Mathematics,
Journal Year:
2024,
Volume and Issue:
12(24), P. 3948 - 3948
Published: Dec. 15, 2024
Cryptography
is
one
of
the
most
important
branches
information
security.
ensures
secure
communication
and
data
privacy,
it
has
been
increasingly
applied
in
healthcare
related
areas.
As
a
significant
cryptographic
method,
Hill
cipher
attracted
attention
from
experts
scholars.
To
enhance
security
traditional
(THC)
expand
its
application
medical
image
encryption,
novel
dynamic
with
Arnold
scrambling
technique
(DHCAST)
proposed
this
work.
Unlike
THC,
DHCAST
uses
time-varying
matrix
as
secret
key,
which
greatly
increases
new
successfully
images
encryption.
In
addition,
method
employs
Zeroing
Neural
Network
(ZNN)
decryption
to
find
inversion
key
(TVIKM).
order
efficiency
ZNN
for
solving
TVIKM,
fuzzy
zeroing
neural
network
(NFZNN)
model
constructed,
convergence
robustness
NFZNN
are
validated
by
both
theoretical
analysis
experiment
results.
Simulation
experiments
show
that
time
about
0.05
s,
while
(TZNN)
2
means
speed
400
times
TZNN
model.
Moreover,
Peak
Signal
Noise
Ratio
(PSNR)
Number
Pixel
Change
Rate
(NPCR)
algorithm
reach
9.51
99.74%,
respectively,
effectively
validates
excellent
encryption
quality
attack
prevention
ability.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2025,
Volume and Issue:
35(1)
Published: Jan. 1, 2025
Memristors
are
commonly
used
to
introduce
various
chaotic
systems
and
can
be
enhance
their
characteristics.
However,
due
the
strict
construction
conditions
of
Hamiltonian
systems,
there
has
been
limited
research
on
development
memristive
conservative
(MHCCSs).
In
this
work,
a
method
for
constructing
three-terminal
memristors
is
proposed,
incorporated
into
system,
resulting
in
class
n-D
MHCCS.
Based
method,
we
model
4D
MHCCS
as
standard
detailed
dynamic
analysis.
The
analysis
reveals
that
exhibits
complex
behaviors,
including
conservativeness,
symmetry,
chaos
depending
parameters,
extreme
multistability,
under
wide
parameter
range.
shows
not
only
retains
favorable
characteristics
system
but
also
more
nonlinear
dynamics
incorporation
memristors,
thereby
further
enhancing
its
Furthermore,
pseudo-random
number
generator
based
excellent
randomness
terms
NIST
test.
Finally,
physical
realizability
verified
through
Field
Programmable
Gate
Array
experiments.
This
study
demonstrates
constructed
MHCCSs
good
entropy
source
applied
embedded
secure
communication,
cryptographic
generator.
Fractal and Fractional,
Journal Year:
2025,
Volume and Issue:
9(2), P. 115 - 115
Published: Feb. 13, 2025
Memristor-based
fractional-order
chaotic
systems
can
record
information
from
the
past,
present,
and
future,
describe
real
world
more
accurately
than
integer-order
systems.
This
paper
proposes
a
novel
memristor
model
verifies
its
characteristics
through
pinched
loop
(PHL)
method.
Subsequently,
new
memristive
Hopfield
neural
network
(4D-FOMHNN)
is
introduced
to
simulate
induced
current,
accompanied
by
Caputo’s
definition
of
fractional
order.
An
Adomian
decomposition
method
(ADM)
employed
for
system
solution.
By
varying
parameters
order
4D-FOMHNN,
rich
dynamic
behaviors
including
transient
chaos,
coexistence
attractors
are
observed
using
methods
such
as
bifurcation
diagrams
Lyapunov
exponent
analysis.
Finally,
proposed
FOMHNN
implemented
on
field-programmable
gate
array
(FPGA),
oscilloscope
observation
results
consistent
with
MATLAB
numerical
simulation
results,
which
further
validate
theoretical
analysis
provide
basis
application
in
field
encryption.
International Journal of Bifurcation and Chaos,
Journal Year:
2024,
Volume and Issue:
34(06)
Published: May 1, 2024
This
paper
presents
a
novel
discrete
memristor
model
that
incorporates
exponential
and
absolute
value
functions.
A
coupled
neural
network
is
constructed
based
on
this
design.
The
periodic
chaotic
regions
of
the
are
determined
using
bifurcation
Lyapunov
exponent
spectrum.
Furthermore,
by
varying
initial
values
memristive
network,
we
observe
coexistence
chaos
attractors,
as
well
attractors.
Additionally,
an
application
to
color
image
encryption
system
given.
Security
analysis
conducted
in
aspects
key
space,
histogram
analysis,
correlation
sensitivity
Peak
Signal-to-Noise
Ratio
(PSNR),
information
entropy
analysis.
results
show
algorithm
has
space
size
[Formula:
see
text],
baboon
graph
7.9993,
which
very
close
ideal
8.
It
shows
feasible
effective.
Finally,
implementation
realized
Field
Programmable
Gate
Array
(FPGA).
experimental
Verilog
language
Vivado
2018.3
platform,
obtained
align
with
numerical
simulation
through
MATLAB.
Mathematics,
Journal Year:
2024,
Volume and Issue:
12(14), P. 2227 - 2227
Published: July 17, 2024
The
design
of
chaotic
systems
with
complex
dynamic
behaviors
has
always
been
a
key
aspect
chaos
theory
in
engineering
applications.
This
study
introduces
novel
fractional-order
system
characterized
by
hidden
dynamics,
hyperchaotic
behavior,
and
multi-scroll
attractors.
By
employing
fractional
calculus,
the
system’s
order
is
extended
beyond
integer
values,
providing
richer
behavior.
dynamics
are
revealed
through
detailed
numerical
simulations
theoretical
analysis,
demonstrating
attractors
bifurcations.
nature
verified
Lyapunov
exponents
phase
portraits,
showing
multiple
positive
that
indicate
higher
degree
unpredictability
complexity.
Additionally,
analyzed,
showcasing
their
potential
for
secure
communication
encryption
approach
enhances
flexibility
adaptability,
making
it
suitable
wide
range
practical
uses,
including
data
transmission,
image
encryption,
signal
processing.
Finally,
based
on
proposed
system,
we
designed
simple
efficient
medical
scheme
analyzed
its
security
performance.
Experimental
results
validate
findings,
confirming
robustness
effectiveness
generating
behaviors.
Fractal and Fractional,
Journal Year:
2024,
Volume and Issue:
8(9), P. 530 - 530
Published: Sept. 11, 2024
We
utilize
Lyapunov
exponents
to
quantitatively
assess
the
hyperchaos
and
categorize
limit
sets
of
complex
dynamical
systems.
While
there
are
numerous
methods
for
computing
in
integer-order
systems,
these
not
suitable
fractional-order
systems
because
nonlocal
characteristics
derivatives.
This
paper
introduces
innovative
eight-dimensional
chaotic
that
investigate
dynamics.
These
exploit
memory
effect
inherent
Grünwald–Letnikov
(G-L)
derivative.
approach
enhances
system’s
applicability
compatibility
with
traditional
An
8D
Chen’s
system
is
utilized
showcase
effectiveness
presented
methodology
hyperchaotic
The
simulation
results
demonstrate
proposed
algorithm
outperforms
existing
algorithms
both
accuracy
precision.
Moreover,
study
utilizes
0–1
Test
Chaos,
Kolmogorov–Sinai
(KS)
entropy,
Kaplan–Yorke
dimension,
Perron
Effect
analyze
system.
additional
metrics
offer
a
thorough
insight
into
behavior
stability
characteristics.
Mathematics,
Journal Year:
2025,
Volume and Issue:
13(2), P. 182 - 182
Published: Jan. 8, 2025
The
widespread
distribution
of
medical
images
in
smart
healthcare
systems
will
cause
privacy
concerns.
unauthorized
sharing
decrypted
remains
uncontrollable,
though
image
encryption
can
discourage
disclosure.
This
research
proposes
a
double-level
security
scheme
for
to
overcome
this
problem.
proposed
joint
and
watermarking
is
based
on
singular-value
decomposition
(SVD)
chaotic
maps.
First,
three
different
random
sequences
are
used
encrypt
the
LL
subband
discrete
wavelet
transform
(DWT)
domain;
then,
HL
LH
sub-bands
embedded
with
watermark
information;
end,
we
obtain
watermarked
encrypted
inverse
DWT
(IDWT)
transform.
In
study,
SVD
domain.
main
originality
that
decryption
extraction
be
performed
separately.
Experimental
results
demonstrate
superiority
method
key
spaces
(10225),
PSNR
(76.2543),
UACI
(0.3329).
implementation,
following
achievements
attained.
our
meet
requests
levels.
Second,
Third,
detected
Thus,
experiment
analysis
effectiveness
scheme.
Mathematics,
Journal Year:
2025,
Volume and Issue:
13(2), P. 201 - 201
Published: Jan. 9, 2025
In
this
paper,
we
first
design
the
corresponding
integration
algorithm
and
matlab
program
according
to
Gauss–Legendre
principle.
Then,
select
Lorenz
system,
Duffing
hidden
attractor
chaotic
system
Multi-wing
for
dynamics
analysis.
We
apply
integral
Runge–Kutta
solution
of
dissipative
systems
time
analyze
compare
differences
between
two
algorithms.
propose
a
basin
attraction
estimation
method
based
on
Lyapunov
exponent
decision
criterion
method.
This
can
better
obtain
region
distinguish
pseudo-attractor,
which
provides
new
way
Finally,
use
FPGA
technology
realize
four
algorithm.
Mathematics,
Journal Year:
2025,
Volume and Issue:
13(5), P. 726 - 726
Published: Feb. 24, 2025
In
comparison
with
dissipative
chaos,
conservative
chaos
is
better
equipped
to
handle
the
risks
associated
reconstruction
of
phase
space
due
absence
attractors.
This
paper
proposes
a
novel
five-dimensional
(5D)
memristive
hyperchaotic
system
(CMHS),
by
incorporating
memristors
into
four-dimensional
(4D)
chaotic
(CCS).
We
conducted
comprehensive
analysis,
using
Lyapunov
exponent
diagrams,
bifurcation
portraits,
equilibrium
points,
and
spectral
entropy
maps
thoroughly
verify
system’s
properties.
The
exhibited
characteristics
such
as
hyperchaos
multi-stability
over
an
ultra-wide
range
parameters
initial
values,
accompanied
transient
quasi-periodic
phenomena.
Subsequently,
pseudorandom
sequences
generated
new
were
tested
demonstrated
excellent
performance,
passing
all
tests
set
National
Institute
Standards
Technology
(NIST).
final
stage
research,
image-encryption
application
based
on
5D
CMHS
was
proposed.
Through
security
feasibility
algorithm
confirmed.