Totally positive matrix: Difference between revisions

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A '''mimic function''' changes a file <math>A</math> so it assumes the statistical properties of another file <math>B</math>. That is, if <math>p(t,A)</math> is the probability of some substring <math>t</math> occurring in <math>A</math>, then a mimic function <math>f</math>, recodes <math>A</math> so that <math>p(t,f(A))</math> approximates <math>p(t,B)</math> for all strings <math>t</math> of length less than some <math>n</math>. It is commonly considered to be one of the basic techniques for [[Information hiding|hiding information]], often called [[steganography]].


The simplest mimic functions use simple statistical models to pick the symbols in the output. If the statistical model says that item <math>x</math> occurs with [[probability]] <math>p(x,A)</math> and item <math>y</math> occurs with probability <math>p(y,A)</math>, then a random number is used to choose between outputting <math>x</math> or <math>y</math> with probability <math>p(x,A)</math> or <math>p(y,A)</math> respectively.
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More sophisticated mimic functions use grammar-based models of <math>B</math> to structure the output. One example, [http://www.spammimic.com "SpamMimic"], uses a [[context free grammar]] to model the structure of a typical spam email message. It will convert the input file A to read like a spam message.
 
Even more sophisticated models use reversible [[Turing machine]]s.
 
==References==
* Peter Wayner. [http://www.funet.fi/pub/crypt/old/mimic/mimic.text "Mimic Functions"]
* Peter Wayner. [http://www.wayner.org/books/discrypt2/ "Disappearing Cryptography"]
 
[[Category:Cryptography]]
[[Category:Steganography]]
 
{{Crypto-stub}}

Latest revision as of 21:21, 10 October 2014


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