Chebyshev Polynomial-Based Authentication Scheme in Multiserver Environment

Table 6

The assumptions in BAN-logic.

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Assumption

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A₁: U_X | ≡ (U_X  S_j) − U_X believes U_X can share UID_X with S_j

A₂: U_X | ≡ (U_X  S_j) − U_X believes U_X can share with S_j

A₃: U_X | ≡ (S_j ⇒ (U_X  S_j)) − U_X believes S_j controls the sharing of the session key between U_X and S_j

A₄: S_j | ≡ (U_X ⇒ (U_X  S_j)) − S_j believes U_X controls the sharing of UID_X between U_X and S_j

A₅: S_j | ≡ (U_X ⇒ (U_X  S_j)) − S_j believes U_X controls the sharing of the session key between U_X and S_j

A₆: S_j | ≡ (S_j  U_X) − S_j believes S_j can share with U_X

A₇: U_X | ≡ # (r_S ⊗ ) − U_X believes challenge messages from S_j are fresh

A₈: S_j | ≡ # (r_U ⊗ ) − S_j believes challenge messages from U_X are fresh

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