import hashlib

def schnorr_verify(public_key, message, signature_r, signature_s, generator):
 """
 Simulates the Schnorr Verification Equation: sG = R + eP
 """
 print(f"--- Schnorr Signature Audit ---")
 print(f"[*] Message: {message}")
 print(f"[*] Signature: (r: {signature_r}, s: {signature_s})")

 # 1. Calculate the 'Challenge' (e)
 # In reality, this is a tagged hash of R, P, and the message
 challenge_input = f"{signature_r}{public_key}{message}"
 e = int(hashlib.sha256(challenge_input.encode()).hexdigest(), 16) % 1000 # Small for demo

 # 2. Left Side of Equation: s * G
 left_side = signature_s * generator

 # 3. Right Side of Equation: R + e * P
 # Note: In ECC, these are point additions, here we use simple math
 right_side = signature_r + (e * public_key)

 print(f"[*] Challenge (e): {e}")
 print(f"[*] Left Side (sG): {left_side}")
 print(f"[*] Right Side (R+eP): {right_side}")

 if left_side == right_side:
 print("[SUCCESS] Signature is VALID!")
 return True
 else:
 print("[ERROR] Signature is INVALID!")
 return False

# --- Simulation ---

# Dummy values for demonstration
# G = Generator, d = Private Key, P = d*G (Public Key)
G = 7
d = 123
P = d * G # 861

# To sign, we pick a random nonce k and calculate R = k*G
k = 45
R = k * G # 315

# Calculate challenge e (simplified)
msg = "Spend 1 BTC"
e_demo = 12 # Assume hash result
s = (k + e_demo * d) # The Signature equation

# Audit the generated signature
schnorr_verify(P, msg, R, s, G)