Examination of cryptographic properties of lightweight involutive substitution boxes

Lightweight encryption methods have reached wider use with the diversification and proliferation of IoT devices. The resistance of substitution boxes, the only non-linear layer used in lightweight encryption, to cryptanalysis methods, it also means that encryption is resistant to attacks. For this reason, within the scope of the thesis study; by examining S-boxes used in lightweight encryption according to various cryptographic properties, it was aimed to present S-boxes that are most resistant to linear/differential cryptanalysis methods. All bijective and involutive S-box permutations, mapped from 4-bit input to 4-bit output and from 3-bit input to 3-bit output, were examined according to 10 cryptographic features and the S-boxes most resistant to cryptanalysis methods were determined. In the thesis study, involutive S-boxes of 3 × 3 size defined as 'Optimal' like this; largest absolute value in the linear approximation table is 2, the largest value in the difference distribution table is 2 and the algebraic degree is 2. Involutive S-boxes of 4 × 4 size defined as 'Optimal' like this; largest absolute value in the approximation table is 4, the largest value in the difference distribution table is 4 and the algebraic degree is 3. The optimal S-boxes are the remaining 7 cryptographic features; BIBO Pattern, Linear Branch Number, Differential Branch Number, Frequency of Linearity, Frequency of Differential Uniformity, Boomerang Connectivity Table Uniformity and Differential Linear Connectivity Table Uniformity were examined and the results were presented. S-boxes of 5 × 5 size with the largest absolute value in the linear approximation table, the largest value in the difference distribution table and algebraic degree good properties were found with the genetic algorithm and their cryptographic properties were analyzed. Bitslice gate complexities were analyzed without optimizing the algebraic expressions consisting of vectorial output Boolean functions of S-boxes, which have the best values according to the cryptographic features examined. In the thesis study; while selecting the S-boxes to be used in lightweight encryption, 10 cryptographic features were taken into consideration and the S-boxes with the best values according to these features were presented.