Privacy-Preserving Two-Factor Key Agreement Protocol Based on Chebyshev Polynomials

Table 3

Simulation of hash, reveal, test, corrupt, and execute oracle queries.

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(i) Hash simulation query performs as follows:
If the record (; h) is found in the list L_h corresponding to the hash query h(), return the hash function h. Otherwise, select a string and add (; h) into L_h. If the query is initiated by A, (; h) is stored in L_A.

(ii) Reveal(Uⁱ/S^j) simulation query performs as follows:
If Uⁱ/S^j is in the accepting state, the current session key SK formed by Uⁱ/S^j and its partner is returned.

(iii) Test(Uⁱ/S^j) simulation query performs as follows:
Through Reveal(Uⁱ/S^j) query, obtain the current session SK and then flip an unbiased coin b. If b = 1, return SK. Otherwise, return a random string from {0,1}^l.

(iv) Corrupt(U, a) simulation query performs as follows:
If a = 1, the query returns the password PW of U. If a = 2, the query returns the secret information stored in the user smart card.

(v) Simulation of Execute(Uⁱ, S^j) query occurs in succession with the simulation of Send queries as shown below.
←Send(Uⁱ; start), ←Send(S^j; ) and {}←Send(Uⁱ; ). Finally, M₁ = , M₂ = , and M₃ = {} are returned.

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