Common use of Initialization Clause in Contracts

Initialization. Set (i) t = 0; (ii) WeakEpochs, WeakUsers = 𝜙; and (iii) G[∗], Rand[∗], ST[∗], K[∗] → ⊥. • Gen() executes (ST, PK) →$ Gen(), sets ST[PK] → ST, and returns PK. • Add(PK, PK∗) first aborts if (i) PK = PK∗; (ii) t =/ 0 and PK ∈/ G[t]; or (iii) PK∗ ∈ G[t]. Otherwise it:

Initialization. Set (i) t = 0; (ii) WeakEpochs, WeakUsers = 𝜙; and (iii) G[∗], Rand[∗], ST[∗], K[∗] →← ⊥. • Gen() executes (ST, PK) →$←$ Gen(), sets ST[PK] →← ST, and returns PK. • Add(PK, PK∗) first aborts if (i) PK = PK∗; (ii) t =/ 0 and PK ∈/ G[t]; or (iii) PK∗ ∈ G[t]. Otherwise it:

Initialization. Set (i) t = 0; (ii) WeakEpochs, WeakUsers = �∅�; and (iii) G[∗], Rand[∗], ST[∗] ← ⊥], K[∗] →← ⊥. • Gen() executes (ST, PK) →$←$ Gen(), sets ST[PK] →← ST, and returns PK. • Add(PK, PK∗) first aborts if (i) PK = PK∗; (ii) t =/ƒ= 0 and PK ∈/ G[t]; or (iii) PK∗ ∈ G[t]. Otherwise it: ← ←: