  After a general introduction, the thesis is divided into four parts. In the
first, we discuss the task of coin tossing, principally in order to highlight
the effect different physical theories have on security in a straightforward
manner, but, also, to introduce a new protocol for non-relativistic strong coin
tossing. This protocol matches the security of the best protocol known to date
while using a conceptually different approach to achieve the task.
  In the second part variable bias coin tossing is introduced. This is a
variant of coin tossing in which one party secretly chooses one of two biased
coins to toss. It is shown that this can be achieved with unconditional
security for a specified range of biases, and with cheat-evident security for
any bias. We also discuss two further protocols which are conjectured to be
unconditionally secure for any bias.
  The third section looks at other two-party secure computations for which,
prior to our work, protocols and no-go theorems were unknown. We introduce a
general model for such computations, and show that, within this model, a wide
range of functions are impossible to compute securely. We give explicit
cheating attacks for such functions.
  In the final chapter we discuss the task of expanding a private random
string, while dropping the usual assumption that the protocol's user trusts her
devices. Instead we assume that all quantum devices are supplied by an
arbitrarily malicious adversary. We give two protocols that we conjecture
securely perform this task. The first allows a private random string to be
expanded by a finite amount, while the second generates an arbitrarily large
expansion of such a string.
