Let Setup' be the Setup algorithm for a multilinear map, where outputs group with order p, respectively.
Run Setup'(2n) to obtain the public parameters params' for a multilinear map of target group [G.sub.2n].
(2) Combining the subset-cover framework, this paper puts forward an efficient revocable key-aggregate encryption scheme based on multilinear maps, realizing the user's access control and revocation.
The rest of the paper is organized as follows: Section 2 introduces some related knowledge, including multilinear maps, complexity assumption, and subset-cover framework.
Multilinear Maps. Multilinear maps were first put forward by Boneh and Silverberg , making the research and application of multilinear maps be more and more widely.
In the asymmetric multilinear maps , group is divided by a vector and the map operations make [mathematical expression not reproducible].
Our main construction of the revocable key-aggregate encryption scheme is based on multilinear maps and realizes data sharing and user revocation in cloud storage securely and efficiently.
We will need to know the form of B(K,H)-valued multilinear maps on [Alpha] x ...
Since [Beta] is finite dimensional, multilinear maps on [Beta] may be extended to multilinear maps on B(K), and so it suffices to prove the result when [Beta] = B(K).
Sinclair, Completely bounded multilinear maps and [C.sup.*]-algebraic cohomology, Invent.