Efficiency of TP-AMP Sample Clauses

Efficiency of TP-AMP. We may consider the number of expensive operations, for example, multiple precision multiplications (MPM) in Zp∗, in order to analyze the performance of TP-AMP. We approximate the number of multiplications on average, by assum- ing the use of a left-to-right binary exponentiation method or a simultaneous exponentiation method (denoted by sim) [27]. A slight computational difference between squaring and multiplication can be ignored for convenience. − Let κj = κjj = κjjj = κ for secure prime p while κj = κjj = κjjj = A 2/3 for safe prime p for simple analysis. Practically we can set κjj = 2κ with intentionally R R smaller exponents, for example, x ← {0, 1}κrr and not ← Z∗q for safe prime − − p though it is not general for security argument. For the client, γ may take 1.5(A κj) while m may need 1.5κjj + 1 MPM. For the server, β may take 1.5(κ + κjj) + 2 or 2κjj + 1(sim) MPM. Finally the client may need 1.5κjjj for α. As a result, the client may need 1.5(A κj + κjj + κjjj) + 1 while the server may require 1.5(κ + 2κjj) + 2 MPM totally. Also if we assume an ideal cipher for γ as like EKE2 and AuthA [3, 4], the client may need 1.5(κjj + κjjj) MPM only. One can easily see that the TP-AMP protocol is efficient especially when we use a secure prime, p, since κj = κjj = κjjj = κ. TP-AMP is comparable to the most closely related protocol PAK-Z (with an efficient instance Y using Xxxxxxx’x signature [30]) [25, 26] and AuthA [4, 8] in terms of efficiency. In general, TP-AMP is more efficient than those related schemes under the same assumption, for example, on a safe or secure prime with group size exponents, or an ideal cipher. However, when we use a safe prime with intentionally smaller exponents, PAK-Y shows better in the client, while TP-AMP does still better in the server. Though TP-AMP is not a direct instance of PAK-Z, we can say it provides efficiency on the framework of PAK in the augmented model. As we mentioned already, TP-AMP can be instantiated on EKE2 [3, 4, 8] and provide efficiency on that framework. Thus, we would like to address that TP-AMP is a practical password authenticated key agreement protocol with sufficient security and generic features in the augmented model.
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