Cryptographic protocols depend on the hardness of some computational problems for their security. Joux briefly summarized known relations between assumptions related bilinear map in a sense that if one problem can be solved easily, then another problem can be solved within a polynomial time [6]. In this paper, we investigate additional relations between them. Firstly, we show that the computati...

Predicate encryption is a new paradigm of public key encryption that enables searches on encrypted data. Using the predicate encryption, we can search keywords or attributes on encrypted data without decrypting the ciphertexts. In predicate encryption, a ciphertext is associated with attributes and a token corresponds to a predicate. The token that corresponds to a predicate f can decrypt the c...

In predicate encryption systems, given a capability, one can evaluate one or more predicates on the encrypted data, while all other information about the plaintext remains hidden. We consider the first such systems to permit delegation of capabilities. In a system that supports delegation, a user Alice who has a capability can delegate to Bob a more restrictive capability, which allows him to l...

This paper focuses on the problem of sliding mode control for delay-dependent stabilization criterion of bilinear state-delay systems. Based on the linear matrix inequality (LMI) method and a parameterized model transformation technique, we provide a sufficient condition for the existence of sliding surface and we give an explicit formula of sliding surface guaranteeing the asymptotic stability...

In this paper we address the problem of closed loop stabilization of switched control systems. First we propose a general definition of closed loop switched solution of a control system. Then we use it in order to get a stabilizability result for planar bilinear systems. This result is finally compared with existing literature.

In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on  a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of  level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...

Two classes of rational solutions to a KdV-like nonlinear differential equation are constructed. The basic object is a generalized bilinear differential equation based on a prime number p 1⁄4 3. A conjecture is made that the two presented classes of rational solutions contain all rations solutions to the considered KdV-like equation, which are generated from polynomial solutions to the correspo...

By means of the idea of three-wave method, we obtain some analytic solutions for high nonlinear form of Benjamin-BonaMahony-Burgers (shortly BBMB) equations in its bilinear form. Keywords—Benjamin-Bona-Mahony-Burgers equations, Hirota’s bilinear form, Three-wave method.

In this work, we present a bilinear Tb theorem for singular integral operators of Calderón-Zygmund type. We prove some new accretive type Littlewood-Paley results and construct a bilinear paraproduct for a para-accretive function setting. As an application of our bilinear Tb theorem, we prove product Lebesgue space bounds for bilinear Riesz transforms defined on Lipschitz curves.