After a general introduction, the thesis is divided into four parts. In thefirst, we discuss the task of coin tossing, principally in order to highlightthe effect different physical theories have on security in a straightforwardmanner, but, also, to introduce a new protocol for non-relativistic strong cointossing. This protocol matches the security of the best protocol known to datewhile using a conceptually different approach to achieve the task. In the second part variable bias coin tossing is introduced. This is avariant of coin tossing in which one party secretly chooses one of two biasedcoins to toss. It is shown that this can be achieved with unconditionalsecurity for a specified range of biases, and with cheat-evident security forany bias. We also discuss two further protocols which are conjectured to beunconditionally 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 ageneral model for such computations, and show that, within this model, a widerange of functions are impossible to compute securely. We give explicitcheating attacks for such functions. In the final chapter we discuss the task of expanding a private randomstring, while dropping the usual assumption that the protocol's user trusts herdevices. Instead we assume that all quantum devices are supplied by anarbitrarily malicious adversary. We give two protocols that we conjecturesecurely perform this task. The first allows a private random string to beexpanded by a finite amount, while the second generates an arbitrarily largeexpansion of such a string.
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