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

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 ( 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.

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

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 ( 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.
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## Turk. J. Elec. Eng. & Comp. Sci., 9, (2001), 137-146. Full text: pdf Other articles published in the same issue: Turk. J. Elec. Eng. & Comp. Sci. vol.9, iss.2.,

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 Bibtex @ { tbtkelektrik144606, journal = {Turkish Journal of Electrical Engineering and Computer Science}, issn = {1300-0632}, eissn = {1303-6203}, address = {}, publisher = {TÜBİTAK}, year = {2001}, volume = {9}, pages = {137 - 146}, doi = {}, title = {Avalanche and Bit Independence Properties for the Ensembles of Randomly Chosen n \\times n S-Boxes}, key = {cite}, author = {Vergili, İşıl and Yücel, Melek D.} } APA Vergili, İ , Yücel, M . (2001). Avalanche and Bit Independence Properties for the Ensembles of Randomly Chosen n \times n S-Boxes . Turkish Journal of Electrical Engineering and Computer Science , 9 (2) , 137-146 . MLA Vergili, İ , Yücel, M . "Avalanche and Bit Independence Properties for the Ensembles of Randomly Chosen n \times n S-Boxes" . Turkish Journal of Electrical Engineering and Computer Science 9 (2001 ): 137-146 < Chicago Vergili, İ , Yücel, M . "Avalanche and Bit Independence Properties for the Ensembles of Randomly Chosen n \times n S-Boxes". Turkish Journal of Electrical Engineering and Computer Science 9 (2001 ): 137-146 RIS TY - JOUR T1 - Avalanche and Bit Independence Properties for the Ensembles of Randomly Chosen n \times n S-Boxes AU - İşıl Vergili , Melek D. Yücel Y1 - 2001 PY - 2001 N1 - DO - T2 - Turkish Journal of Electrical Engineering and Computer Science JF - Journal JO - JOR SP - 137 EP - 146 VL - 9 IS - 2 SN - 1300-0632-1303-6203 M3 - UR - Y2 - 2021 ER - EndNote %0 Turkish Journal of Electrical Engineering and Computer Science Avalanche and Bit Independence Properties for the Ensembles of Randomly Chosen n \times n S-Boxes %A İşıl Vergili , Melek D. Yücel %T Avalanche and Bit Independence Properties for the Ensembles of Randomly Chosen n \times n S-Boxes %D 2001 %J Turkish Journal of Electrical Engineering and Computer Science %P 1300-0632-1303-6203 %V 9 %N 2 %R %U ISNAD Vergili, İşıl , Yücel, Melek D. . "Avalanche and Bit Independence Properties for the Ensembles of Randomly Chosen n \times n S-Boxes". Turkish Journal of Electrical Engineering and Computer Science 9 / 2 (Şubat 2001): 137-146 . AMA Vergili İ , Yücel M . Avalanche and Bit Independence Properties for the Ensembles of Randomly Chosen n \times n S-Boxes. Turkish Journal of Electrical Engineering and Computer Science. 2001; 9(2): 137-146. Vancouver Vergili İ , Yücel M . Avalanche and Bit Independence Properties for the Ensembles of Randomly Chosen n \times n S-Boxes. Turkish Journal of Electrical Engineering and Computer Science. 2001; 9(2): 137-146. IEEE İ. Vergili ve M. Yücel , "Avalanche and Bit Independence Properties for the Ensembles of Randomly Chosen n \times n S-Boxes", Turkish Journal of Electrical Engineering and Computer Science, c. 9, sayı. 2, ss. 137-146, Şub. 2001