. 2014 Jun 10;14(6):10081–10106. doi: 10.3390/s140610081

Table 8.

Local sets specification for principal GW.

Principal GW
POSS(GW) = {x, y, h(x ⊕ y), SK_GS}	Phase 2
BEL(GW) = {#(x), #(y), #(h(x ⊕ y)), #(SK_GS)}	(GW9) Receive(S_n, {ID_U, X, T_U, α, ω, ID_{S_n}, Y, T_S, β})
BL(GW)	(GW10) Check-freshness(T_S)
Phase 1	(GW11) Check (β, Hash(h(·); Concat(SK_GS, ID_U, X, T_U, α, ω, ID_{S_n}, Y, T_S)))
(GW1) Received(U, {ID_U, ${\bar{p w}}_{U}$ )
(GW2) K_U ← Scalar-multiplication(Hash(h(·); Concat(ID_U, x)), P)	(GW12) X′ ← Scalar-multiplication(Hash(h(·); Concat(ID_U, x)), X)
(GW3) A_U ← XOR ( ${\bar{p w}}_{U}$ , h(x ⊕ y))	(GW13)
(GW4) B_U ← Hash(h(·); Concat(ID_U, ${\bar{p w}}_{U}$ , h(x ⊕ y)))	Check(α, Hash(h(·); Concat(ID_U, ID_{S_n}, X, X′, T_U, ω)))
(GW5)	(GW14) γ ←
W_U ← XOR(Hash(h(·); Concat(ID_U, ${\bar{p w}}_{U}$ )), K_U)	Hash(h(·); Concat(SK_GS, ID_U,X,T_U,α,ID_{S_n},Y,T_s,T_G))
(GW6) Send(U, {A_U, B_U, W_U, h(·)})	(GW15) δ ← Hash(h(·);Contat(ID_U, X, X′, T_U, ID_{S_n}, Y, T_S))
(GW7) Update(A_U, B_U, W_U, h(·))	(GW16) Send(S_n, {T_G, γ, δ})
(GW8) Forget(ID_U, ${\bar{p w}}_{U}$ , A_U, B_U, K_U, W_U)	(GW17) Update(T_G, γ, δ)