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A cyclic redundancy check (CRC) is a short value calculated from a block of data and used to detect accidental changes. A sender includes the value with the data; the receiver calculates the corresponding CRC and checks it against the received value. If they do not match, the data has likely been corrupted.
How a CRC is calculated
A CRC treats the message bits as coefficients in a polynomial over GF(2), a binary system in which addition and subtraction are both XOR operations. The calculation multiplies the message polynomial by a power of x determined by the CRC width, then divides it by a chosen generator polynomial. The remainder is the CRC: a fixed-width check value whose degree is lower than the generator polynomial’s degree. The sender attaches that remainder to the message, and the receiver applies the agreed procedure to check the result.
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In practical terms, the CRC is not an arbitrary tag or a count of the bits in a message. It is the remainder produced by a defined calculation. RFC 9260’s SCTP specification puts it simply: “The CRC is computed using polynomial division.” RFC 9260, Appendix A
What a CRC can—and cannot—tell you
A mismatch is evidence that the checked data does not match the expected CRC. A CRC can detect many accidental error patterns, but it does not tell you which bit changed or restore the original data. Systems that need recovery must add another mechanism, such as retransmitting the data or using an error-correcting code.
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Detection guarantees depend on the chosen polynomial and the length of the protected message. IEEE Technology Navigator reports that, under its stated CRC-32 assumptions, a CRC-32 detects all single-bit errors, all double-bit errors, all odd numbers of errors, and all bursts shorter than 33 bits for messages up to 231 bits. These are specific guarantees, not a promise that every CRC catches every possible corruption. IEEE Technology Navigator: Cyclic redundancy check
Why “CRC-32” does not uniquely identify an algorithm
The number in a name such as CRC-8, CRC-16, CRC-32, or CRC-64 describes the check width. It does not, by itself, specify the generator polynomial or every convention needed for compatible results. Implementations may also differ in bit ordering, initialization and finalization, and how the check field is incorporated or interpreted.
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For example, SCTP specifies CRC32c using the Castagnoli polynomial, while Ethernet uses its own CRC-32 frame-check-sequence convention. Both are 32-bit CRCs, but the width alone does not make them interchangeable. For a protocol implementation, use the exact algorithm and conventions specified for that protocol. RFC 9260 IEEE Technology Navigator: Cyclic redundancy check codes
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Where CRCs are used
CRCs are used to check data in communication and storage contexts. Ethernet carries a CRC in its frame check sequence, and USB packet formats also use CRC fields. The USB source cited here is a draft document, so it establishes the context but should not be treated as confirmation of the current normative USB specification. USB Implementers Forum: Cyclic Redundancy Checks in USB
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What to check when choosing a CRC
When implementing or comparing CRCs, verify the complete specification rather than choosing by width alone. The important details include:
- Width and generator polynomial: These define the check size and influence which error patterns the CRC detects.
- Protected message length: Detection guarantees can depend on how much data is covered.
- Bit ordering and reflection: These conventions affect how bits are processed.
- Initialization and finalization: These affect the calculated value.
- Protocol compatibility: The sender and receiver must follow the same specified variant and field-handling rules.
Using a different polynomial or convention can produce a different check value for the same data, even when both algorithms have the same width.
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