Research Article

# Improving an Anonymous and Provably Secure Authentication Protocol for a Mobile User

## Algorithm 3

Role specification for application server AS.
 role applicationserver (Ui, AS: agent, SKuas: symmetric_key, H, F: function, SND, RCV: channel(dy)) played_by AS def= local State: nat, IDi, PWi, BIOi, RPWi, DPWi, T, Ai: text, Hi, Vi, VVi, R, S, Xi, Yi, Wi: text, CIDi, Zi, T1, T3, SK, Y2, Ys, Zs: text const as_ui_y2, sc1, sc2, sc3, sc4: protocol_id init State:= 1 transition (1) State = 1 ∧ RCV(IDi.xor(H(PWi.Ai),T’)) =|> State’ ≔ 3 ∧ Hi’ ≔ H(S.IDi) ∧ Vi’ ≔ xor(H(IDi.xor(H(PWi.Ai),T’)),F(R.H(S.IDi))) ∧ Yi’ ≔ new() ∧ Xi’ ≔ xor((Yi’.H(Yi’.S)),xor(H(PWi.Ai),T’)) ∧ secret(F(R.H(S.IDi)), sc4, , ) ∧ SND(_SKuas) (2) State = 5 ∧ RCV(xor(IDi,H(Yi’.S).Yi’.H(IDi.F(R.H(S.IDi).Yi’.T1’)).T1’)) =|> State’ ≔ 7 ∧ Hi’ ≔ H(S.IDi) ∧ Y2’ ≔ new() ∧ T3’ ≔ new() ∧ SK’ ≔ H(IDi.F(R.H(S.IDi)).H(Y2’.S).T1’.T3’) ∧ Ys’ ≔ xor((Y2’.H(Y2’.S)),F(R.H(S.IDi))) ∧ Zs’ ≔ H(SK’.F(R.H(S.IDi)).T1’.T3’) ∧ SND(Ys’.Zs’.T3’) ∧ witness(AS, Ui, as_ui_y2, Y2’) end role

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