Cyclic Redundancy Check: A scheme for checking the correctness of data that has been transmitted or stored and retrieved. Abbreviated CRC. A CRC consists of a fixed number of bits computed as a function of the data to be protected, and appended to the data. When the data is read or received, the function is recomputed, and the result is compared to that appended to the data. Cyclic redundancy checks differ from error correcting codes in that they can detect a wide range of errors, but are not capable of correcting them. cf. error correcting code.
The CRC-32 used by Fibre Channel is:
( X32 + X26 + X23 + X22 + X16 + X12 + X11 + X10 + X8 + X7 + X5 + X4 + X2 + X + 1 )
In some versions of UNIX the encoding for the CRC checksum is defined by the generating polynomial:
G(x) = 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
Mathematically, the CRC value corresponding to a given message is defined by the following procedure:
The n bits to be evaluated are considered to be the coefficients of a mod 2 polynomial M(x) of degree n-1. These n bits are the bits from the file, with the most significant bit being the most significant bit of the first octet of the file and the last bit being the least significant bit of the last octet, padded with zero bits (if necessary) to achieve an integral number of octets, followed by one or more octets representing the length of the file as a binary value., least significant octet first. The smallest number of octets capable of representing this integer is used.
M(x) is multiplied by x**32 (that is, shifted left 32 bits) and divided by G(x) using mod 2 division, producing a remainder R(x) of degree < 31.
The coefficients of R(x) are considered to be a 32-bit sequence.
The bit sequence is complemented and the result is the CRC.