from ecdsa.ellipticcurve import Point
from ecdsa.curves import SECP256k1

# secp256k1 parameters
curve = SECP256k1.curve
p = curve.p()
G = SECP256k1.generator

# Compute β = 2^((p-1)/3) mod p
beta   = pow(2, (p - 1) // 3, p)
beta2  = 60197513588986302554485582024885075108884032450952339817679072026166228089408
lmbda  = 37718080363155996902926221483475020450927657555482586988616620542887997980018
lmbda2 = 78074008874160198520644763525212887401909906723592317393988542598630163514319

# print(p)
def parse_pubkey(pubkey: str):
    """Extracts x, y coordinates from an uncompressed '04' format public key."""
    if not pubkey.startswith('04') or len(pubkey) != 130:
        raise ValueError("Invalid uncompressed public key format")
    x = int(pubkey[2:66], 16)
    y = int(pubkey[66:], 16)
    return Point(SECP256k1.curve, x, y, SECP256k1.order)

# beta * P.x == lambda * P (mod p)
def endomorphism(P: Point) -> Point:
    x_new = (beta * P.x()) % p
    return Point(curve, x_new, P.y())
# p - P.y() == inverse of p * G (mod p) (negation of y)
def endomorphism2(P: Point) -> Point:
    # x_new = ( P.x() * beta2) % p
    y_new = ( p - P.y() ) % p
    return Point(curve, P.x(), y_new)

def endomorphism3(P: Point) -> Point:
    x_new = (beta2 * P.x()) % p
    return Point(curve, x_new, P.y())
def endomorphism4(P: Point) -> Point:
    x_new = (beta * P.x()) % p
    y_new = (p - P.y()) % p
    return Point(curve, x_new, y_new)
def endomorphism5(P: Point) -> Point:
    x_new = (beta2 * P.x()) % p
    y_new = (p - P.y()) % p
    return Point(curve, x_new, y_new)



pubkey = "042f8bde4d1a07209355b4a7250a5c5128e88b84bddc619ab7cba8d569b240efe4d8ac222636e5e3d6d4dba9dda6c9c426f788271bab0d6840dca87d3aa6ac62d6"
# compute given public key or P integer, decomment one or another.
P = 6 * G
# P = parse_pubkey(pubkey)

P_endomorph = endomorphism(P)
P_endomorph2 = endomorphism2(P)
P_endomorph3 = endomorphism3(P)
P_endomorph4 = endomorphism4(P)
P_endomorph5 = endomorphism5(P)

print("Original P  :", (P.x(), P.y()))
print(f"Originak P key 04{P.x():x}{P.y():x}")
print('---------------------------------')
print("Endomorph P [beta * P.x == lambda * P (mod p)]:", (P_endomorph.x(), P_endomorph.y()))
print(f"Endomorph φ(P) key 04{P_endomorph.x():064x}{P_endomorph.y():064x}")
print('---------------------------------')
print("Endomorph2 P [p - P.y() == inverse of p * G (mod p) (negation of y)]:", (P_endomorph2.x(), P_endomorph2.y()))
print(f"Endomorph2 φ(P) key 04{P_endomorph2.x():x}{P_endomorph2.y():x}")
print('---------------------------------')
print("Endomorph3 P [beta2 * P.x == 2nd beta iteration]:", (P_endomorph3.x(), P_endomorph3.y()))
print(f"Endomorph3 φ(P) key 04{P_endomorph3.x():x}{P_endomorph3.y():x}")
print('---------------------------------')
print("Endomorph4 P [x*beta%p, p-y == N-pvk*lmda%N]:", (P_endomorph4.x(), P_endomorph4.y()))
print(f"Endomorph4 φ(P) key 04{P_endomorph4.x():x}{P_endomorph4.y():x}")
print('---------------------------------')
print("Endomorph5 P [x*beta2%p, p-y == N-pvk*lmda2%N]:", (P_endomorph5.x(), P_endomorph5.y()))
print(f"Endomorph5 φ(P) key 04{P_endomorph5.x():x}{P_endomorph5.y():x}")