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

Algorithm 2

Role specification for user .

role user (Ui, AS: agent,

SKuas: symmetric_key,

H, F: function,

SND, RCV: channel (dy))

played_by Ui 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 ≔ 0

transition

(1) State = 0 ∧ RCV(start) =|>

State’ ≔ 1 ∧ T’ ≔ new()

∧ RPWi’ ≔ H(PWi.Ai)

∧ DPWi’ ≔ xor(RPWi’,T’)

∧ secret(, sc1, Ui)

∧ secret(IDi, sc2, )

∧ SND(SKuas)

(2) State = 2 ∧ RCV(xor(H(IDi.xor(H(PWi.Ai),T’)),F(R.H(S.IDi))).xor((Yi’.H(Yi’.S)),

xor(H(PWi.Ai),T’)) _SKuas) =|>

State’ ≔ 4 ∧ secret(R, S, sc3, AS)

∧ secret(F(R.H(S.IDi)), sc4, Ui, AS)

∧ VVi’ ≔ xor(H(IDi.H(PWi.Ai)), F(R.H(S.IDi)))

∧ Wi’ ≔ H(H(IDi.H(PWi.Ai)).F(R.H(S.IDi)))

∧ Xi’ ≔ xor((Yi’.H(Yi’.S)),H(PWi.Ai))

∧ CIDi’ ≔ xor(IDi, H(Yi’.S))

∧ T1’ ≔ new()

∧ Zi’ ≔ H(IDi.F(R.H(S.IDi)).Yi’.T1’)

∧ SND(CIDi’.Yi’.Zi’.T1’)

(3) State = 6 ∧ RCV(xor((Y2’.H(Y2’.S)),F(R.H(S.IDi))).H(SK.F(R.H(S.IDi)).T1’.T3’).T3’) =|>

State’ ≔ 8 ∧ SK’ ≔ H(IDi.F(R.H(S.IDi)).H(Y2’.S).T1’.T3’)

∧ Xi’ ≔ xor((Y2’.H(Y2’.S)),H(PWi.Ai))

∧ request(Ui, AS, as_ui_y2, Y2’)

end role