This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more precise result using the real interpolation theory and we clarify the use of Hardy spaces. Then with the help of the bilinear interpolation theory, we then give ap...

Let Fq be a finite field of cardinality q, where q is a power of a prime number p, t ≥ 2 an even number satisfying t 6≡ 1 (mod p) and Fqt an extension field of Fq with degree t. First, a new trace bilinear form on F n qt which is called ∆-bilinear form is given, where n is a positive integer coprime to q. Then according to this new trace bilinear form, bases and enumeration of cyclic ∆-self-ort...

We investigate commitment schemes whose messages, keys, commitments, and decommitments are elements of bilinear groups, and whose openings are verified by pairing product equations. Such commitments facilitate efficient zero-knowledge proofs of knowledge of a correct opening. We show two lower bounds on such schemes: a commitment cannot be shorter than the message and verifying the opening in a...

A new instantiation of the Cramer-Shoup paradigm for secure encryption is presented, which is built using bilinear map groups. The security is based on the Bilinear Decisional Diffie-Hellman assumption. The recent efficiency improvements introduced in [KD04,GS04] are also applied to our constructions. One of the schemes thereby obtained presents efficiency similar to the most efficient encrypti...

In this paper a comparison between a linear-model-based and a bilinear-modelbased identification and predictive control methodology is presented. Input-output data from a nonlinear first-principles simulation model of the free-radical polymerization of methylmethacrylate are used for black-box identification of a linear and a bilinear model. These black-box models are used within a model-based ...

Diffie-Hellman problems have been widely involved in the design of various cryptographic protocols. Its general family is based on the discrete logarithm over a finite field. Since 2000, its another family which is based on elliptic curve discrete logarithm as well as bilinear pairing, e.g. Weil or Tate pairing, has been attracted significant studies. Thereafter, various cryptographic protocols...

Despite the wide application of bilinear problems to problems both in computer vision and in other fields, their behaviour under the effects of noise is still poorly understood. In this paper, we show analytically that marginal distributions on the solution components of a bilinear problem can be bimodal, even with Gaussian measurement error. We demonstrate and compare three different methods o...

This paper presents the closed-loop composite control of singularly perturbed bilinear systems with a quadratic performance criterion, using successive Galerkin approximation(SGA). The singularly perturbed bilinear system is decomposed into two subsystems of a slow-time and fast-time scale by the singular perturbation theory, and we obtain feedback control laws from each subsystem using SGA. We...

Non-degenerate bilinear forms over fields of characteristic 2, in particular, nonsymmetric ones, are classified with respect to various equivalences, and the Lie algebras preserving them are described. Although it is known that there are two series of distinct finite simple Chevalley groups preserving the non-degenerate symmetric bilinear forms on the space of even dimension, the description of...