@INPROCEEDINGS{Webster86onthe, author = {A. F. Webster and S. E. Tavares}, title = {On The Design Of S-Boxes}, booktitle = {}, year = {1986}, pages = {523--534}, publisher = {Springer-Verlag} }

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Abstract

each of which contains n bits, or avalanche variables. If this procedure is repeated for all i such that 1 < i < m, and one half of the avalanche variables are equal to 1 for each i, then the function f has good avalanche effect. Of course this method can be pursued only if m is fairly small; otherwise, the number of plaintext vectors becomes too large. If that is the case then the best that can be done is to take a random sample of plaintext vectors X, and for each value of i calculate all the avalanche vectors V i . If approximately one half the resulting avalanche variables are equal to 1 for all values of i, then we can conclude that the function has a good avalanche effect. THE STRICT AVALANCHE CRITERION AND THE INDEPENBENCE OF AVALANCHE VARIABLES The concepts of completeness and the avalanche effect can be combined to define a new prope