Slovak University of Technology, Bratislava
Faculty of Electrical Engineering and Information Technology
Degree Course: INFORMATICS
Author: Martin Šalgovič
Diploma thesis: Classification and distribution of S-boxes
Supervisor: RNDr. Karol Nemoga, CSc.
This thesis is focused on the transformations used in cryptograpy, called S-boxes, which are usually composed from Boolean funcions. It looks at parameter called differential uniformity, which is important indicator of cipher algorithm resistance against differentila cryptanalysis. Main task of the thesis is to find out S-box distribution regarding differential uniformity of S-boxes with dimensions three, four and five. Another task besides that is to find out affine equivalence classes of S-boxes with dimension three, and also classes count and sizes. Solution of this tasks offers distribution of bijective and nonbijective S-boxes with dimension of three accomplished by evaluating full set of functions, and distribution of bijective S-boxes with dimension four and estimation of distribution of bijective S-boxes with dimension five. Last two ditribution were computed from random selection of functions. Second part of solution are computed equivalence classes of bijective and nonbijective S-boxes of dimension three. Together with that, it was theoretically developed method for searching for the representants of equivalence classes. Also it was, for the purpose of computations, designed and implemented an application, which allows doing computations, mentioned earlier, on the computer. Application has ability to search for distribution of bijective and nonbijective S-boxes with various input and output dimensions on the set of all functions or random selection of functions. It also can compute inner, outer or inner-outer equvalence classes of bijective and nonbijective S-boxes.