Resource requirements for quantum cryptography

In this thesis we explore communication between parties with access to quantum resources, such as channels, qudits, and computers. We start by studying types of quantum channels. In particular, we consider a scenario where the sender knows a classical description of the qudit they intend to send, and the receiver’s operations are restricted to classical ones. Our main result is that the accuracy of the transmission scales inverse exponentially with the number of pre-shared entangled qudits. We later look into possible extra properties of quantum channels by giving a protocol for authenticating a noisy channel. Moreover, we prove that our protocol requires access to poly-logarithmic fewer qubits than the previously known techniques. For the rest of the dissertation we look at what ideal quantum channels could be useful for. Our first result is a round-optimal quantum protocol for oblivious transfer which can be instantiated both in the plain and quantum random oracle models (by basically lifting the properties of an underlying zero-knowledge protocol), but we obtain round optimality in the quantum random oracle model only. The last chapters of this dissertation are an exploration of a particular set-up assumption, quantum pseudorandomness; i.e. assuming the existence of random (looking) quantum states. We first show that in contrast to the classical case, the size of a quantum pseudorandom object cannot be shrunk. Finally, we prove that if there is a promise problem that admits a quantum reduction that loses information about its input, then certain quantum pseudorandom primitives exit.