Algorithm 1 Client registration protocol.

Alice generates a key pair (${\mathrm{prk}}_{\mathrm{BS}},{\mathrm{pbk}}_{\mathrm{BS}}$$)\leftarrow \mathrm{KeyGen}\left(1^{\lambda }\right)$. C sends [RegisterClient, ${\mathrm{pbk}}_{\mathrm{A}}$ ] to BS. Upon receiving [RegisterClient, ${\mathrm{pbk}}_{\mathrm{A}}$], BS performs the following steps: (a) Abort if ${\mathrm{pbk}}_{\mathrm{A}},·)\in$ BS.Registry. (b) Add (${\mathrm{pbk}}_{\mathrm{A}},\mathrm{NULL})$ to BS.Registry. (c) Initialize Alice’s account balance to zero: BS.onBal${}_{\mathrm{A}}\leftarrow$0. (d) Create a certificate ${\mathrm{cert}}_{\mathrm{A}}$ such that ${\mathrm{cert}}_{\mathrm{A}}$.pbk ← ${\mathrm{pbk}}_{\mathrm{A}}$ and ${\mathrm{cert}}_{\mathrm{A}}$.sig ← Sign(${\mathrm{pbk}}_{\mathrm{A}}$, ${\mathrm{prk}}_{\mathrm{BS}}$), where ${\mathrm{prk}}_{\mathrm{BS}}$ is BS’s private signing key. (e) Send ${\mathrm{cert}}_{\mathrm{A}}$ to Alice.