589 research outputs found
Efficient unified Montgomery inversion with multibit shifting
Computation of multiplicative inverses in finite fields GF(p) and GF(2/sup n/) is the most time-consuming operation in elliptic curve cryptography, especially when affine co-ordinates are used. Since the existing algorithms based on the extended Euclidean algorithm do not permit a fast software implementation, projective co-ordinates, which eliminate almost all of the inversion operations from the curve arithmetic, are preferred. In the paper, the authors demonstrate that affine co-ordinate implementation provides a comparable speed to that of projective co-ordinates with careful hardware realisation of existing algorithms for calculating inverses in both fields without utilising special moduli or irreducible polynomials. They present two inversion algorithms for binary extension and prime fields, which are slightly modified versions of the Montgomery inversion algorithm. The similarity of the two algorithms allows the design of a single unified hardware architecture that performs the computation of inversion in both fields. They also propose a hardware structure where the field elements are represented using a multi-word format. This feature allows a scalable architecture able to operate in a broad range of precision, which has certain advantages in cryptographic applications. In addition, they include statistical comparison of four inversion algorithms in order to help choose the best one amongst them for implementation onto hardware
Structure theory of central simple ℤd-graded algebras
This paper investigates the structure theory of ℤd- central simple graded algebras and gives the complete decomposition into building block algebras. The results are also applied to generalized Clifford algebras, which are motivating examples of ℤd-central simple graded algebras. © TÜBİTAK
N-fold Supersymmetry in Quantum Systems with Position-dependent Mass
We formulate the framework of N-fold supersymmetry in one-body quantum
mechanical systems with position-dependent mass (PDM). We show that some of the
significant properties in the constant-mass case such as the equivalence to
weak quasi-solvability also hold in the PDM case. We develop a systematic
algorithm for constructing an N-fold supersymmetric PDM system. We apply it to
obtain type A N-fold supersymmetry in the case of PDM, which is characterized
by the so-called type A monomial space. The complete classification and general
form of effective potentials for type A N-fold supersymmetry in the PDM case
are given.Comment: 18 pages, no figures; Refs. updated, typos correcte
New approach to (quasi)-exactly solvable Schrodinger equations with a position-dependent effective mass
By using the point canonical transformation approach in a manner distinct
from previous ones, we generate some new exactly solvable or quasi-exactly
solvable potentials for the one-dimensional Schr\"odinger equation with a
position-dependent effective mass. In the latter case, SUSYQM techniques
provide us with some additional new potentials.Comment: 11 pages, no figur
Exactly solvable effective mass D-dimensional Schrodinger equation for pseudoharmonic and modified Kratzer problems
We employ the point canonical transformation (PCT) to solve the D-dimensional
Schr\"{o}dinger equation with position-dependent effective mass (PDEM) function
for two molecular pseudoharmonic and modified Kratzer (Mie-type) potentials. In
mapping the transformed exactly solvable D-dimensional ()
Schr\"{o}dinger equation with constant mass into the effective mass equation by
employing a proper transformation, the exact bound state solutions including
the energy eigenvalues and corresponding wave functions are derived. The
well-known pseudoharmonic and modified Kratzer exact eigenstates of various
dimensionality is manifested.Comment: 13 page
Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations
The interest of quadratic algebras for position-dependent mass Schr\"odinger
equations is highlighted by constructing spectrum generating algebras for a
class of d-dimensional radial harmonic oscillators with and a
specific mass choice depending on some positive parameter . Via some
minor changes, the one-dimensional oscillator on the line with the same kind of
mass is included in this class. The existence of a single unitary irreducible
representation belonging to the positive-discrete series type for and
of two of them for d=1 is proved. The transition to the constant-mass limit
is studied and deformed su(1,1) generators are constructed.
These operators are finally used to generate all the bound-state wavefunctions
by an algebraic procedure.Comment: 21 pages, no figure, 2 misprints corrected; published versio
Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass
Known shape-invariant potentials for the constant-mass Schrodinger equation
are taken as effective potentials in a position-dependent effective mass (PDEM)
one. The corresponding shape-invariance condition turns out to be deformed. Its
solvability imposes the form of both the deformed superpotential and the PDEM.
A lot of new exactly solvable potentials associated with a PDEM background are
generated in this way. A novel and important condition restricting the
existence of bound states whenever the PDEM vanishes at an end point of the
interval is identified. In some cases, the bound-state spectrum results from a
smooth deformation of that of the conventional shape-invariant potential used
in the construction. In others, one observes a generation or suppression of
bound states, depending on the mass-parameter values. The corresponding
wavefunctions are given in terms of some deformed classical orthogonal
polynomials.Comment: 26 pages, no figure, reduced secs. 4 and 5, final version to appear
in JP
First-order intertwining operators and position-dependent mass Schrodinger equations in d dimensions
The problem of d-dimensional Schrodinger equations with a position-dependent
mass is analyzed in the framework of first-order intertwining operators. With
the pair (H, H_1) of intertwined Hamiltonians one can associate another pair of
second-order partial differential operators (R, R_1), related to the same
intertwining operator and such that H (resp. H_1) commutes with R (resp. R_1).
This property is interpreted in superalgebraic terms in the context of
supersymmetric quantum mechanics (SUSYQM). In the two-dimensional case, a
solution to the resulting system of partial differential equations is obtained
and used to build a physically-relevant model depicting a particle moving in a
semi-infinite layer. Such a model is solved by employing either the
commutativity of H with some second-order partial differential operator L and
the resulting separability of the Schrodinger equation or that of H and R
together with SUSYQM and shape-invariance techniques. The relation between both
approaches is also studied.Comment: 25 pages, no figure, 1 paragraph added in section 4, 1 additional
referenc
Position-dependent mass models and their nonlinear characterization
We consider the specific models of Zhu-Kroemer and BenDaniel-Duke in a
sech-mass background and point out interesting correspondences with the
stationary 1-soliton and 2-soliton solutions of the KdV equation in a
supersymmetric framework.Comment: 8 Pages, Latex version, Two new references are added, To appear in
J.Phys.A (Fast Track Communication
Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework
We formulate a systematic algorithm for constructing a whole class of
Hermitian position-dependent-mass Hamiltonians which, to lowest order of
perturbation theory, allow a description in terms of PT-symmetric Hamiltonians.
The method is applied to the Hermitian analogue of the PT-symmetric cubic
anharmonic oscillator. A new example is provided by a Hamiltonian
(approximately) equivalent to a PT-symmetric extension of the one-parameter
trigonometric Poschl-Teller potential.Comment: 13 pages, no figure, modified presentation, 6 additional references,
published versio
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