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Table 1. Significant differences in DES
product expected actual difference diff
rand
test()
Q
1
× Q
2
0.241739 0.216797 2.5 fail
Q
1
× Q
3
0.204115 0.179688 2.4 fail
Q
1
× Q
4
0.126188 0.077148 4.9 fail
4 Conclusions
Clearly the reason to adopt a FN structure in a block cipher is mainly due to the con-
venience it offers, such as ease of moving between encryption and decryption, and less
due to its diffusion capabilities. High diffusion in a product cipher implies that the input
bits are be treated uniformly in every round. Since this is not the case for a FN, addi-
tional complexity (e.g. more rounds) would be required. The proposed description and
metric of diffusion enables both the investigation of the topology (structure) of a FN
as well as the underlying non-linear function(s). This would allow the investigation of
FNs consisting of different round functions, with varying input and output lengths as
well as different swapping schemes (unbalanced heterogeneous FNs).
Although that the proposed approach initially aimed for studying FNs, most product
block ciphers can benefit from such an analysis.
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