Complexity Assumptions Sample Clauses
Complexity Assumptions. 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.
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 Z∗q is negligible.
2) Elliptic Curve Computational Diffie ▇▇▇▇▇▇▇ Problem
Complexity Assumptions. In this section we present the complexity assumptions required for our construction.
Complexity Assumptions. In this section, we present the hard problem assumptions that we will be using to prove the security of our protocol.
Complexity Assumptions. The complexity assumptions for this scheme are the same as for the original scheme by ▇▇▇, ▇▇ ▇▇▇ 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. (Computational ▇▇▇▇▇▇-▇▇▇▇▇▇▇ (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, 𝑔𝑎, 𝑔𝑏) , where 𝑔 and (𝑎, 𝑏) are represent the generator of 𝐺 and the random number in 𝑍∗, respectively. The probability of solving the CDH problem for any algorithm in probabilistic polynomial time (PPT) is negligible. (Decisional ▇▇▇▇▇▇-▇▇▇▇▇▇▇ (DDH) Assumption). let 𝐺 represent a finite cyclic group of order n . The DDH problem is distinguishing 𝑔𝑐 and 𝑔𝑎𝑏 based on the given elements 𝑝 (𝑔, 𝑔𝑎, 𝑔𝑏, 𝑔𝑐), where 𝑔 and (𝑎, 𝑏, 𝑐) are represent the generator of G and the random number in 𝑍∗, respectively. The probability of solving the DDH problem for any algorithm in PPT is negligible.
Complexity Assumptions. Computational ▇▇▇▇▇▇-▇▇▇▇▇▇▇ Assumption q G