Thin package implements Content Defined Chunking (CDC) based on a rolling Rabin Checksum.
The function Pol.getRandom() returns a new random polynomial of degree 53 for use with the chunker. The degree 53 is chosen because it is the largest prime below 64-8 = 56, so that the top 8 bits of an ulong can be used for optimising calculations in the chunker.
A random polynomial is chosen selecting 64 random bits, masking away bits 64..54 and setting bit 53 to one (otherwise the polynomial is not of the desired degree) and bit 0 to one (otherwise the polynomial is trivially reducible), so that 51 bits are chosen at random.
This process is repeated until Pol.irreducible returns true, then this polynomials is returned. If this doesn't happen after 1 million tries, the function returns an error. The probability for selecting an irreducible polynomial at random is about 7.5% ( (2^53-2)/53 / 2^51), so the probability that no irreducible polynomial has been found after 100 tries is lower than 0.04%.
During development the results have been verified using the computational discrete algebra system GAP, which can be obtained from the website at http://www.gap-system.org/.
For filtering a given list of polynomials in hexadecimal coefficient notation, the following script can be used:
# create x over F_2 = GF(2); x := Indeterminate(GF(2), "x"); # test if polynomial is irreducible, i.e. the number of factors is one; IrredPoly := function (poly); return (Length(Factors(poly)) = 1); end;; # create a polynomial in x from the hexadecimal representation of the; # coefficients; Hex2Poly := function (s); return ValuePol(CoefficientsQadic(IntHexString(s), 2), x); end;; # list of candidates, in hex; candidates := [ "3DA3358B4DC173" ]; # create real polynomials; L := List(candidates, Hex2Poly); # filter and display the list of irreducible polynomials contained in L; Display(Filtered(L, x -> (IrredPoly(x))));
All irreducible polynomials from the list are written to the output.
An introduction to Rabin Fingerprints/Checksums can be found in the following articles:
Michael O. Rabin (1981): "Fingerprinting by Random Polynomials" http://www.xmailserver.org/rabin.pdf
Ross N. Williams (1993): "A Painless Guide to CRC Error Detection Algorithms" http://www.zlib.net/crc_v3.txt
Andrei Z. Broder (1993): "Some Applications of Rabin's Fingerprinting Method" http://www.xmailserver.org/rabin_apps.pdf
Shuhong Gao and Daniel Panario (1997): "Tests and Constructions of Irreducible Polynomials over Finite Fields" http://www.math.clemson.edu/~sgao/papers/GP97a.pdf
Andrew Kadatch, Bob Jenkins (2007): "Everything we know about CRC but afraid to forget" http://crcutil.googlecode.com/files/crc-doc.1.0.pdf
Constructs a new Chunker based on polynomial pol that reads from source.
Splits content with Rabin Fingerprints.
Aim to create chunks of 20 bits or about 1MiB on average.
Default maximal size of a chunk.
Default minimal size of a chunk.
Copyright 2014 Alexander Neumann. All rights reserved. Use of this source code is governed by a BSD-style license that can be found in the LICENSE file.