[Python] I have created an original crytographic hash function is python, and would want...

I’ve created a new cryptographic hash function and would like your help in thoroughly testing its security and reliability. Please begin by verifying its determinism—ensure that the same input consistently produces the same output. Next, test for pre-image resistance by attempting to reverse a given hash to its original input. Try evaluating its second pre-image resistance as well: given one input and its hash, it should be computationally infeasible to find a different input with the same hash.

Also, please test the function’s collision resistance by trying to find two different inputs that generate the same hash. I’d like to confirm that it demonstrates a strong avalanche effect—a single-bit change in the input should cause a drastic change in the output. Run a uniformity test by hashing a large set of diverse inputs and analyzing whether the output bits are evenly distributed, indicating randomness and lack of bias.

Check the efficiency of the function—measure its performance on inputs of various sizes to ensure it's fast enough for practical use. Regardless of input length, the function should produce outputs of a fixed length, so please confirm that too. I’d also appreciate it if you could assess its resistance to known attacks, such as length extension and differential cryptanalysis. Lastly, examine the function for any signs of backdoors or hidden vulnerabilities.

Your feedback on these points will be invaluable in determining whether this hash function meets modern cryptographic standards. Made in python, the hash function is as follows:

import hashlib
import os
import struct
import time
from typing import Union, Tuple, List
import secrets
import threading
from concurrent.futures import ThreadPoolExecutor
import numpy as np

class CustomHash:
"""
An advanced custom cryptographic hash function implementation.
WARNING: This is for educational purposes only. Use established hash functions in production.
"""

def __init__(self,
salt_length: int = 64, # Increased salt length
rounds: int = 20000, # Increased rounds
memory_cost: int = 2048, # Increased memory cost
parallel_chains: int = 4): # Number of parallel hash chains
"""
Initialize the hash function with enhanced security parameters.

Args:
salt_length: Length of the salt in bytes (default: 64)
rounds: Number of hashing rounds (default: 20000)
memory_cost: Memory cost in KB for memory-hard operations (default: 2048)
parallel_chains: Number of parallel hash chains (default: 4)
"""
self.salt_length = salt_length
self.rounds = rounds
self.memory_cost = memory_cost
self.parallel_chains = parallel_chains
self.block_size = 128 # Increased block size to 1024 bits
self.output_size = 64 # Increased output size to 512 bits

# Initialize multiple S-boxes for enhanced substitution
self._init_sboxes()

# Initialize mixing matrices
self._init_mixing_matrices()

def _init_sboxes(self):
"""Initialize multiple substitution boxes for enhanced mixing."""
# Generate multiple S-boxes using different methods
self.sboxes = []

# S-box 1: Random permutation
sbox1 = list(range(256))
secrets.SystemRandom().shuffle(sbox1)
self.sboxes.append(sbox1)

# S-box 2: Multiplicative inverse in GF(2^8)
sbox2 = [self._multiplicative_inverse(i) for i in range(256)]
self.sboxes.append(sbox2)

# S-box 3: Affine transformation
sbox3 = [self._affine_transform(i) for i in range(256)]
self.sboxes.append(sbox3)

# S-box 4: Non-linear transformation
sbox4 = [self._nonlinear_transform(i) for i in range(256)]
self.sboxes.append(sbox4)

def _init_mixing_matrices(self):
"""Initialize mixing matrices for advanced state mixing."""
# Create multiple mixing matrices
self.mixing_matrices = []

# Matrix 1: Random orthogonal matrix
matrix1 = np.random.randn(8, 8)
Q, R = np.linalg.qr(matrix1)
self.mixing_matrices.append(Q)

# Matrix 2: Hadamard matrix
matrix2 = np.array([[1, 1], [1, -1]])
for _ in range(2):
matrix2 = np.kron(matrix2, np.array([[1, 1], [1, -1]]))
self.mixing_matrices.append(matrix2)

# Matrix 3: Circulant matrix
matrix3 = np.zeros((8, 8))
for i in range(8):
matrix3 = np.roll([1, 2, 3, 4, 5, 6, 7, 8], i)
self.mixing_matrices.append(matrix3)

def _multiplicative_inverse(self, x: int) -> int:
"""Calculate multiplicative inverse in GF(2^8)."""
if x == 0:
return 0
for i in range(256):
if (x * i) % 256 == 1:
return i
return 0

def _affine_transform(self, x: int) -> int:
"""Apply affine transformation to byte."""
# Affine transformation: y = Ax + b
A = 0x1F
b = 0x63
return (x * A + b) % 256

def _nonlinear_transform(self, x: int) -> int:
"""Apply non-linear transformation to byte."""
# Complex non-linear transformation
x = ((x << 1) | (x >> 7)) & 0xFF # Rotate left
x = (x * 0x1B) % 256 # Multiply by irreducible polynomial
x = x ^ ((x >> 4) & 0x0F) # Non-linear mixing
return x

def _pad_message(self, message: bytes) -> bytes:
"""
Enhanced padding with multiple security measures.

Args:
message: Input message to pad

Returns:
Padded message
"""
message_length = len(message)
padding_length = (self.block_size - (message_length + 17) % self.block_size) % self.block_size

# Add padding with multiple random bytes
padding = b'\x80' + os.urandom(padding_length)

# Add message length, nonce, and additional entropy
length_bytes = struct.pack('>Q', message_length * 8)
nonce = os.urandom(8)
entropy = struct.pack('>Q', int(time.time() * 1000000))

return message + padding + length_bytes + nonce + entropy

def _mix_block(self, block: bytes, state: bytes, round_num: int) -> bytes:
"""
Enhanced block mixing with multiple operations and advanced mixing.

Args:
block: Block of data
state: Current state
round_num: Current round number

Returns:
New state
"""
# Convert to numpy arrays for matrix operations, making them writable
state_array = np.frombuffer(state, dtype=np.uint8).reshape(-1, 8).copy()
block_array = np.frombuffer(block, dtype=np.uint8).reshape(-1, 8).copy()

# Apply multiple mixing operations
for i in range(len(state_array)):
# Matrix mixing
for matrix in self.mixing_matrices:
state_array = np.mod(np.dot(state_array, matrix), 256).astype(np.uint8)

# S-box substitution
for j in range(8):
for sbox in self.sboxes:
state_array[j] = sbox[state_array[j]]

# Block mixing
state_array = np.mod(state_array.astype(np.uint16) + block_array[i % len(block_array)].astype(np.uint16), 256).astype(np.uint8)

# Round-dependent mixing
round_key = (round_num * 0x1F + i) & 0xFF
state_array = state_array ^ round_key

return state_array.tobytes()

def _memory_hard_operation(self, state: bytes) -> bytes:
"""
Enhanced memory-hard operations with multiple mixing passes.

Args:
state: Current state

Returns:
Modified state
"""
# Create multiple memory buffers
memory_buffers = [bytearray(self.memory_cost * 1024) for _ in range(self.parallel_chains)]

# Fill memory buffers with state-dependent values
for i in range(0, len(memory_buffers[0]), self.output_size):
for j in range(self.parallel_chains):
memory_buffers[j][i:i + self.output_size] = state

# Perform parallel memory-hard mixing
def mix_buffer(buffer_index):
buffer = memory_buffers[buffer_index]
for i in range(0, len(buffer) - self.output_size, self.output_size):
block = buffer[i:i + self.output_size]
next_block = buffer[i + self.output_size:i + 2 * self.output_size]

# Complex mixing operations
for j in range(self.output_size):
buffer[i + j] = (block[j] + next_block[j]) % 256
buffer[i + j] = self.sboxes[buffer_index % len(self.sboxes)][buffer[i + j]]

# Execute mixing in parallel
with ThreadPoolExecutor(max_workers=self.parallel_chains) as executor:
executor.map(mix_buffer, range(self.parallel_chains))

# Final mixing of all buffers
result = bytearray(state)
for buffer in memory_buffers:
for i in range(0, len(buffer), self.output_size):
block = buffer[i:i + self.output_size]
for j in range(self.output_size):
result[j] ^= block[j]

return bytes(result)

def _generate_salt(self) -> bytes:
"""
Generate enhanced cryptographically secure random salt.

Returns:
Random salt bytes
"""
# Combine multiple sources of entropy
salt = os.urandom(self.salt_length)
time_entropy = struct.pack('>Q', int(time.time() * 1000000))
process_entropy = struct.pack('>Q', os.getpid())
thread_entropy = struct.pack('>Q', threading.get_ident())

# Mix entropy sources
mixed_entropy = hashlib.sha512(salt + time_entropy + process_entropy + thread_entropy).digest()
return mixed_entropy[:self.salt_length]

def hash(self, message: Union[str, bytes], salt: bytes = None) -> Tuple[bytes, bytes]:
"""
Enhanced hashing with multiple rounds, parallel chains, and advanced mixing.

Args:
message: Input message (string or bytes)
salt: Optional salt (if None, a new salt will be generated)

Returns:
Tuple of (hash, salt)
"""
if isinstance(message, str):
message = message.encode('utf-8')

if salt is None:
salt = self._generate_salt()

# Initialize multiple hash chains
states = [hashlib.sha512(salt + struct.pack('>I', i)).digest()
for i in range(self.parallel_chains)]

# Add pepper
pepper = os.urandom(32)
salted_message = salt + message + pepper

# Pad the message
padded_message = self._pad_message(salted_message)

# Multiple rounds of processing
for round_num in range(self.rounds):
# Process message in blocks for each chain
for i in range(0, len(padded_message), self.block_size):
block = padded_message[i:i + self.block_size]
for chain in range(self.parallel_chains):
states[chain] = self._mix_block(block, states[chain], round_num)

# Perform memory-hard operation every 1000 rounds
if round_num % 1000 == 0:
for chain in range(self.parallel_chains):
states[chain] = self._memory_hard_operation(states[chain])

# Mix chains together
if round_num % 100 == 0:
mixed_state = bytearray(self.output_size)
for chain in range(self.parallel_chains):
for j in range(self.output_size):
mixed_state[j] ^= states[chain][j]
mixed_state = bytes(mixed_state)
for chain in range(self.parallel_chains):
states[chain] = hashlib.sha512(mixed_state + struct.pack('>I', chain)).digest()

# Final mixing of all chains
final_state = bytearray(self.output_size)
for chain in range(self.parallel_chains):
for j in range(self.output_size):
final_state[j] ^= states[chain][j]

return bytes(final_state), salt

def verify(self, message: Union[str, bytes], stored_hash: bytes, salt: bytes) -> bool:
"""
Verify if a message matches a stored hash.

Args:
message: Input message to verify
stored_hash: Previously stored hash
salt: Salt used in the stored hash

Returns:
True if the message matches the stored hash, False otherwise
"""
computed_hash, _ = self.hash(message, salt)
return secrets.compare_digest(computed_hash, stored_hash)

def main():
"""Example usage of the enhanced hash function."""
# Create hash function with increased security parameters
hasher = CustomHash(
salt_length=64,
rounds=20000,
memory_cost=2048,
parallel_chains=4
)

# Example password
password = "MySecretPassword123!"

# Hash the password
start_time = time.time()
hash_value, salt = hasher.hash(password)
end_time = time.time()

print(f"Password: {password}")
print(f"Salt: {salt.hex()}")
print(f"Hash: {hash_value.hex()}")
print(f"Hashing time: {end_time - start_time:.2f} seconds")

# Verify the password
is_valid = hasher.verify(password, hash_value, salt)
print(f"Password verification: {'Valid' if is_valid else 'Invalid'}")

# Try with wrong password
wrong_password = "WrongPassword"
is_valid = hasher.verify(wrong_password, hash_value, salt)
print(f"Wrong password verification: {'Valid' if is_valid else 'Invalid'}")

if __name__ == "__main__":
main()

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