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To understand the advantages, start with the slice-by-2 case. We wish to compute a CRC two bytes (16 bits) at a time, but the standard table-based approach would require an inconveniently large 65536-entry table. As mentioned in § Generating the lookup table, CRC tables have the property that table[i xor j] = table[i] xor table[j].
The CRC and associated polynomial typically have a name of the form CRC-n-XXX as in the table below. The simplest error-detection system, the parity bit, is in fact a 1-bit CRC: it uses the generator polynomial x + 1 (two terms), [5] and has the name CRC-1.
All the well-known CRC generator polynomials of degree have two common hexadecimal representations. In both cases, the coefficient of x n {\displaystyle x^{n}} is omitted and understood to be 1. The msbit-first representation is a hexadecimal number with n {\displaystyle n} bits, the least significant bit of which is always 1.
XOR/table Paul Hsieh's SuperFastHash [1] 32 bits Buzhash: variable XOR/table Fowler–Noll–Vo hash function (FNV Hash) 32, 64, 128, 256, 512, or 1024 bits xor/product or product/XOR Jenkins hash function: 32 or 64 bits XOR/addition Bernstein's hash djb2 [2] 32 or 64 bits shift/add or mult/add or shift/add/xor or mult/xor PJW hash / Elf Hash ...
Increasing the length of the chain decreases the size of the table. However, it also increases the time required to perform lookups, and this is the time-memory trade-off of the rainbow table. In a simple case of one-item chains, the lookup is very fast, but the table is very big. Once chains get longer, the lookup slows, but the table size ...
In this respect, the Fletcher checksum is not different from other checksum and CRC algorithms and needs no special explanation. An ordering problem that is easy to envision occurs when the data word is transferred byte-by-byte between a big-endian system and a little-endian system and the Fletcher-32 checksum is computed.
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cksum is a command in Unix and Unix-like operating systems that generates a checksum value for a file or stream of data. The cksum command reads each file given in its arguments, or standard input if no arguments are provided, and outputs the file's 32-bit cyclic redundancy check (CRC) checksum and byte count. [1]