In this paper we first show that Tester for an F-algebra A and multilinear forms, [2], is equivalent to multilinear algorithm for the product of elements in A, [3]. Our result is constructive in deterministic polynomial time. We show that given a tester of size ν for an F-algebra A and multilinear forms of degree d one can in deterministic polynomial time construct a multilinear algorithm for t...

As the development of the singular integral operators, their commutators have been well studied (see [1, 2, 3, 14]). From [2, 3, 9, 13], we know that the commutators and multilinear operators generated by the singular integral operators and the Lipschitz functions are bounded on the Triebel-Lizorkin and Lebesgue spaces. The purpose of this paper is to introduce the multilinear commutator associ...

In this work, we provide the first construction of Attribute-Based Encryption (ABE) for general circuits. Our construction is based on the existence of multilinear maps. We prove selective security of our scheme in the standard model under the natural multilinear generalization of the BDDH assumption. Our scheme achieves both Key-Policy and Ciphertext-Policy variants of ABE. Our scheme and its ...

We define the new notion of a multilinear pseudorandom function (PRF), and give a construction with a proof of security assuming the hardness of the decisional Diffie-Hellman problem. A direct application of our construction yields (non-multilinear) PRFs with aggregate security from the same assumption, resolving an open question in [CGV15]. Additionally, multilinear PRFs give a new way of view...

A criterion is established for the validity of multilinear inequalities of a class considered by Brascamp and Lieb, generalizing well-known inequalties of Rogers and Hölder, Young, and Loomis-Whitney. 1. Formulation Consider multilinear functionals (1.1) Λ(f1, f2, · · · , fm) = ∫

An adaptive perceptron with multilinear couplings is introduced. While an adap-tive perceptron exhibits severe shortcomings if it is applied to complex tasks, this is not so for the adaptive multilinear perceptron.

We investigate the relation between multilinear mappings and multipartite states. We show that the isomorphism between multilinear mapping and tensor product completely characterizes decomposable multipartite states in a mathematically well-defined manner.

A multilinear version of Schur’s test is obtained for products of L spaces and is used to derive boundedness for multilinear multiplier operators acting on Sobolev and Besov spaces.