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from typing import List, Tuple
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 bitvec_from_int(x: int, width: int) -> List[int]: return [(x >> i) & 1 for i in range(width)]
def build_matrix_for_length(byte_len: int = 15) -> Tuple[List[int], int, int]: cols = byte_len * 8 rows = 24 mat = [0] * rows for k in range(cols): bindex = k // 8 bitpos = k % 8 msg = bytearray(byte_len) msg[bindex] = 1 << bitpos c16 = compute_crc16(bytes(msg)) c8 = compute_crc8(bytes(msg)) for r in range(16): if (c16 >> r) & 1: mat[r] |= (1 << k) for r in range(8): if (c8 >> r) & 1: mat[16 + r] |= (1 << k) return mat, rows, cols
def gf2_nullspace_one_solution(mat: List[int], rows: int, cols: int) -> List[int]: A = mat[:] pivot_col = [-1] * rows col_to_row = dict() r = 0 for c in range(cols): pivot = None for i in range(r, rows): if (A[i] >> c) & 1: pivot = i break if pivot is None: continue if pivot != r: A[r], A[pivot] = A[pivot], A[r] pivot_col[r] = c col_to_row[c] = r for i in range(rows): if i != r and ((A[i] >> c) & 1): A[i] ^= A[r] r += 1 if r == rows: break
pivot_cols = set([pc for pc in pivot_col if pc != -1]) free_cols = [c for c in range(cols) if c not in pivot_cols] if not free_cols: return [] x = [0] * cols free_choice = free_cols[0] x[free_choice] = 1 for i in range(rows-1, -1, -1): pc = pivot_col[i] if pc == -1: continue s = 0 rowmask = A[i] mask = rowmask & ~(1 << pc) while mask: lb = mask & -mask j = (lb.bit_length() - 1) s ^= x[j] mask ^= lb x[pc] = s
return x
def bits_to_bytes(bits: List[int]) -> bytes: n = len(bits) // 8 ba = bytearray(n) for i in range(len(bits)): if bits[i]: byte_idx = i // 8 bitpos = i % 8 ba[byte_idx] |= (1 << bitpos) return bytes(ba)
if __name__ == "__main__": byte_len = 15 target = b"Enj0yNSSCTF4th!" print("target:", target) t_crc16 = compute_crc16(target) t_crc8 = compute_crc8(target) print("target CRC16:", hex(t_crc16), "CRC8:", hex(t_crc8))
M, rows, cols = build_matrix_for_length(byte_len) sol_bits = gf2_nullspace_one_solution(M, rows, cols) if not sol_bits: print("没有找到非零零空间解(非常罕见)") exit(1)
delta = bits_to_bytes(sol_bits) if set(delta) == {0}: print("得到的 delta 全零,选择另一个自由列重试") exit(1)
cand = bytes([target[i] ^ delta[i] for i in range(byte_len)]) print("delta (hex):", delta.hex()) print("candidate (hex):", cand.hex()) try: print("candidate (ascii):", cand.decode()) except: print("candidate contains non-printable bytes") print("compute_crc16(candidate):", hex(compute_crc16(cand))) print("compute_crc8(candidate): ", hex(compute_crc8(cand))) assert compute_crc16(cand) == t_crc16 and compute_crc8(cand) == t_crc8 and cand != target print("验证通过:candidate 与 target CRC 相同且不同字符串。") import urllib.parse print("url-encoded for POST:", urllib.parse.quote_from_bytes(cand))
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