Abstract
Quantum computing continues to inspire considerable interest, not only as it promises to increase speed at which certain calculations may be performed, but also for the ability to allow new secure protocols. However, despite many cryptographic primitives being possible to implement with information theoretic security, impossibility results regarding oblivious transfer and homomorphic encryption suggest a definite restriction to the power of quantum machines. In this thesis we sidestep many of the existing no-go theorems in a variety of ways to allow for several secure multiparty computing protocols. We first review work on a quantum homomorphic encryption and present a new approach using quantum systems which, in some encodings, may hide a constant fraction of information. We then invert the problem, and examine using quantum states to encode probabilistic one-time programs; computer programs which self-destruct after being run only once. Our new method for probabilistic one-time programs has minimal quantum requirements, and is shown to be both secure and with advantages over any possible classical encoding. We then iterate on this and present a second protocol, which allows probabilistic single evaluation of a function, via insight that our initial encoding allows secure generation of a classical commodity useful for secure computation between mutually distrusting parties. We continue to present experimental implementations of both these methods via the use of single photon polarisation encoding and single photon measurement, with laboratory demonstrations of programs where it is advantageous for another party to be allowed only a single access. Finally, we examine other classical commodities useful for secure multi-party computing, and present new methods applicable to a wide class of computations.