CRC-32

CRC-32 (Cyclic Redundancy Check, 32 bits) is a data integrity verification method that uses a mathematical algorithm to generate a fingerprint from binary data. This fingerprint is used to detect accidental errors during data storage or transmission.

The operation of the CRC-32 is based on the operation of binary polynomial division by treating the data as a large binary polynomial.

The CRC then relies on a predefined binary polynomial, called the generator polynomial (or divisor). For CRC-32, the standard generator polynomial is 04C11DB7 (hexadecimal) or 100110000010001110110110111 (binary) or the polynomial of degree 32 $ x^{32} + x{26} + x^{23} + x^{22} + x^{16} + x^{12} + x^{11} + x^{10} + x^8 + x^7 + x^5 + x^4 + x^2 + x^1 + x^0 $.

Binary polynomial division has a remainder (which is of a length less than that of the generator polynomial). For CRC-32, the remainder will be a block of 32 bits. It is this sequence of 32 bits that constitutes the CRC-32 code.

CRC-32 is lightweight and fast, making it an excellent choice for detecting errors in transmitted or stored data. While it does not prevent or correct errors, it can identify them with high accuracy. CRC-32 is widely used in network communications, storage systems, some file formats (such as ZIP or PNG), and is recommended in environments that require rapid validation of data integrity.

A CRC-32 fingerprint is usually represented by 8 hexadecimal characters (or 32 binary bits).

When stored, they can be displayed as a numeric value between 0 and 4294967295.

CRC32C (Cyclic Redundancy Check 32 bits Castagnoli) is a variant of CRC-32 that uses a different generator polynomial to calculate the checksum. CRC32-C is based on the generator polynomial 1EDC6F41 (hexadecimal).

This evolution gives it better error detection performance than the standard CRC32 that it tends to replace.