The bilinear map whose domain and range are identical is called self-bilinear map. Once such kind of bilinear map exists, the multilinear map can be constructed easily by using self bilinear map as a component. Yamakawa et al. have introduced the first secure self-bilinear map with auxiliary information based on the integer factoring assumption in Crypto 2014. Inspired by their work, we find th...

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...

In this paper we present a finite dimensional iterative algorithm for optimal maximum a posteriori (MAP) state estimation of bilinear systems. Bilinear models are appealing in their ability to represent or approximate a broad class of nonlinear systems. We show that several bilinear models previously considered in the literature are special cases of the general bilinear model we propose. Our it...

‎let $x$‎, ‎$y$ and $z$ be banach spaces and $f:xtimes y‎ ‎longrightarrow z$ a bounded bilinear map‎. ‎in this paper we‎ ‎study the relation between arens regularity of $f$ and the‎ ‎reflexivity of $y$‎. ‎we also give some conditions under which the‎ ‎arens regularity of a banach algebra $a$ implies the arens‎ ‎regularity of certain banach right module action of $a$‎ .

Introduction:  The  advent  of  dual-modality  PET/CT  scanners  has  revolutionized  clinical  oncology  by  improving lesion localization and facilitating treatment planning for radiotherapy. In addition, the use of  CT images for CT-based attenuation correction (CTAC) decreases the overall scanning time and creates  a noise-free  attenuation  map  (6map).  CTAC  methods  include  scaling,  s...

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...

Note that the three vector spaces involved aren’t necessarily the same. What these examples have in common is that in each case, the product is a bilinear map. The tensor product is just another example of a product like this. If V1 and V2 are any two vector spaces over a field F, the tensor product is a bilinear map: V1 × V2 → V1 ⊗ V2 , where V1 ⊗ V2 is a vector space over F. The tricky part i...