  We consider secure computation of randomized functions between two users,
where both the users (Alice and Bob) have inputs, Alice sends a message to Bob
over a rate-limited, noise-free link, and then Bob produces the output. We
study two cases: (i) when privacy condition is required only against Bob, who
tries to learn more about Alice's input from the message than what can be
inferred by his own input and output, and (ii) when there is no privacy
requirement. For both the problems, we give single-letter expressions for the
optimal rates. For the first problem, we also explicitly characterize securely
computable randomized functions when input has full support, which leads to a
much simpler expression for the optimal rate. Recently, Data (ISIT 2016)
studied the remaining two cases (first, when privacy conditions are against
both the users; and second, when privacy condition is only against Alice) and
obtained single-letter expressions for optimal rates in both the scenarios.
