Secure Identification In The Isolated Qubits Model

Oblivious transfer is a powerful cryptographic primitive that is complete for secure multi-party computation. In oblivious transfer protocols a user sends one or more messages to a receiver, while the sender remains oblivious as to which messages have been received. Protocols for oblivious transfer cannot exist in a classical or fully-quantum world, but can be implemented by restricting the users' power. The isolated qubits model is a cryptographic model in which users are restricted to single-qubit operations and are not allowed to use entangling operations. Furthermore, all parties are allowed to store qubits for a long time before measuring them. In this model, a secure single-bit one-out-of-two randomised oblivious transfer protocol was recently presented by Liu. Motivated by this result, we construct a protocol for secure string one-out-of-two randomised oblivious transfer by simplifying and generalising the existing proof. We then study for the first time interactive protocols for more complex two-party functionalities in this model based on the security of our construction. In order to guarantee the composability of our construction, users are restricted to measurement at the end of each sub-protocol. It is then possible to construct secure one-out-of-two and one-out-of-k oblivious transfer protocols in the isolated qubits model. Moreover, we study secure password-based identification, where a user identifies himself to another user by evaluating the equality function on their inputs, or passwords. We use the oblivious transfer constructions mentioned above as sub-protocols to construct a secure identification protocol. Finally, we prove that constructing a secure identification protocol non-interactively is impossible , even using oblivious transfer. Acknowledgements First of all, I would like to thank my supervisor, Christian Schaffner for introducing me to world of quantum cryptography and for giving me the opportunity to work with him, for his valuable contribution throughout the project, the long hours he spent on trying to solve the riddles of isolated qubits. Furthermore, I want to thank Yi-Kai Liu for helpful discussions and suggestions as well as reading through our first try to tackle his model. I would also like to thank the examination committee for taking the time and effort of reading this thesis. Last but not least, I want to thank my family and friends for their motivation and support during the last year. ii Contents Abstract i Acknowledgements ii Contents iii Abbreviations vi 1 Introduction 1 1.