Checksum Algorithms & Security Access Master Reference across all Generations

Below are verified mathematical formulas and executable reference implementations for each generation:

21.1 Siemens MS42 / MS43 16-Bit CRC-CCITT Implementation

The MS42 and MS43 calculate three 16-bit CRC checksums across the bootloader, program code, and calibration blocks using the standard CRC-CCITT polynomial:

Polynomial: x16 + x12 + x5 + 1 (0x1021)
Initialization Value: 0xFFFF
Bit Order: Most Significant Bit (MSB) first (no reflection).

code

def calculate_ms4x_crc16(  
    data: bytes, start_offset: int, end_offset: int  
) -> int:  
  # Siemens MS42 / MS43 16-bit CCITT checksum  
  # Memory boundaries:  
  #   - MS43 Calibration: start=0x70000, end=0x73FDF, stored at 0x73FE0  
  #   - MS43 Program: start=0x10000, end=0x6FDDF, stored at 0x6FDE0  
  crc = 0xFFFF  
  for i in range(start_offset, end_offset + 1):  
    byte = data[i]  
    crc ^= byte << 8  
    for _ in range(8):  
      if crc & 0x8000:  
        crc = ((crc << 1) ^ 0x1021) & 0xFFFF  
      else:  
        crc = (crc << 1) & 0xFFFF  
  return crc

21.2 Siemens MS43 32-Bit Addition Monitor Checksum

Before evaluating CRC16, the MS43 monitors calibration memory integrity via a 32-bit DWORD additive accumulation located at 0x72FFC:

code

def calculate_ms43_32bit_addition(data: bytes, start: int, end: int) -> int:  
  # 32-bit addition checksum for MS43 calibration block  
  # Boundary: 0x70000 to 0x72FFB, stored at 0x72FFC as Big-Endian DWORD  
  total_sum = 0  
  for i in range(start, end + 1, 4):  
    dword = int.from_bytes(data[i : i + 4], byteorder="big")  
    total_sum = (total_sum + dword) & 0xFFFFFFFF  
  return total_sum

21.3 Siemens MS45 Standard Ethernet CRC32 Implementation

The MS45 monitors its calibration sector (0x40200 to 0x5CFFF) using a 32-bit CRC stored at 0x40100:

Polynomial: 0x04C11DB7
Initial Value: 0xFFFFFFFF
XOR Output: 0x00000000

code

def calculate_ms45_crc32(  
    data: bytes, start: int = 0x40200, end: int = 0x5CFFF  
) -> int:  
  # Ethernet CRC32 for Siemens MS45  
  crc = 0xFFFFFFFF  
  poly = 0x04C11DB7  
  for i in range(start, end + 1):  
    byte = data[i]  
    crc ^= (byte << 24) & 0xFFFFFFFF  
    for _ in range(8):  
      if crc & 0x80000000:  
        crc = ((crc << 1) ^ poly) & 0xFFFFFFFF  
      else:  
        crc = (crc << 1) & 0xFFFFFFFF  
  return crc

21.4 Cryptographic RSA-1024 Signature Structure (MS45 & MSD80)

The bootloader validates flash signatures using the RSA asymmetric public-key cryptosystem:

Mathematical Principle: Given public modulus n (1024 bits = 128 bytes) and public exponent e (typically 65537 = 0x10001), the signature s stored at 0x40170 is verified against the SHA-1 digest H of the calibration image: m = se mod n
The decrypted block m must match the standard PKCS#1 v1.5 padding string: Padding: ext 0x00 0x01 [0xFF × 105 bytes] 0x00 [20-Byte SHA-1 Digest]
Because factory private signing keys are strictly protected within BMW engineering servers, OBD flashing tools (MS45 Flasher) patch the bootloader instruction verification sequence or use specialized development keys to recalculate valid RSA signature envelopes.