  Two user secure computation of randomized functions is considered, where only
one user computes the output. Both the users are semi-honest; and computation
is such that no user learns any additional information about the other user's
input and output other than what cannot be inferred from its own input and
output. First we consider a scenario, where privacy conditions are against both
the users. In perfect security setting Kilian [STOC 2000] gave a
characterization of securely computable randomized functions, and we provide
rate-optimal protocols for such functions. We prove that the same
characterization holds in asymptotic security setting as well and give a
rate-optimal protocol. In another scenario, where privacy condition is only
against the user who is not computing the function, we provide rate-optimal
protocols. For perfect security in both the scenarios, our results are in terms
of chromatic entropies of different graphs. In asymptotic security setting, we
get single-letter expressions of rates in both the scenarios.
