Quantum And Relativistic Protocols For Secure Multi-Party Computation

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.