Rabin fingerprint explained

The Rabin fingerprinting scheme (aka Polynomial fingerprinting) is a method for implementing fingerprints using polynomials over a finite field. It was proposed by Michael O. Rabin.^[1]

Scheme

Given an n-bit message m₀,...,m_n-1, we view it as a polynomial of degree n-1 over the finite field GF(2).

f(x) = m _{0} + m _{1} x + \ldots + m _{n-1} x ^{n-1}

We then pick a random irreducible polynomial of degree k over GF(2), and we define the fingerprint of the message m to be the remainder

r(x) after division of f(x) by p(x) over GF(2) which can be viewed as a polynomial of degree or as a k-bit number.

Applications

Many implementations of the Rabin–Karp algorithm internally use Rabin fingerprints.

The Low Bandwidth Network Filesystem (LBFS) from MIT uses Rabin fingerprints to implement variable size shift-resistant blocks.^[2] The basic idea is that the filesystem computes the cryptographic hash of each block in a file. To save on transfers between the client and server,they compare their checksums and only transfer blocks whose checksums differ. But one problem with this scheme is that a single insertion at the beginning of the file will cause every checksum to change if fixed-sized (e.g. 4 KB) blocks are used. So the idea is to select blocks not based on a specific offset but rather by some property of the block contents. LBFS does this by sliding a 48 byte window over the file and computing the Rabin fingerprint of each window. When the low 13 bits of the fingerprint are zero LBFS calls those 48 bytes a breakpoint and ends the current block and begins a new one. Since the output of Rabin fingerprints are pseudo-random the probability of any given 48 bytes being a breakpoint is

2 ^{-13} (1 in 8192). This has the effect of shift-resistant variable size blocks. Any hash function could be used to divide a long file into blocks (as long as a cryptographic hash function is then used to find the checksum of each block): but the Rabin fingerprint is an efficient rolling hash, since the computation of the Rabin fingerprint of region B can reuse some of the computation of the Rabin fingerprint of region A when regions A and B overlap.

Note that this is a problem similar to that faced by rsync.

See also

• W-shingling
• Rolling hash

References

1. Web site: . Fingerprinting by Random Polynomials . Center for Research in Computing Technology, Harvard University . Tech Report TR-CSE-03-01 . 1981 . 2007-03-22 .
2. Athicha Muthitacharoen, Benjie Chen, and David Mazières "A Low-bandwidth Network File System"

External links

• Web site: Andrei Z. Broder . 1993 . Some applications of Rabin's fingerprinting method . 143–152 . 2011-09-12 .
• Web site: David Andersen . 2007 . Exploiting Similarity for Multi-Source Downloads using File Handprints . 2007-04-12 .
• Ross N. Williams (1993). "A painless guide to CRC Error detection algorithms".