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Email me if you want a copy. The web server won't let me store them because
of the file size. I have the formats listed below
Daryl Rauhala, Investigations of Higher Order Differences in Cryptographic Algorithms.
Master's Thesis, Queen's University. Kingston, Ontario, Canada. January 2000.
Postscript format ( 1.4 Megs )
Abstract
An investigation into higher order differences of vector
Boolean
functions is performed in an attempt to find high probability
characteristics that will be used to attack cryptographic
ciphers.
The current tests available to a cryptographic developer are
explained in detail, and then both conventional and higher order
differential attacks are reviewed and evaluated to understand
their limitations. Two new statistical tests are proposed that
produce variations of the standard XOR table and look at two
changes in the input and output as they are applied to a function
simultaneously. A conjecture is made based on experimental
evidence, that the characteristics created from studying two
changes in the input to a cipher has a characteristic probability
less than or equal to the characteristic probability of the
characteristics used in a conventional differential attack.
Results related to the construction of S-boxes from quadratic
bent
functions are also presented.