Sentence examples for existed an efficient from inspiring English sources

It is not difficult to see that if there existed an efficient algorithm for deciding \(\sc{FACTORIZATION}\), then there would also exist an efficient algorithm for determining prime factorizations.[3] It is also easy to see that the function taking \(x\) to its prime factorization is effectively computable in the traditional sense of computability theory.

In general, suppose that there exists an efficient mechanism with an "ex post" equilibrium.

Computability: there exists an efficient algorithm to calculate e u,v), for all u,v∈G.  .

In particular, whenever the UCEM property holds, there exists an efficient (i.e., polynomial-time) randomized algorithm.

CDH assumption: There does not exist an efficient PPT (probabilistic polynomial time) algorithm in G 1 to solve CDH problem.

(6) q-SDH assumption: There does not exist an efficient PPT algorithm to solve q-SDH problem.

Then by a version of the revelation principle there exists an efficient direct mechanism in which truth-telling is an "ex post" equilibrium.

In this paper, we provide a proof that the problem is indeed NP-hard, so it is not likely that there exists an efficient algorithm that solves the problem optimally.

(4) Gap Diffie-Hellman (GDH) group: If there exists an efficient PPT algorithm to solve the DDH problem and no PPT algorithm to solve the CDH problem, then G 1, a prime group, is defined as a GDH group.

(1) Computational Diffie-Hellman (CDH) problem: Sample: (P ,a, P b Pfor some (a,b in Z_{q}^) Output: abP   (2) CDH assumption: There does not exist an efficient PPT (probabilistic polynomial time) algorithm in G 1 to solve CDH problem.

Bilinearity: e u a,v b )=e u,v) a b, for all u,v∈G,a,b∈Z p ; Non-degeneracy: (e g,g neq 1_{G_{1}}) ; Computability: there exists an efficient algorithm to calculate e u,v), for all u,v∈G.