Curvature of the bit selection function in the binary representation of a number

We consider the function $\varphi_{t}$ of allocating the $t$-th digit in the binary representation of a number from the ring $\mathbb{Z}_n$ of deductions modulo $n$. For $\varphi_{t}$ we give curvature estimates at odd $n$ for boundary cases $t$ and for all $t$-discharges at $n=2^{k+1} - 1$ or $n=2^{k} + 1$. These results are applied to estimates of the frequency characteristics of sequences produced by the stream cipher algorithm ZUC.