CRC Hash Calculator

CRC (Cyclic Redundancy Check) algorithm

CRC is a hash function that generates a short fixed-bit check code based on data such as network data packets or computer files, which is mainly used to detect or verify errors that may occur after data transmission or storage

CRC overview

Cyclic redundancy check (CRC) is a hash function that generates a short fixed-bit check code based on data such as network packets or computer files, which is mainly used to detect or verify errors that may occur after data transmission or storage

CRC was published by W. Wesley Peterson in 1961. It uses the principle of division and remainder to detect errors

Algorithm characteristics

Strong ability to detect sudden errors
Hardware implementation is simple
Fast calculations
It is widely used in the field of data storage and data communication
Detects the vast majority of possible errors

Advantages and limitations

Advantages:

Powerful error detection capabilities
Low compute overhead
Easy to implement in hardware

Limitations:

Not a cryptographic hash and does not provide security
Collisions can occur (different data produce the same CRC).

CRC calculation procedure

select to generate polynomials

→

append zero bits to the original data

→

modulo 2 division operation

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CRC checksum is obtained

CRC calculation example:

Assuming raw data: 11010011101100

Generate polynomials: x³ + x + 1 (binary is represented as 1011).

Calculation process:

Add 3 zeros after the original data (because the highest order of the generated polynomial is 3) → 11010011101100000
Use modulus 2 division by 1011
The remainder obtained is the CRC code


 // Simplified CRC calculation pseudocode
 function calculateCRC(data, polynomial) {
     let n = polynomial.length - 1;
     let paddedData = data << n; // Add n zeros after the data
     let remainder = paddedData;
     while (remainder >= polynomial) {
         let shift = remainder.toString(2).length - polynomial.toString(2).length;
         remainder = remainder ^ (polynomial << shift);
     }
     return remainder;
 }

CRC application areas

network communication

Protocols such as Ethernet, Wi-Fi, and Bluetooth use CRC to verify the integrity of data frames

data store

Storage devices such as hard disks, optical disks, flash memory, etc. use CRC to detect data errors

file compression

ZIP, RAR, and other compression formats use CRC to verify the integrity of the decompressed data

digital communication

Digital television, satellite communication, etc. use CRC to ensure transmission quality

Commonly used CRC models

model	polynomial	the initial value	output XOR	application scenarios
CRC-32	0x04C11DB7	0xFFFFFFFF	0xFFFFFFFF	ZIP, GZIP, PNG
CRC-16-CCITT	0x1021	0xFFFF	0x0000	XMODEM, Bluetooth
CRC-8	0x07	0x00	0x00	SMBus, RFID
CRC-64-ECMA	0x42F0E1EBA9EA3693	0x0000000000000000	0x0000000000000000	ECMA-182, ISO 3309

CRC Hash Calculator

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About CRC