The heart of symmetric block cipher is the F function. This function relies on the use of the Sbox.rnTherefore S-box should be constructed to be strong against cryptanalytic attack. Onerncharacteristics of strong S-box is nonlinearity that is the difficulty to approximate S-box by a setrnof linear equation. This thesis presents the design of stronger S-box using an optimized dynamicrnhill climbing method.rnBoolean functions have application in a variety of systems; including block ciphers, streamrnciphers and hash functions. In particular in block cipher it is applicable in S-box development.rnThe strengths of both Boolean function and S-box are able to provide a cipher with strongrnproperties to resist known and potential cryptanalytic attacks. Thus, in order to get a desirablernmeasure we work on the cryptographic properties of Boolean function and S-box.rnThe main cryptographic properties required by strong Boolean functions and S-boxes arernnonlinearity, autocorrelation, algebraic order, Strict Avalanche Criteria, Avalanche and Bitrnindependency with different cryptographic applications requiring different acceptable measuresrnof these and other properties. As combinations of cryptographic properties exhibited by functionsrncan be conflicting, finding cryptographically strong functions often means that a trade-off needsrnto be made when optimizing property values.rnThis thesis focused on obtaining stronger S-box by customizing one of the heuristic Booleanrnfunction optimization method named as Dynamic Hill Climbing. Dynamic hill climbing methodrnis efficient in optimizing one or more cryptographic properties of a single Boolean function, butrnstrength of individual Boolean functions may not lead to strong S-box. Thus, we optimized thernDynamic Hill Climbing method to get both stronger Boolean functions for cryptographicrnapplication and S-box. The Optimized Dynamic Hill Climbing method and the overall value ofrnOptimized Dynamic Hill Climbing method in optimizing S-box is clearly presented in this thesis.rnTherefore, 15 S-boxes are generated using the customized Dynamic Hill Climbing algorithm tornoptimize the nonlinearity of S-box. The newly generated S-boxes are tested and compared withrnAdvanced Encryption Standard, Camellia, Hierocrypt and Skipjack. As result, we have found Sboxesrnwith nonlinearity 102.rnKeywords: Boolean function, S-box, nonlinearity, algebraic order, autocorrelation