  In classical two-party computation, a trusted initializer who prepares
certain initial correlations, known as one-time tables, can help make the
inputs of both parties information-theoretically secure. We propose some
bipartite quantum protocols with possible aborts for approximately generating
such bipartite classical correlations with varying degrees of privacy, without
introducing a third party. Under some weak requirements for the parties, the
security level is nontrivial for use in bipartite computation. We show that the
security is sometimes dependent on the noise level, but we propose a method for
dealing with noise. The security is "forced security", which implies that the
probability that some useful one-time tables are generated can approach $1$ in
the noiseless case under quite weak assumptions about the parties, although the
protocols allow aborts. We show how to use the generated one-time tables to
achieve nontrivial information-theoretic security in generic two-party
classical or quantum computation tasks, including (interactive) quantum
homomorphic encryption. Our methods provide check-based implementations of some
no-signaling correlations, including the PR-box type, with the help of
communication which carry no information about the inputs in the generated
correlations.
