"""
crc_collision.py
Find a different message (same length) that is NOT equal to the secret but has identical CRC16 and CRC8.
Method:
- Choose k byte positions to allow flipping (default k=3 -> 24 binary variables).
- For a given base message, precompute the 24-bit effect ("columns") of flipping each single bit
in those positions. The combined CRC (CRC16<<8 | CRC8) is a 24-bit linear function over GF(2).
- Build a GF(2) basis from the columns, then try to represent the difference between base_crc24 and
target_crc24 as an XOR of columns. If representable, we get which bits to flip -> candidate message.
- Repeat for random base messages or different position sets until a valid candidate is found.
"""
import argparse
import random
import sys
from typing import List, Optional
def compute_crc16(data: bytes) -> int:
checksum = 0xFFFF
for b in data:
checksum ^= b
for _ in range(8):
if checksum & 1:
checksum = ((checksum >> 1) ^ 0xA001)
else:
checksum >>= 1
return checksum & 0xFFFF
crc8_table = [
0x00, 0x07, 0x0E, 0x09, 0x1C, 0x1B, 0x12, 0x15, 0x38, 0x3F, 0x36, 0x31, 0x24, 0x23, 0x2A, 0x2D,
0x70, 0x77, 0x7E, 0x79, 0x6C, 0x6B, 0x62, 0x65, 0x48, 0x4F, 0x46, 0x41, 0x54, 0x53, 0x5A, 0x5D,
0xE0, 0xE7, 0xEE, 0xE9, 0xFC, 0xFB, 0xF2, 0xF5, 0xD8, 0xDF, 0xD6, 0xD1, 0xC4, 0xC3, 0xCA, 0xCD,
0x90, 0x97, 0x9E, 0x99, 0x8C, 0x8B, 0x82, 0x85, 0xA8, 0xAF, 0xA6, 0xA1, 0xB4, 0xB3, 0xBA, 0xBD,
0xC7, 0xC0, 0xC9, 0xCE, 0xDB, 0xDC, 0xD5, 0xD2, 0xFF, 0xF8, 0xF1, 0xF6, 0xE3, 0xE4, 0xED, 0xEA,
0xB7, 0xB0, 0xB9, 0xBE, 0xAB, 0xAC, 0xA5, 0xA2, 0x8F, 0x88, 0x81, 0x86, 0x93, 0x94, 0x9D, 0x9A,
0x27, 0x20, 0x29, 0x2E, 0x3B, 0x3C, 0x35, 0x32, 0x1F, 0x18, 0x11, 0x16, 0x03, 0x04, 0x0D, 0x0A,
0x57, 0x50, 0x59, 0x5E, 0x4B, 0x4C, 0x45, 0x42, 0x6F, 0x68, 0x61, 0x66, 0x73, 0x74, 0x7D, 0x7A,
0x89, 0x8E, 0x87, 0x80, 0x95, 0x92, 0x9B, 0x9C, 0xB1, 0xB6, 0xBF, 0xB8, 0xAD, 0xAA, 0xA3, 0xA4,
0xF9, 0xFE, 0xF7, 0xF0, 0xE5, 0xE2, 0xEB, 0xEC, 0xC1, 0xC6, 0xCF, 0xC8, 0xDD, 0xDA, 0xD3, 0xD4,
0x69, 0x6E, 0x67, 0x60, 0x75, 0x72, 0x7B, 0x7C, 0x51, 0x56, 0x5F, 0x58, 0x4D, 0x4A, 0x43, 0x44,
0x19, 0x1E, 0x17, 0x10, 0x05, 0x02, 0x0B, 0x0C, 0x21, 0x26, 0x2F, 0x28, 0x3D, 0x3A, 0x33, 0x34,
0x4E, 0x49, 0x40, 0x47, 0x52, 0x55, 0x5C, 0x5B, 0x76, 0x71, 0x78, 0x7F, 0x6A, 0x6D, 0x64, 0x63,
0x3E, 0x39, 0x30, 0x37, 0x22, 0x25, 0x2C, 0x2B, 0x06, 0x01, 0x08, 0x0F, 0x1A, 0x1D, 0x14, 0x13,
0xAE, 0xA9, 0xA0, 0xA7, 0xB2, 0xB5, 0xBC, 0xBB, 0x96, 0x91, 0x98, 0x9F, 0x8A, 0x8D, 0x84, 0x83,
0xDE, 0xD9, 0xD0, 0xD7, 0xC2, 0xC5, 0xCC, 0xCB, 0xE6, 0xE1, 0xE8, 0xEF, 0xFA, 0xFD, 0xF4, 0xF3
]
def compute_crc8(data: bytes) -> int:
crc = 0
for b in data:
crc = crc8_table[(crc ^ b) & 0xff]
return crc & 0xff
def crc24(data: bytes) -> int:
return (compute_crc16(data) << 8) | compute_crc8(data)
def build_columns_for_positions(base: bytes, positions: List[int]) -> List[int]:
"""
For each (position, bit) produce a 24-bit column representing effect on crc24 when toggling that bit.
The order is for each position in positions (in order) and for bit 0..7 within each position.
"""
columns = []
for pos in positions:
for bit in range(8):
b = bytearray(base)
b[pos] ^= (1 << bit)
eff = crc24(bytes(b)) ^ crc24(base)
columns.append(eff)
return columns
def try_solve_with_columns(columns: List[int], target_diff: int) -> Optional[int]:
"""
Given columns (list of 24-bit ints) and target_diff (24-bit int),
try to represent target_diff as XOR of some columns.
If possible, return an integer mask where bit j means use columns[j].
Otherwise return None.
"""
BASIS_BITS = 24
basis = [0] * BASIS_BITS
basis_repr = [0] * BASIS_BITS
for j, col in enumerate(columns):
v = col
repr_mask = 1 << j
for bit in reversed(range(BASIS_BITS)):
if (v >> bit) & 1:
if basis[bit] != 0:
v ^= basis[bit]
repr_mask ^= basis_repr[bit]
else:
basis[bit] = v
basis_repr[bit] = repr_mask
break
v = target_diff
repr = 0
for bit in reversed(range(BASIS_BITS)):
if (v >> bit) & 1:
if basis[bit] == 0:
return None
v ^= basis[bit]
repr ^= basis_repr[bit]
if v == 0:
return repr
return None
def build_candidate_from_mask(base: bytes, positions: List[int], mask: int) -> bytes:
L = len(base)
delta = bytearray(L)
for j in range(len(positions) * 8):
if (mask >> j) & 1:
pos_idx = j // 8
bit_idx = j % 8
pos = positions[pos_idx]
delta[pos] ^= (1 << bit_idx)
candidate = bytearray(base)
for i in range(L):
candidate[i] ^= delta[i]
return bytes(candidate)
def find_collision(secret: bytes, k: int = 3, tries_per_positions_set: int = 1000, seed: Optional[int] = None, position_sets: Optional[List[List[int]]] = None):
"""
secret: bytes (the true password)
k: number of bytes that may be toggled (choose positions set size k)
tries_per_positions_set: for each chosen set of positions, try this many random base messages
position_sets: optional explicit list of position lists to try; otherwise we try a few heuristics + random sets
"""
random.seed(seed)
L = len(secret)
target_crc24 = crc24(secret)
if position_sets is None:
pos_sets = []
if L >= k:
pos_sets.append(list(range(L-k, L)))
pos_sets.append(list(range(0, k)))
pos_sets.append(sorted(random.sample(range(L), k)))
for _ in range(10):
pos_sets.append(sorted(random.sample(range(L), k)))
else:
pos_sets = position_sets
for positions in pos_sets:
for attempt in range(tries_per_positions_set):
base = bytearray(secret)
for i in range(L):
base[i] = random.randrange(256)
base = bytes(base)
columns = build_columns_for_positions(base, positions)
d = crc24(base) ^ target_crc24
mask = try_solve_with_columns(columns, d)
if mask is not None:
candidate = build_candidate_from_mask(base, positions, mask)
if candidate != secret and crc24(candidate) == target_crc24:
return {
"secret": secret,
"candidate": candidate,
"positions": positions,
"base": base,
"mask": mask
}
return None
def as_hex(b: bytes) -> str:
return b.hex()
def is_printable(b: bytes) -> bool:
try:
s = b.decode('utf-8')
except Exception:
return False
return all(0x20 <= c < 0x7f for c in b)
def main():
p = argparse.ArgumentParser(
description="Find a different message with same CRC16+CRC8 as secret (same length).")
p.add_argument("--secret", required=True,
help="the secret string (exact bytes).")
p.add_argument("--k", type=int, default=3,
help="number of byte positions to allow flipping (default 3).")
p.add_argument("--tries", type=int, default=2000,
help="random bases to try per positions set.")
p.add_argument("--seed", type=lambda s: int(s, 0), default=0x414141,
help="random seed (accepts decimal or hex, e.g. 0x414141).")
args = p.parse_args()
secret = args.secret.encode('latin1')
print("Secret:", secret)
print("Secret hex:", as_hex(secret))
print("Secret CRC16=0x%04x, CRC8=0x%02x, combined=0x%06x" %
(compute_crc16(secret), compute_crc8(secret), crc24(secret)))
result = find_collision(
secret, k=args.k, tries_per_positions_set=args.tries, seed=args.seed)
if result is None:
print("No collision found. Try increasing k or the number of tries, or provide specific position sets.")
return 2
cand = result["candidate"]
print("Found candidate:")
print(" Candidate bytes repr:", cand)
print(" Candidate hex:", as_hex(cand))
print(" Candidate CRC16=0x%04x, CRC8=0x%02x" %
(compute_crc16(cand), compute_crc8(cand)))
print(" Positions used:", result["positions"])
print(" Base used:", as_hex(result["base"]))
print(" Printable?:", is_printable(cand))
return 0
if __name__ == "__main__":
sys.exit(main())
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