Ejigu, Dejene (PhD)Adane, Haymanot2018-06-202023-11-292018-06-202023-11-292013-11http://etd.aau.edu.et/handle/123456789/2111The heart of symmetric block cipher is the F function. This function relies on the use of the Sbox. Therefore S-box should be constructed to be strong against cryptanalytic attack. One characteristics of strong S-box is nonlinearity that is the difficulty to approximate S-box by a set of linear equation. This thesis presents the design of stronger S-box using an optimized dynamic hill climbing method. Boolean functions have application in a variety of systems; including block ciphers, stream ciphers and hash functions. In particular in block cipher it is applicable in S-box development. The strengths of both Boolean function and S-box are able to provide a cipher with strong properties to resist known and potential cryptanalytic attacks. Thus, in order to get a desirable measure we work on the cryptographic properties of Boolean function and S-box. The main cryptographic properties required by strong Boolean functions and S-boxes are nonlinearity, autocorrelation, algebraic order, Strict Avalanche Criteria, Avalanche and Bit independency with different cryptographic applications requiring different acceptable measures of these and other properties. As combinations of cryptographic properties exhibited by functions can be conflicting, finding cryptographically strong functions often means that a trade-off needs to be made when optimizing property values. This thesis focused on obtaining stronger S-box by customizing one of the heuristic Boolean function optimization method named as Dynamic Hill Climbing. Dynamic hill climbing method is efficient in optimizing one or more cryptographic properties of a single Boolean function, but strength of individual Boolean functions may not lead to strong S-box. Thus, we optimized the Dynamic Hill Climbing method to get both stronger Boolean functions for cryptographic application and S-box. The Optimized Dynamic Hill Climbing method and the overall value of Optimized Dynamic Hill Climbing method in optimizing S-box is clearly presented in this thesis. Therefore, 15 S-boxes are generated using the customized Dynamic Hill Climbing algorithm to optimize the nonlinearity of S-box. The newly generated S-boxes are tested and compared with Advanced Encryption Standard, Camellia, Hierocrypt and Skipjack. As result, we have found Sboxes with nonlinearity 102. Keywords: Boolean function, S-box, nonlinearity, algebraic order, autocorrelationenBoolean Function; S-Box, Nonlinearity; Algebraic Order; AutocorrelationThesis