Complexity Assumptions Sample Clauses

Complexity Assumptions.Β Let G be a cyclic additive group generated by point P, whose order is a prime q. We review the following well-known problems to be used in the security analysis of our scheme.
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Complexity Assumptions.Β (Computational Xxxxxx-Xxxxxxx (CDH) Assumption). Let 𝑝 𝐺 represent a finite cyclic group of order 𝑛 . The CDH problem is computing gab based on the given elements (𝑔, π‘”π‘Ž, 𝑔𝑏) , where 𝑔 and (π‘Ž, 𝑏) are represent the generator of 𝐺 and the random number in π‘βˆ—, respectively. The probability of solving the CDH problem for any algorithm in probabilistic polynomial time (PPT) is negligible. (Decisional Xxxxxx-Xxxxxxx (DDH) Assumption). let 𝐺 represent a finite cyclic group of order n . The DDH problem is distinguishing 𝑔𝑐 and π‘”π‘Žπ‘ based on the given elements 𝑝 (𝑔, π‘”π‘Ž, 𝑔𝑏, 𝑔𝑐), where 𝑔 and (π‘Ž, 𝑏, 𝑐) are represent the generator of G and the random number in π‘βˆ—, respectively. The probability of solving the DDH problem for any algorithm in PPT is negligible.
Complexity Assumptions.Β In this section we present the complexity assumptions required for our construction.
Complexity Assumptions. The complexity assumptions for this scheme are the same as for the original scheme by Xxx, Xx Xxx and Pluˆt [6]. We list them here. As before, let p be a prime of the form le1 le2 · · · len · ƒ ± 1, and fix a super- singular curve E over Fp2 together with bases P1, Q1 , P2, Q2 , . . . , Pn, Qn of E[le1 ], E[le2 ], . . . , E[len ], respectively.
Complexity Assumptions.Β Computational Xxxxxx-Xxxxxxx Assumption q G
Complexity Assumptions. ∈ ∈ { } 1) Elliptic Curve Discrete Logarithm Problem (ECDLP): Given one tuple P, Q where Q = xP , the advantage for any probabilistic polynomial time (PPT) adversary to calculate x R Zβˆ—q is negligible. 2) Elliptic Curve Computational Diffie Xxxxxxx Problem

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