Threshold Things That Think: Authorisation for Resharing

As we are evolving towards ubiquitous computing, users carry an increasing number of mobile devices with sensitive information. The security of this information can be protected using threshold cryptography, in which secret computations are shared between multiple devices. Threshold cryptography can be made more robust by resharing protocols, which allow recovery from partial compromises. This paper introduces user-friendly and secure protocols for the authorisation of resharing protocols. We present both automatic and manual protocols, utilising a group manual authentication protocol to add a new device. We analyse the security of these protocols: our analysis considers permanent and temporary compromises, denial of service attacks and manual authentications errors of the user.