Checksum Algorithms Reference
Non-cryptographic checksums: CRC32, Adler-32, Fletcher, 和其 多项式 representations.
CRC Family
Cyclic Redundancy Check codes treat the input as a polynomial over GF(2) and compute the remainder after division by a generator polynomial. The generator determines the error-detection capability: CRC-32 with the standard polynomial detects all single and double-bit errors and all burst errors up to 32 bits. Different CRC variants use different polynomials, bit reflection, and initial values, so a CRC-32 from one library may not match another.
- CRC-32
- Standard Ethernet polynomial 0x04C11DB7, 32-bit
- CRC-32C
- Castagnoli polynomial, better error detection
- CRC-16-CCITT
- 16-bit, polynomial 0x1021
- Adler-32
- Sum and modulo checksum, faster than CRC-32
zlib, PNGiSCSI, SCTPX.25, Bluetoothzlib headerError Detection Capability
Checksums detect accidental corruption but are not resistant to intentional modification. CRC-32 detects burst errors up to its degree with probability 1, and longer bursts with high probability. Random data corruption is detected with probability roughly 1 minus 2 to the negative 32. For adversarial tampering, a cryptographic MAC is required because an attacker can recompute the checksum after modifying the data.
Performance Considerations
CRC computations can be accelerated with table-based lookups that process one byte per iteration, or slice-by-N variants that process multiple bytes per table lookup. Modern CPUs offer hardware CRC-32C instructions that process bytes at memory bandwidth. Adler-32 is simpler and faster on short inputs but has weaker error detection than CRC-32. The choice depends on the throughput requirements and error model of the application.