Implement toeplizt

da/kzg_rs/fk20.py

@@ -3,7 +3,7 @@ from typing import List, Sequence
 from eth2spec.deneb.mainnet import KZGProof as Proof
 
 from da.kzg_rs.common import G1, BLS_MODULUS
-from da.kzg_rs.fft import fft
+from da.kzg_rs.fft import fft, ifft
 from da.kzg_rs.poly import Polynomial
 from da.kzg_rs.utils import is_power_of_two
 
@@ -26,6 +26,17 @@ def toeplitz1(global_parameters: List[G1], roots_of_unity: Sequence[int], polyno
     vector_x_extended_fft = fft(vector_x_extended, BLS_MODULUS, roots_of_unity)
     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)
+    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 fk20_generate_proofs(polynomial: Polynomial) -> List[Proof]:
     # 1 - Build toeplitz matrix for h values
     # 1.1 y = dft([s^d-1, s^d-2, ..., s, 1, *[0 for _ in len(polynomial)]])