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S

New
publication 1999
ETH Series in Information Processing Vol. 14
Editor: James L. Massey
Richard J. De Moliner
On the Statistical Testing of Block Ciphers.
1st edition 1999. VIII,
110 pages. EUR 50,11.
ISBN 3896494899
Tests that are capable of analyzing any practical block cipher, no
matter what the internal structure of the block cipher may be, are the subject of
this work. It is argued that such tests must be statistical.
A discrete memoryless source producing a fixedlength sequence of output
digits from a finite alphabet is considered. The problem of
deciding whether the single letter probability distribution of the discrete memoryless
source is equal to a given probability distribution or not is analyzed in
detail. For this problem of statistical hypothesis testing the Pearson
statistic is used. What can validly be concluded from statistical hypothesis
testing is carefully considered.
We show that if a cryptanalyst cannot solve at least one of two basic problems
for a given block cipher, then he cannot
"break" this block cipher. These two basic problems are (1) to find
an algorithm that is distinguishing for the given block cipher and (2) to find an
algorithm that is keysubset distinguishing for the given block cipher and for
a given decomposition of the key space.
An approach to finding an algorithm that is distinguishing for a given
block cipher as well as an approach to finding an algorithm that is keysubset
distinguishing for a given block cipher and for a given decomposition of the
key space are described. These two approaches form the framework for the
statistical testing of block ciphers.
A family of tests called bitdependency tests is presented. The aim of a
bitdependency test is to say as much as possible about the quality of a block
cipher when only a given subset of bits of the plaintext blocks and a given
subset of bits of the corresponding ciphertext blocks
are observed.
Keywords: cryptography, cryptanalysis, block ciphers, bitdependency tests,
statistical hypothesis testing, statistical tests, Pearson statistic.
ETH Series in Information Processing
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