Several choices for the hardware implementation of the modular multiplication operator are presented. It proposes a cost function to evaluate these design choices and compares them for the optimization of parameters such as area and execution time. This last parameter is very important in cryptographic applications, where the modular multiplication operator is widely used.

We give definitions and some properties of the shift operator SL(H2) and multiplication operator on L(H ). In addition, we obtain some properties of the commutant of the shift operator SL(H2) and characterize SL(H2)-invariant subspaces.

The problem of multiplying elements of the conjugate dual of certain kind of commutative generalized Hilbert algebras, which are dense in the set of C∞-vectors of a self-adjoint operator, is considered in the framework of the so-called duality method. The multiplication is defined by identifying each distribution with a multiplication operator acting on the natural rigged Hilbert space. Certain...

In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded multiplication operator, for a large class of weights. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the unif...

acting in L(R). This means that we consider a system of N interacting quantum particles in R. Here x = (x1, . . . , xN ) ∈ R Nd is for the joint position vector, where each component xj ∈ R d represents the position of the jth particle, 1 ≤ j ≤ N . Next, ∆ stands for the Laplacian in R. The interaction energy operator U(x) acts as multiplication by a function U(x). Finally, the term V(ω;x) repr...