  This paper considers the problem of single-server Private Computation (PC) in
the presence of Side Information (SI). In this problem, there is a server that
stores $K$ i.i.d. messages, and a user who has a subset of $M$ uncoded messages
or a coded linear combination of them as side information, where the identities
of these messages are unknown to the server. The user wants to privately
compute (via downloading information from the server) a linear combination of a
subset of $D$ other messages, where the identities of these messages must be
kept private individually or jointly. For each setting, we define the capacity
as the supremum of all achievable download rates.
  We characterize the capacity of both PC with coded and uncoded SI when
individual privacy is required, for all $K, M, D$. Our results indicate that
both settings have the same capacity. In addition, we establish a non-trivial
lower bound on the capacity of PC with coded SI when joint privacy is required,
for a range of parameters $K, M, D$. This lower bound is the same as the lower
bound we previously established on the capacity of PC with uncoded SI when
joint privacy is required.
