Construction of Graded Broadcast (GBC Sample Clauses

Construction of Graded Broadcast (GBC from GPKI As a next step, we construct a graded broadcast protocol that is an adaptation of the protocol in [MV17]. The resulting protocol ΠGBC only requires a graded PKI whereas the · ⌊ ⌋ − original required a full PKI. In the GPKI setting, parties neither have a global consistent view of all parties’ keys, nor do they know the exact number of parties (only an upper bound n). Henceforth, parties rely on their local KeySet obtained as an output of the ΠKeyGrade protocol. The total number of keys obtained after running the ΠKeyGrade protocol is set to N = n + q ( κ 1). Before describing protocol ΠGBC in Figure 3, we introduce some nomenclatures that will help to present our protocol succinctly. In the following, we assume a fixed sender S. – A signature ⟨x⟩i is valid in the view of party P , if (i) P has assigned grade 2 for pki, i.e., (pki, 2) ∈ KeySetP and (ii) VrfySig(⟨x⟩i , pki) = 1. – A signature ⟨x⟩i is weakly valid in the view of party P , if (i) (pki, gi) ∈ KeySetP , where gi ≥ 1 and (ii) VrfySig(⟨x⟩i , pki) = 1. ⟨⟨ ⟩ ⟩ – We refer to an iterated signature of the form x S j (i.e., by S and some party Pj) as a countersignature and say that Pj is the outer signer. – A countersignature ⟨⟨x⟩S⟩j is said to be valid in the view of party P if the following holds. (i) (pkS, 2) ∈ KeySetP , (ii) VrfySig(⟨x⟩S , pkS ) = 1, (iii) (pkj, 2) ∈ KeySetP , and
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