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...

In many pairing-based cryptosystems, the secret keys are elements of bilinear groups. For safeguarding such secret keys or decrypting or signing in a threshold manner, Verifiable Secret Sharing (VSS) in bilinear groups is required. In this paper, we show a method of verifiably sharing a random secret in a bilinear group. Our method is simple and practical. It can be regarded as a generalisation...

L p estimates for non smooth bilinear Littlewood-Paley square functions on R. Abstract In this work, some non smooth bilinear analogues of linear Littlewood-Paley square functions on the real line are studied. Mainly we prove boundedness-properties in Lebesgue spaces for them. Let us consider the function φn satisfying c φn(ξ) = 1 [n,n+1] (ξ) and consider the bilinear operator Sn(f, g)(x) := R ...

Bilinear operators are investigated in the context of Sobolev spaces and various techniques useful in the study of their boundedness properties are developed. In particular, several classes of symbols for bilinear operators beyond the so called CoifmanMeyer class are considered. Some of the Sobolev space estimates obtained apply to both the bilinear Hilbert transform and its singular multiplier...

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...