Table 7.

Local sets specification for principal S_n.

Principal Sn
POSS(Sn) = {SKGS, h(x ⊕ y), {IDSn}}	(SN7)
BEL(Sn) = {#(SKGS), #(h(x ⊕ y))}	Send(GW, {IDU, X, TU, α, ω, IDSn, Y, TS, β})
BL(Sn)	(SN8) Update(IDU, X, TU, α, ω, IDSn, Y, TS, β)
Phase 2	(SN9) Receive(GW, {TG, γ, δ})
(SN1) Receive(U, {IDU, IDSn, X, TU, α, ω})	(SN10) Check-freshness(TG)
(SN2) Check-freshness(TU)	(SN11) Check
(SN3) Check	(γ,Hash(h(·); Concat(SKGS,IDU,X,TU,α,IDSn,Y,TS,TG)))
(ω, Hash(h(·);Concat(IDU,Hash(h(·);IDSn,h(x ⊕ y)),TU)))	(SN12) KSU ← Scalar-multiplication(rS, X)
(SN4) Generate-nonce(rS)	(SN13) τ ← Hash(h(·); Concat(Y, T′S, δ, KSU))
(SN5) Y ← Scalar-multiplication(rS, P)	(SN14) sk ← Hash(h(·); Contat(X, Y, KSU))
(SN6) β ← Hash	(SN15) Send(U, {Y, TS, T′S, δ, τ})
(h(·); Concat (SKGS, IDU, X, TU, α, ω, IDSn, Y, TS))	(SN16) Update(Y, TS,T′S,δ, τ)