# SOME STUDIES ON c-DIFFERENTIAL UNIFORMITY OF SWAPPED INVERSE FUNCTION

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.