Adaptive χ2 Test for Discriminating between Close Hypotheses with a Large Number of Classes and Its Application to Some Cryptography Problems

Adaptive χ2 Test for Discriminating between Close Hypotheses with a Large Number of Classes and... The main problem considered consists in testing the hypothesis H 0 that letters of an alphabet A = a 1, a 2, . . ., a k are generated with equal probabilities 1/k against the alternative complex hypothesis H 1, the negation of H 0. In many applications, in particular, those connected with cryptography, k is large, but possible deviations from the uniform distribution are small. Therefore, application of Pearson's χ2 test, which is one of the most wide-spread and efficient tests, requires samples of a very large size, certainly exceeding k. We propose a so-called adaptive χ2 test, whose power can be considerably higher than that of the traditional method in the case described. This conclusion is based on the theoretical analysis of the proposed criterion for some classes of alternatives as well as on experimental results related to discriminating between enciphered Russian texts and random sequences. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Adaptive χ2 Test for Discriminating between Close Hypotheses with a Large Number of Classes and Its Application to Some Cryptography Problems

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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2003 by MAIK “Nauka/Interperiodica”
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1023/A:1025104406075
Publisher site
See Article on Publisher Site

Abstract

The main problem considered consists in testing the hypothesis H 0 that letters of an alphabet A = a 1, a 2, . . ., a k are generated with equal probabilities 1/k against the alternative complex hypothesis H 1, the negation of H 0. In many applications, in particular, those connected with cryptography, k is large, but possible deviations from the uniform distribution are small. Therefore, application of Pearson's χ2 test, which is one of the most wide-spread and efficient tests, requires samples of a very large size, certainly exceeding k. We propose a so-called adaptive χ2 test, whose power can be considerably higher than that of the traditional method in the case described. This conclusion is based on the theoretical analysis of the proposed criterion for some classes of alternatives as well as on experimental results related to discriminating between enciphered Russian texts and random sequences.

Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 3, 2004

References

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