This paper describes a hardware implementation of an arithmetic processor which is efficient for bit-lengths suitable for both commonly used types of Public Key Cryptography (PKC), i.e., Elliptic Curve (EC) and RSA Cryptosystems. Montgomery modular multiplication in a systolic array architecture is used for modular multiplication. The processor consists of special operational blocks for Montgom...

Table 1. Location and spatial distribution of individual vibrissa intrinsic map peaks. ML: lateral distance of map peak relative to the horizontal midline passing through bregma point. RC: caudal distance of map peak relative to bregma. s.d.: standard deviation of the spread of mapped eIOS centroids after affine transformation (cf. figure 4b). s.d.: standard deviation of the spread of mapped eI...

We define the Mordell exceptional locus Z(V ) for affine varieties V ⊂ Ga with respect to the action of a product of Drinfeld modules on the coordinates of Ga. We show that Z(V ) is a closed subset of V . We also show that there are finitely many maximal algebraic φmodules whose translates lie in V . Our results are motivated by DenisMordell-Lang conjecture for Drinfeld modules.

We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean R 3 and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces in R 3 , as we illustrate with a number of explicit examples. The correspondence between oriented affine lines in R 3 and the tangent bundle to the 2-sphere has a lon...

Provably stable flux reconstruction (FR) schemes are derived for partial differential equations cast in curvilinear coordinates. Specifically, energy (ESFR) considered as they allow design flexibility well stability proofs the linear advection problem on affine elements. Additionally, split forms examined enable development of proofs. The first critical step proves, that coordinates, discontinu...

Edge images derived from compressed image databases are described using fractal techniques. The proposed method is able to give affine transformation-invariant description suitable for use in a query-by-example database application. Comparison among the proposed method, polynomial interpolation and spline interpolation is given. It is concluded that fractal interpolation can give a compact desc...

Translational symmetry provides a powerful constraint that enables recognition of three-dimensional (3D) objects from a single view. Under ideal conditions, affine invariants of 3D points reconstructed from corresponding points would serve as accurate indices for object recognition. In real images, however, inaccurate 2D coordinates of corresponding points can lead to erroneous invariants. In t...

For any affine variety equipped with coordinates, there is a surjective, continuous map from its Berkovich space to its tropicalisation. Exploiting torus actions, we develop techniques for finding an explicit, continuous section of this map. In particular, we prove that such a section exists for linear spaces, Grassmannians of planes (reproving a result due to Cueto, Häbich, and Werner), matrix...

Using the differential-geometric control theory, we present in this note a necessary and sufficient condition under which an affine system is locally feedback equivalent to, via a change of coordinates and restricted smooth state feedback, a generalized normal form called —normal form, which includes Brunovsky canonical form and feedback linearizable systems in a lower-triangular form as its sp...