Mostly existing quantum image models represent image in Cartesian coordinates. Some complicated affine transformation can not be easily handled in Cartesian coordinates. In this paper, a new representation of Multi-Channel log-polar quantum image (MCLPQI) sampled in log-polar coordinates is proposed. This form contains the image RGB color information and transparency αof the corresponding pixel...

One of the most efficient ways to implement a scalar multiplication on elliptic curves with precomputed points is to use mixed coordinates (affine and Jacobian). We show how to relax these preconditions by introducing relative Jacobian coordinates and give an algorithm to compute a scalar multiplication where the precomputed points can be given in Jacobian coordinates. We also show that this ne...

Postnikov constructed a decomposition of a totally nonnegative Grassmannian (Grkn)≥0 into positroid cells. We provide combinatorial formulas that allow one to decide which cell a given point in (Grkn)≥0 belongs to and to determine affine coordinates of the point within this cell. This simplifies Postnikov’s description of the inverse boundary measurement map and generalizes formulas for the top...

In this paper we elaborate on the idea of an emergent spacetime which arises due to the dynamical breaking of diffeomorphism invariance in the early universe. In preparation for an explicit symmetry breaking scenario, we consider nonlinear realizations of the group of analytical diffeomorphisms which provide a unified description of spacetime structures. We find that gravitational fields, such ...

The implementation of a microcoded elliptic curve processor using field-programmable gate array technology is described. This processor implements optimal normal basis field operations in 2 . The design is synthesized by a parameterized module generator, which can accommodate arbitrary and also produce field multipliers with different speed/area tradeoffs. The control part of the processor is m...

Moments of a Wigner distribution are defined based on both the space and spatial frequency coordinates and are considered as a summarization of the distribution. A method is proposed in this paper to derive functions called affine Wigner moment invariants (AWMI) based on these moments. These functions remain unchanged when the underlying images are affine transformed. As Wigner distributions co...

Computation of multiplicative inverses in finite fields GF (p) and GF (2) is the most time consuming operation in elliptic curve cryptography especially when affine coordinates are used. Since the existing algorithms based on extended Euclidean algorithm do not permit a fast software implementation, projective coordinates, which eliminate almost all of the inversion operations from the curve ar...

The bent functions are the Boolean functions of an even number of variables which are at the maximum possible distance from the set of all affine functions. In this paper, it is shown that each isometric mapping of the set of Boolean functions of n variables to itself preserving the class of bent functions is a combination of an affine transformation of coordinates and a shift by an affine func...

Generalized barycentric coordinates are widely used to represent a point inside a polygon as an affine combination of the polygon’s vertices, and it is desirable to have coordinates that are non-negative, smooth, and locally supported. Unfortunately, the existing coordinate functions that satisfy all these properties do not have a simple analytic expression, making them expensive to evaluate an...