global_parameters: List[G1], roots_of_unity: Sequence[int], polyno
     assert is_power_of_two(len(global_parameters))
     roots_of_unity = roots_of_unity[:2*polynomial_degree]
     vector_x_extended = global_parameters + [G1(0) for _ in range(len(global_parameters))]
-    vector_x_extended_fft = fft(vector_x_extended, BLS_MODULUS, roots_of_unity)
+    vector_x_extended_fft = fft(vector_x_extended, roots_of_unity, BLS_MODULUS)
     return vector_x_extended_fft
 
 
 def toeplitz2(coefficients: List[G1], roots_of_unity: Sequence[int], extended_vector: Sequence[G1]) -> List[G1]:
     assert is_power_of_two(len(coefficients))
-    toeplitz_coefficients_fft = fft(coefficients, BLS_MODULUS, roots_of_unity)
+    toeplitz_coefficients_fft = fft(coefficients, roots_of_unity, BLS_MODULUS)
     return [v*c for v, c in zip(extended_vector, toeplitz_coefficients_fft)]
 
 
-def toeplitz3(h_extended_fft: Sequence[G1], roots_of_unity: Sequence[int]) -> List[G1]:
-    return ifft(h_extended_fft, BLS_MODULUS, roots_of_unity)
+def toeplitz3(h_extended_fft: Sequence[G1], roots_of_unity: Sequence[int], polynomial_degree: int) -> List[G1]:
+    return ifft(h_extended_fft, roots_of_unity, BLS_MODULUS)[:polynomial_degree]
 
 
-def fk20_generate_proofs(polynomial: Polynomial) -> List[Proof]:
+def fk20_generate_proofs(
+        polynomial: Polynomial, global_parameters: List[G1], roots_of_unity: Sequence[int]
+) -> List[Proof]:
+    polynomial_degree = len(polynomial)
+    assert len(roots_of_unity) >= 2 * polynomial_degree
+    assert len(global_parameters) >= polynomial_degree
+    assert is_power_of_two(len(polynomial))
+
     # 1 - Build toeplitz matrix for h values
     # 1.1 y = dft([s^d-1, s^d-2, ..., s, 1, *[0 for _ in len(polynomial)]])
     # 1.2 z = dft([*[0 for _ in len(polynomial)], f1, f2, ..., fd])
     # 1.3 u = y * v * roots_of_unity(len(polynomial)*2)
+    global_parameters = [*global_parameters[polynomial_degree-2::-1], 0]
+    extended_vector = toeplitz1(global_parameters, roots_of_unity[:polynomial_degree*2], polynomial_degree)
     # 2 - Build circulant matrix with the polynomial coefficients (reversed N..n, and padded)
+    toeplitz_coefficients = [
+        polynomial.coefficients[-1], *(0 for _ in range(polynomial_degree+1)), *polynomial.coefficients[1:-1]
+    ]
+    h_extended_vector = toeplitz2(toeplitz_coefficients, roots_of_unity[:len(extended_vector)], extended_vector)
     # 3 - Perform fft and nub the tail half as it is padding
-    pass
+    h_vector = toeplitz3(h_extended_vector, roots_of_unity[:len(h_extended_vector)], polynomial_degree)
+    # 4 - proof are the dft of the h vector
+    proofs = fft(h_vector, roots_of_unity[:polynomial_degree], BLS_MODULUS)
+    return proofs