Crc

A cyclic redundancy check (CRC) is a method used to detect accidental changes to raw data in digital networks and storage systems. It works by treating a block of data as a binary polynomial and dividing it by a fixed generator polynomial. The remainder of this division, expressed as a set of bits, is appended to the data as the CRC. When the data are later read or received, the same polynomial division is performed; if the remainder is zero (or matches an expected value after a final transformation), the data are considered error-free. CRCs are designed to catch common transmission and storage errors, including burst errors affecting multiple consecutive bits.

The CRC process relies on binary arithmetic over GF(2). The generator polynomial is chosen for a given protocol or standard and has a degree n, producing an n-bit CRC. Different configurations use different polynomials, initial values, and final XOR values. In practice, CRCs can be implemented in software or hardware, often with table-driven or bitwise shift-register approaches to speed calculation. The choice of polynomial and configuration defines the error-detection capabilities, such as the types and likelihood of error patterns they can reliably detect.

Common CRCs include CRC-32 and CRC-16 variants. CRC-32 (IEEE 802.3) uses a 32-bit polynomial (0x04C11DB7) and typical configurations with an initial value of all ones and a final XOR of all ones; it is widely used in Ethernet, ZIP archives, and other data formats. CRC-16 variants (for example CRC-16-CCITT and CRC-16-IBM) use 16-bit polynomials and are used in protocols and storage systems where smaller checksums are sufficient. While CRCs are effective for detecting accidental errors, they are not designed for cryptographic security.

CRCs are pervasive in data communications and storage due to their efficiency and strong but non-cryptographic error-detection properties.