A novel method of S-box design based on discrete chaotic map

S-box design method based on improved one-dimensional discrete chaotic map

“…Example of S-box generated by proposed approach was compared with some representative random bijective chaos-based S-boxes presented in papers (Cavusoglu et al, 2016;Chen, 2008;Lambić, 2014Lambić, , 2017Liu et al, 2015;Ozkaynak & Ozer, 2010). In Lambić & Živković (2013) several random S-box generation methods based on chaotic 208 165 65 140 228 68 44 150 170 87 172 74 157 133 22 255 105 53 75 225 156 173 58 131 216 117 158 27 152 235 61 250 51 36 37 177 176 238 88 223 77 20 98 236 135 66 3 45 ...…”

“…Bounds for criteria used to measure quality of S-boxes presented in that paper will also be used for comparison. S-box generated by the proposed method have all different output values from interval [0, 255] so it satisfies the requirement of bijectivity (Lambić, 2017).…”

“…are widely used for random S-box design (Belazi, Khan, Abd El-Latif, & Belghith, 2016;Cavusoglu, Zengin, Pehlivan, & Kacar, 2016;Chen, 2008;Jakimoski & Kocarev, 2001;Lambić, 2014;Liu, Yang, Liu, & Dai, 2015;Ozkaynak, Celik, & Ozer, 2016;Ozkaynak & Ozer, 2010;Wang, Wong, Liao, & Xiang, 2009). Besides these, there are many other methods for the generation of random S-boxes based on various chaotic maps, which to our knowledge all have continuous space domain, except for the method presented in Lambić (2017).…”

“…Taking into account the high sensitivity to initial conditions of the chaotic maps, small differences caused by the use of approximations has a great influence on the obtained S-boxes. Method presented in Lambić (2017) uses discrete chaotic map based on the composition of permutations which represents fully digital approach, so there is no need for discretization of continuous values (Lambić, 2015). Therefore, the process of generation of S-boxes is not affected by approximations of any kind.…”

“…Because proposed method uses chaotic map with significantly greater length of periodic orbits than method presented in paper Lambić (2017), it has potential to function properly with a smaller number of elements of the permutation, which could result in greater speed and smaller memory requirements.…”