  A spacetime singularity, identified by the existence of incomplete causal
geodesics in the spacetime, is called a (Tipler) strong curvature singularity
if the volume form acting on independent Jacobi fields along causal geodesics
vanishes in the approach of the singularity. It is called naked if at least one
of these causal geodesics is past incomplete. Here, we study the formation of
strong curvature naked singularities arising from spherically symmetric
gravitational collapse of general type-I matter fields in an arbitrarily finite
number of dimensions. In the spirit of Joshi and Dwivedi [26], and Goswami and
Joshi [31], we first construct regular initial data in terms of matter
variables and geometric quantities, subject to the dominant and null energy
conditions. Using this initial data, we derive two distinct (but not mutually
exclusive) conditions, which we call the positive root condition (PRC) and the
simple positive root condition (SPRC), that serve as necessary and sufficient
conditions, respectively, for the existence of naked singularities. In doing
so, we generalize the results of [26] and [31]. We further restrict the PRC and
the SPRC by imposing the curvature growth condition (CGC) of Clarke and Krolak
[24] on all causal curves that satisfy the causal convergence condition. The
CGC gives a sufficient condition for the naked singularities implying the PRC
and implied by the SPRC, to be of strong curvature type; thereby also implying
the inextendibility of the spacetime. Using the CGC, we extend the results of
[28] (that hold for dimension $N=4$) to the case $N=5$, showing that strong
curvature naked singularities can occur in this case. However, for the case
$N\geq6$, we show that past-incomplete causal curves that identify naked
singularities do not satisfy the CGC. These results shed light on the validity
of the cosmic censorship conjectures in arbitrary dimensions.
