David Touchette

We introduce the idea of temporarily trusted quantum nodes. We introduce a new primitive in that model, erasable bit commitment, which is a variant on standard two-party bit commitment. We show how to implement this primitive in our new model with temporarily trusted nodes. The erasable property allows Alice, in the case that the trust period is about to expire, to ask the trusted nodes to erase her commitment in such a way that a future coalition, after the trust period, of all trusted nodes together with Bob cannot extract any information about the commitment. This is impossible classically. A caveat is that after such an erasure, Alice is not committed to a classical value anymore. We provide a robust protocol which requires a constant number of trusted nodes and which can handle a small fraction of dishonest trusted nodes as well as implementation errors. Our approach lends itself to actual optical implementations, and requires memory during the trust period.