Adler-32

Adler-32 is a checksum algorithm which was invented by Mark Adler in 1995, and is a modification of the Fletcher checksum. Compared to a cyclic redundancy check of the same length, it trades reliability for speed (preferring the latter). Adler-32 is more reliable than Fletcher-16, and slightly less reliable than Fletcher-32.

The Adler-32 checksum is part of the widely used zlib compression library, as both were developed by Mark Adler. A "rolling checksum" version of Adler-32 is used in the rsync utility.

An Adler-32 checksum is obtained by calculating two 16-bit checksums A and B and concatenating their bits into a 32-bit integer. A is the sum of all bytes in the stream plus one, and B is the sum of the individual values of A from each step.

At the beginning of an Adler-32 run, A is initialized to 1, B to 0. The sums are done modulo 65521 (the largest prime number smaller than 2¹⁶). The bytes are stored in network order (big endian), B occupying the two most significant bytes.

The function may be expressed as

where D is the string of bytes for which the checksum is to be calculated, and n is the length of D.

The Adler-32 sum of the ASCII string "" would be calculated as follows:

The modulo operation had no effect in this example, since none of the values reached 65521.

The first difference between the two algorithms is that Adler-32 sums are calculated modulo a prime number, whereas Fletcher sums are calculated modulo 2⁴−1, 2⁸−1, or 2¹⁶−1 (depending on the number of bits used), which are all composite numbers. Using a prime number makes it possible for Adler-32 to catch differences in certain combinations of bytes that Fletcher is unable to detect.

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