Lately, Ellingsen et al created a new concept by making minor changes on the old concept of (multiplicative) differential. This new definition which has potential to be capable of extending differential cryptanalysis in a completely new way is named as c-differential and brought with it the concept of c-differential uniformity. We examlify that how some known functions' behaviour, especially inverse function, would be under this extended differential. The main purpose of this thesis is to observe how the swapped inverse function, which is one of the variety of ways to modify the binary inverse function, impacts the function's c-differential uniformity. In this thesis, we proposed a new theorem including the new characterization of the $(0,\alpha)$-swapped inverse function in even characteristic under this new concept, $x^{2^n-2}+x^{2^n-1}/\alpha+(x-\alpha)^{2^n-1}/\alpha$ on $\matbb{F}_{2^n}$, and reached two conclusions for all $c\neq1$: we prove that its c-differential uniformity value can take 1,2,3 and 4 and attains its maximum value 4 under two special conditions satisfied by the trace mapping.


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This study presents a new nonlinear dynamic model for a gear-shaft-disk-bearing system. A nonlinear dynamic model of a spur gear pair is coupled with linear finite element models of shafts carrying them, and with discrete models of bearings and disks. The nonlinear elasticity term resulting from backlash is expressed by a describing function, and a method developed in previous studies to determine multi harmonic responses of nonlinear multi-degree-of-freedom systems is employed for the solution. The excitat...
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We propose a feedback quantization scheme for downlink multiuser diversity systems. The scheme is designed for heterogeneous users, i.e., users operating under different levels of mean signal-to-noise ratios (SNRs). The proposed scheme equally distributes the channel access time to user clusters and, at the same time, maximizes the sum-rate capacity under equal-channel-access-time constraint. The method is compared to a normalized SNR scheduler, full-feedback scheduler, and finite-rate feedback scheduler wi...
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Citation Formats
B. ÜNVER, “SOME STUDIES ON c-DIFFERENTIAL UNIFORMITY OF SWAPPED INVERSE FUNCTION,” M.S. - Master of Science, Middle East Technical University, 2021.