Avalanche and Bit Independence Properties for the Ensembles of Randomly Chosen n \times n S-Boxes

Authors : İşıl VERGİLİ, Melek D YÜCEL

Pages : 137-146

View : 19 | Download : 9

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Cryptographic test methods such as avalanche, strict avalanche and bit independence criteria, which measure the degree of security of the s-boxes of substitution-permutation networks, are applied to randomly generated ensembles of insert ignore into journalissuearticles values( n \times n \); s-boxes. Statistical analysis of experimental data directs the work towards defining ``relative errors`` and examining the avalanche and strict avalanche criteria within ``relative error ranges``. Histograms of relative errors in each ensemble are evaluated, and combining the results of different ensembles corresponding to different values of the s-box size, variations of maximum relative errors versus the size of the s-box are depicted. Some predictions follow that the larger the s-box size, the more probable that these criteria are satisfied; thus it is possible to form more secure substitution-permutation networks. Correlations among the test criteria are also evaluated in random ensembles to find out to what extent those criteria measure different cryptographic aspects of s-boxes.
Keywords : Turk J Elec Eng Comp Sci, 9, 2001, 137 146 Turk J Elec Eng Comp Sci, vol 9, iss 2