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The cost of sending one message is several magnitudes lower than the cost of solving a puzzle. Hence, Eve’s cost of running online dictionary attacks and her cost of running many-to-many attacks 28 Peng Wang et al. Client (C) Server (S) enter C, π x ∈R Z∗ q X = f1 (x, π) find ticket and cookie abort if ticket is expired find a in the ticket k1 = f3 (C, S, x, Y, π) kp = h(k1 , a) abort if kp = kp k2 = f5 (C, S, x, Y, π) C, X, cookie −−−−−−−−−−−−−−− → Y, kp , cookienew , l ←−−−−−−−−−−−−−−− kq kq = h(k2 , a) compute sk generate ticketnew save cookienew and ticketnew −−−−−−→ abort if the cookie is invalid find a in the cookie lookup client’s verifier v y ∈R Z∗ q Y = f2 (C, S, X, y, v) k1 = f4 (C, S, X, y, v) kp = h(k1 , a ) compute sk generate cookienew k2 = f6 (C, S, X, y, v) kq = h(k2 , a ) abort if kq = kq Fig.

F. Bao. Security Analysis of a Password Authenticated Key Exchange Protocol. In Proc. ISC 2003, LNCS 2851, pp. 208-217, 2000. Cryptanalysis of an Improved C2C-PAKE Scheme 39 2. W. R. H. S. Park. Password-Authenticated Key Exchange between Clients with Different Passwords. In Proc. ICICS 2002, LNCS 2513, pp. 134-146, 2002. 3. L. Chen. A Weakness of the Password-Authenticated Key Agreement between Clients with Different Passwords Scheme. 24, 2003. 4. J. Kim, S. Kim, J. Kwak, and D. Won. Cryptanalysis and Improvement of Password-Authenticated Key Exchange Scheme between Clients with Different Passwords.

Hence, our cookie-ticket pair approach is more secure than the cookie only approach used in Pinkas and Sander’s approach. Further, our scheme requires less server storage than that required in [22]. In their approach, a server keeps a counter for every cookie stored on users’ computers. In our approach, on one hand, if we assume that users’ computers are secure, then the server does not cache cookies, it only stores one global counter. On the other hand, if users’ computers are not assumed to be secure and the “resisting stolen tickets” protocol (explained at the end of section 4) is used, then the number of cookies and the corresponding counters maintained by the server is equal to the number tickets stolen by an attacker, which is still less than their approach.

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