1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66
| import numpy as np
SECRET_PASS = b"Enj0yNSSCTF4th!" length = len(SECRET_PASS)
CRC16_POLY = 0xA001
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 ]
# 生成 CRC16 和 CRC8 矩阵(这里简化处理:只修改最后 3 个字节) def compute_crc16_simple(data): crc = 0xFFFF for b in data: crc ^= b for _ in range(8): crc = (crc >> 1) ^ CRC16_POLY if crc & 1 else crc >> 1 return crc
def compute_crc8_simple(data): crc = 0 for b in data: crc = CRC8_TABLE[(crc ^ b) & 0xFF] return crc
# 构造线性系统求解修改字节 def gf2_solve(crc_target16, crc_target8, original): # 我们修改最后3个字节,创建 24 位 GF(2) 方程 # 这里用暴力线性搜索示例,可优化为矩阵求解 for b1 in range(256): for b2 in range(256): for b3 in range(256): candidate = bytearray(original) candidate[-3] ^= b1 candidate[-2] ^= b2 candidate[-1] ^= b3 if candidate != original and compute_crc16_simple(candidate) == crc_target16 and compute_crc8_simple(candidate) == crc_target8: return bytes(candidate) return None
crc16_val = compute_crc16_simple(SECRET_PASS) crc8_val = compute_crc8_simple(SECRET_PASS)
collision = gf2_solve(crc16_val, crc8_val, SECRET_PASS) if collision: print(f"原密码: {SECRET_PASS}") print(f"碰撞密码: {collision}") print(f"CRC16: {compute_crc16_simple(collision)}, CRC8: {compute_crc8_simple(collision)}") else: print("未找到碰撞密码")
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