  $X$-secure and $T$-private information retrieval (XSTPIR) is a form of
private information retrieval where data security is guaranteed against
collusion among up to $X$ servers and the user's privacy is guaranteed against
collusion among up to $T$ servers. The capacity of XSTPIR is characterized for
arbitrary number of servers $N$, and arbitrary security and privacy thresholds
$X$ and $T$, in the limit as the number of messages $K\rightarrow\infty$.
Capacity is also characterized for any number of messages if either $N=3,
X=T=1$ or if $N\leq X+T$. Insights are drawn from these results, about aligning
versus decoding noise, dependence of PIR rate on field size, and robustness to
symmetric security constraints. In particular, the idea of cross subspace
alignment, i.e., introducing a subspace dependence between Reed-Solomon code
parameters, emerges as the optimal way to align undesired terms while keeping
desired terms resolvable.
