  Boolean functions are important primitives in different domains of
cryptology, complexity and coding theory. In this paper, we connect the tools
from cryptology and complexity theory in the domain of Boolean functions with
low polynomial degree and high sensitivity. It is well known that the
polynomial degree of of a Boolean function and its resiliency are directly
connected. Using this connection we analyze the polynomial degree-sensitivity
values through the lens of resiliency, demonstrating existence and
non-existence results of functions with low polynomial degree and high
sensitivity on small number of variables (upto 10). In this process, borrowing
an idea from complexity theory, we show that one can implement resilient
Boolean functions on a large number of variables with linear size and
logarithmic depth. Finally, we extend the notion of sensitivity to higher order
and note that the existing construction idea of Nisan and Szegedy (1994) can
provide only constant higher order sensitivity when aiming for polynomial
degree of $n-\omega(1)$. In this direction, we present a construction with low
($n-\omega(1)$) polynomial degree and super-constant $\omega(1)$ order
sensitivity exploiting Maiorana-McFarland constructions, that we borrow from
construction of resilient functions. The questions we raise identify novel
combinatorial problems in the domain of Boolean functions.
