Quantum cryptography builds upon decades of advances both in classical cryptography and networks. However, contrary to its classical counterparts, it is still in its infancy applicability-wise, even in the scenario where powerful quantum computers are readily available, and more theoretical work is required before it can provide concrete benefits. The first goal is to formalise in rigorous quantum security frameworks the properties of various techniques that have been transposed, often without proper justification, from the classical world.Then, the recent developments in quantum technologies suggest a mostly cloud-based future availability of quantum devices. Therefore, quantum computation and communication cost of protocol participants must be lowered before being useful.Finally, in most situations, additional steps need to be taken to tailor protocols to the specifications of devices. This allows for optimisations both in terms of quantum memory and operation requirements.This thesis contributes to these three aspects by: (i) giving the first general security definition of the Quantum Cut-and-Choose, a technique for proving the correctness of a quantum message; (ii) presenting a more realistic framework of security against superposition attacks, where classical protocols run on inherently quantum devices; (iii) constructing an efficient delegated multi-party quantum computation protocol, allowing clients to delegate securely to a quantum server a private computation; (iv) building a method for verifying the honesty of a quantum server performing computations on behalf of a client with no operation or memory overhead compared to the unprotected computation.