What is the purpose of the local public key tpk_i?

[akileshtangella]

What happens if we don't verify that $A_{0}^{(a)} = tpk_{(a)}^{old}$ in step 2 of the FS-DKR protocol?

Also why does $tpk$, the group public key stay the same from FS-DKG to FS-DKR?

[akileshtangella]

@elichai @tudorcebere