By Boris Ryabko, Jaakko Astola, Mikhail Malyutov
Universal codes successfully compress sequences generated by way of desk bound and ergodic assets with unknown facts, and so they have been initially designed for lossless information compression. meanwhile, it was once discovered that they are often used for fixing very important difficulties of prediction and statistical research of time sequence, and this e-book describes contemporary leads to this area.
The first bankruptcy introduces and describes the applying of common codes to prediction and the statistical research of time sequence; the second one bankruptcy describes functions of chosen statistical easy methods to cryptography, together with assaults on block ciphers; and the 3rd bankruptcy describes a homogeneity try out used to figure out authorship of literary texts.
The publication may be priceless for researchers and complicated scholars in details concept, mathematical records, time-series research, and cryptography. it really is assumed that the reader has a few grounding in facts and in details theory.
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Extra resources for Compression-Based Methods of Statistical Analysis and Prediction of Time Series
Transm. 2(2), 3–11 (1966) 14. : Information Theory and Reliable Communication. Wiley, New York (1968) 15. : There is no universal code for infinite alphabet. IEEE Trans. Inf. Theory 40, 267–271 (1994) 16. org/resources/time-series-data/ (2011) 17. : A lower bound on compression of unknown alphabets. Theor. Comput. Sci. 332, 293–311 (2004) 18. : A new interpretation of information rate. Bell Syst. Tech. J. 35, 917–926 (1956) 19. : A unified approach to weak universal source coding. IEEE Trans. Inf.
Random number (RNG) and pseudorandom number generators (PRNG) are widely used in cryptography and more generally in data security systems. That is why statistical tests for detecting deviations are of great interest for cryptography [26, 27, 33]. ) Stream ciphers and block ciphers are very important tools of cryptography, and both of them are connected with PRNG. More precisely, a stream cipher generates a so-called keystream which, in fact, is a bit-sequence which must be similar to the sequence obtained by tossing a perfect coin.
1 The described test can be modified in such a way that the Type I error will be equal to ˛. g C 1/ the hypothesis H0 is accepted with the probability . gC1 X jAj j ˛jAjn /=jAgC1 j jD1 and rejected with the probability 1 . ) We denote this test by ˛;' . n/ ˛;' is equal to ˛. Proof is given in Sect. 4. 1), has the level of significance that could be less than ˛. In spite of this drawback, the first criterion may be more useful due to its simplicity. x/j; x 2 An is not known. 2 We have considered codes for which different words of the same length have different codewords.