This
paper
comprehensively
addresses
homomorphic
encryption
from
both
theoretical
and
practical
perspectives.
The
delves
into
the
mathematical
foundations
required
to
understand
fully
FHE.
It
consequently
covers
design
fundamentals
security
properties
of
FHE,
describes
main
FHE
schemes
based
on
various
problems.
On
a
more
level,
presents
view
privacy-preserving
Machine
Learning
using
encryption,
then
surveys
at
length
an
engineering
angle,
covering
potential
application
in
fog
computing,
cloud
computing
services.
also
provides
comprehensive
analysis
existing
state-of-the-art
libraries
tools,
implemented
software
hardware,
performance
thereof.
Proceedings of the IEEE,
Journal Year:
2022,
Volume and Issue:
110(10), P. 1572 - 1609
Published: Oct. 1, 2022
Data
privacy
concerns
are
increasing
significantly
in
the
context
of
Internet
Things,
cloud
services,
edge
computing,
artificial
intelligence
applications,
and
other
applications
enabled
by
next-generation
networks.
Homomorphic
encryption
addresses
challenges
enabling
multiple
operations
to
be
performed
on
encrypted
messages
without
decryption.
This
article
comprehensively
homomorphic
from
both
theoretical
practical
perspectives.
delves
into
mathematical
foundations
required
understand
fully
(
$\textsf
{FHE}$
).
It
consequently
covers
design
fundamentals
security
properties
describes
main
schemes
based
various
problems.
On
a
more
level,
this
presents
view
privacy-preserving
machine
learning
using
then
surveys
at
length
an
engineering
angle,
covering
potential
application
fog
computing
services.
also
provides
comprehensive
analysis
existing
state-of-the-art
libraries
tools,
implemented
software
hardware,
performance
thereof.
IACR Communications in Cryptology,
Journal Year:
2025,
Volume and Issue:
1(4)
Published: Jan. 13, 2025
Fully
Homomorphic
Encryption
(FHE)
is
a
cryptographic
primitive
that
allows
performing
arbitrary
operations
on
encrypted
data.
Since
the
conception
of
idea
in
[RAD78],
it
has
been
considered
holy
grail
cryptography.
After
first
construction
2009
[Gen09],
evolved
to
become
practical
with
strong
security
guarantees.
Most
modern
constructions
are
based
well-known
lattice
problems
such
as
Learning
With
Errors
(LWE).
Besides
its
academic
appeal,
recent
years
FHE
also
attracted
significant
attention
from
industry,
thanks
applicability
considerable
number
real-world
use-cases.
An
upcoming
standardization
effort
by
ISO/IEC
aims
support
wider
adoption
these
techniques.
However,
one
main
challenges
standards
bodies,
developers,
and
end
users
usually
encounter
establishing
parameters.
This
particularly
hard
case
because
parameters
not
only
related
level
system,
but
type
system
able
handle.
In
this
paper
we
provide
examples
parameter
sets
for
LWE
targeting
particular
levels,
can
be
used
context
constructions.
We
give
complete
sets,
including
relevant
correctness
performance,
alongside
those
security.
As
an
additional
contribution,
survey
selection
offered
open-source
libraries.
Computing
on
encrypted
data
is
a
promising
approach
to
reduce
security
and
privacy
risks,
with
homomorphic
encryption
serving
as
facilitator
in
achieving
this
goal.
In
work,
we
accelerate
operations
using
the
Processing-in-Memory
(PIM)
paradigm
mitigate
large
memory
capacity
frequent
movement
requirements.
Using
real-world
PIM
system,
Brakerski-Fan-Vercauteren
(BFV)
scheme
for
addition
multiplication.
We
evaluate
implementations
of
these
statistical
workloads
(arithmetic
mean,
variance,
linear
regression)
compare
CPU
GPU
implementations.
Our
results
demonstrate
50
–
100×
speedup
real
system
(UPMEM)
over
2
15×
vector
addition.
For
multiplication,
outperforms
by
40
50×.
However,
it
lags
10
behind
due
lack
native
sufficiently
wide
multiplication
support
evaluated
first-generation
system.
regression,
performance
improvements
vary
between
30×
300×
10×
GPU,
uncovering
trade-offs
terms
scalability
varying
amounts
data.
plan
make
our
implementation
open-source
future.
This
paper
comprehensively
addresses
homomorphic
encryption
from
both
theoretical
and
practical
perspectives.
The
delves
into
the
mathematical
foundations
required
to
understand
fully
FHE.
It
consequently
covers
design
fundamentals
security
properties
of
FHE,
describes
main
FHE
schemes
based
on
various
problems.
On
a
more
level,
presents
view
privacy-preserving
Machine
Learning
using
encryption,
then
surveys
at
length
an
engineering
angle,
covering
potential
application
in
fog
computing,
cloud
computing
services.
also
provides
comprehensive
analysis
existing
state-of-the-art
libraries
tools,
implemented
software
hardware,
performance
thereof.
With
the
popularization
of
cloud
computing
model,
outsourcing
data
storage
and
services
has
become
an
indispensable
trend,
which
lead
to
related
security
privacy
protection
issues
that
have
attracted
extensive
attention
in
industry.
Fully
homomorphic
encryption,
as
encryption
technology
can
process
ciphertext
information
without
exposing
plaintext
information,
natural
user
characteristics.
Meanwhile,
excellent
quantum-resistant
performance
properties
lattice
ciphers
made
lattice-based
schemes
a
much-attend
research
hotspot
field
cryptography
recent
years.
In
this
paper
we
mainly
introduce
status
all-pass
several
typical
references
for
all-homomorphic
cryptography.
