@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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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

... S. E. Tavares Department of Electrical Engineering Queen's University Kingston, Ont. Canada The ideas of completeness and the avalanche effect were first introduced by Kam and Davida [1] and Feistel =-=[2]-=-, respectively. If a cryptographic transformation is complete, then each ciphertext bit must depend on all of the plaintext bits. Thus, if it were possible to find the simplest Boolean expression for ...

...he input) was complemented, the correlation coefficients between bits 1 and 2 and between bits 3 and 4 in the output of S 4 were equal to-1. This is equivalent to the discovery made by Heilman et al. =-=[6]-=- that the exclusive-or sums of the output bits, y y 1 2sand y y 3 4s, of S 4 are complemented whenever input bit x1 changes its value. It can also be shown that both of these results can be derived fr...

... the variables are independent. In addition, the variables will always be identical if the correlation coefficient equals 1, and a value of-1 means that they will always be complements of one another =-=[4]-=-. If either the strict avalanche criterion or the avalanche variable independence requirement is not satisfied, then a cryptanalyst can gain some information about the statistical properties of the fu...

...hanged. Figure 3 Mean and variance of DES dependence matrix vs. number of encryption rounds: These values of mean and variance are only for elements in one quarter of the dependence matrix, but Meyer =-=[7]-=- shows that these results will propagate through the rest of the matrix within two rounds. The strict avalanche criterion is satisfied after four rounds for this portion of the matrix; therefore, it w...

.... F. Webster and S. E. Tavares Department of Electrical Engineering Queen's University Kingston, Ont. Canada The ideas of completeness and the avalanche effect were first introduced by Kam and Davida =-=[1]-=- and Feistel [2], respectively. If a cryptographic transformation is complete, then each ciphertext bit must depend on all of the plaintext bits. Thus, if it were possible to find the simplest Boolean...