At Eurocrypt 2010, Freeman proposed a transformation from pairing-based schemes in composite-order bilinear groups to equivalent ones in prime-order bilinear groups. His transformation can be applied to pairing-based cryptosystems exploiting only one of two properties of composite-order bilinear groups: cancelling and projecting. At Asiacrypt 2010, Meiklejohn, Shacham, and Freeman showed that p...

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...

f(x, y) = a x + x Qy + b y, where a, x ∈ R, b, y ∈ R, and Q is a matrix of dimension n ×m. It is easy to see that bilinear functions compose a subclass of quadratic functions. We refer to optimization problems with bilinear objective and/or constraints as bilinear problems, and they can be viewed as a subclass of quadratic programming. Bilinear programming has various applications in constraine...

We consider cohomology of diagrams of algebras by Beck’s approach, using comonads. We then apply this theory to computing the cohomology of Ψ-rings. Our main result is that there is a spectral sequence connecting the cohomology of the diagram of an algebra to the cohomology of the underlying algebra.

Chen and Ruan [6] defined a very interesting cohomology theory-Chen-Ruan orbifold cohomology. The primary objective of this paper is to compute the Chen-Ruan orbifold cohomology of weighted projective space, one of the most important space used in physics. The classical tools (orbifold cohomology defined by Chen and Ruan,toric varieties, the localization formula) which have been proved to be su...

States in the absolute (semi-relative) cohomology but not in the relative cohomology are examined through the component decomposition of the string field theory action for the 2-D string. It is found that they are auxiliary fields without kinetic terms, but are important for instance in the master equation for the Ward-Takahashi identities. The ghost structure is analyzed in the Siegel gauge, b...

We study the image of the natural map from group cohomology to Galois cohomology by using motivic cohomology of classifying spaces.