<s>
Kyber	B-Algorithm
is	O
a	O
key	B-Algorithm
encapsulation	I-Algorithm
method	O
(	O
KEM	O
)	O
designed	O
to	O
be	O
resistant	O
to	O
cryptanalytic	O
attacks	O
with	O
future	O
powerful	O
quantum	B-Architecture
computers	I-Architecture
.	O
</s>
<s>
This	O
asymmetric	B-Application
cryptosystem	I-Application
uses	O
a	O
variant	O
of	O
the	O
learning	B-General_Concept
with	I-General_Concept
errors	I-General_Concept
lattice	O
problem	O
as	O
its	O
basic	O
trapdoor	O
function	O
.	O
</s>
<s>
Kyber	B-Algorithm
is	O
named	O
after	O
the	O
fictional	O
kyber	B-Algorithm
crystals	O
used	O
to	O
power	O
lightsabers	O
in	O
the	O
Star	B-Application
Wars	I-Application
universe	O
(	O
compare	O
[Light-]SABER	O
)	O
.	O
</s>
<s>
The	O
system	O
is	O
based	O
on	O
module	O
learning	B-General_Concept
with	I-General_Concept
errors	I-General_Concept
(	O
M-LWE	O
)	O
from	O
the	O
field	O
of	O
machine	O
learning	O
,	O
in	O
conjunction	O
with	O
cyclotomic	O
rings	O
.	O
</s>
<s>
in	O
regard	O
to	O
runtime	B-Library
as	O
well	O
as	O
the	O
size	O
of	O
the	O
ciphertexts	O
and	O
the	O
key	O
material	O
.	O
</s>
<s>
At	O
a	O
complexity	O
of	O
161	O
bits	O
,	O
the	O
secret	O
keys	O
are	O
2400	O
,	O
the	O
public	B-Application
keys	I-Application
1088	O
,	O
and	O
the	O
ciphertexts	O
1184	O
bytes	O
in	O
size	O
.	O
</s>
<s>
For	O
a	O
chat	B-Protocol
encryption	O
scenario	O
using	O
liboqs	O
,	O
replacing	O
the	O
extremely	O
efficient	O
,	O
non-quantum-safe	O
ECDH	B-Protocol
key	O
exchange	O
using	O
Curve25519	O
was	O
found	O
to	O
increase	O
runtime	B-Library
by	O
a	O
factor	O
of	O
about	O
2.3	O
(	O
1.5	O
–	O
7	O
)	O
,	O
an	O
estimated	O
2.3-fold	O
(	O
1.4	O
–	O
3.1	O
)	O
increase	O
in	O
energy	O
consumption	O
,	O
and	O
have	O
about	O
70	O
times	O
(	O
48	O
–	O
92	O
)	O
more	O
data	O
overhead	O
.	O
</s>
<s>
Internal	O
hashing	B-Algorithm
operations	O
account	O
for	O
the	O
majority	O
of	O
the	O
runtime	B-Library
,	O
which	O
would	O
thus	O
potentially	O
benefit	O
greatly	O
from	O
corresponding	O
hardware	B-General_Concept
acceleration	I-General_Concept
.	O
</s>
<s>
Kyber	B-Algorithm
is	O
derived	O
from	O
a	O
method	O
published	O
in	O
2005	O
by	O
Oded	O
Regev	O
,	O
developed	O
by	O
developers	O
from	O
Europe	O
and	O
North	O
America	O
,	O
who	O
are	O
employed	O
by	O
various	O
government	O
universities	O
or	O
research	O
institutions	O
,	O
or	O
by	O
private	O
companies	O
,	O
with	O
funding	O
from	O
the	O
European	O
Commission	O
,	O
Switzerland	O
,	O
the	O
Netherlands	O
,	O
and	O
Germany	O
.	O
</s>
<s>
Like	O
other	O
PQC-KEM	O
methods	O
,	O
Kyber	B-Algorithm
makes	O
extensive	O
use	O
of	O
hashing	B-Algorithm
internally	O
.	O
</s>
<s>
In	O
Kyber	B-Algorithm
's	O
case	O
,	O
variants	O
of	O
Keccak	B-Algorithm
(	O
SHA-3/SHAKE	O
)	O
are	O
used	O
here	O
,	O
to	O
generate	B-Algorithm
pseudorandom	I-Algorithm
numbers	I-Algorithm
,	O
among	O
other	O
things	O
.	O
</s>
<s>
It	O
is	O
the	O
only	O
key	B-Algorithm
encapsulation	I-Algorithm
mechanism	I-Algorithm
that	O
has	O
been	O
selected	O
for	O
standardization	O
at	O
the	O
end	O
of	O
the	O
third	O
round	O
of	O
the	O
NIST	O
standardization	O
process	O
.	O
</s>
<s>
In	O
the	O
second	O
phase	O
of	O
the	O
selection	O
process	O
,	O
several	O
parameters	O
of	O
the	O
algorithm	O
were	O
adjusted	O
and	O
the	O
compression	O
of	O
the	O
public	B-Application
keys	I-Application
was	O
dropped	O
.	O
</s>
<s>
Most	O
recently	O
,	O
NIST	O
paid	O
particular	O
attention	O
to	O
costs	O
in	O
terms	O
of	O
runtime	B-Library
and	O
complexity	O
for	O
implementations	O
that	O
mask	O
runtimes	B-Library
in	O
order	O
to	O
prevent	O
corresponding	O
side-channel	O
attacks	O
(	O
SCA	O
)	O
.	O
</s>
<s>
During	O
the	O
NIST	O
standardization	O
process	O
,	O
Kyber	B-Algorithm
has	O
undergone	O
changes	O
.	O
</s>
<s>
In	O
particular	O
,	O
in	O
the	O
submission	O
for	O
round	O
2	O
(	O
so	O
called	O
Kyber	B-Algorithm
v2	O
)	O
,	O
the	O
following	O
features	O
have	O
been	O
changed	O
:	O
</s>
<s>
public	B-Application
key	I-Application
compression	O
removed	O
(	O
due	O
to	O
NIST	O
comments	O
on	O
the	O
security	O
proof	O
)	O
;	O
</s>
<s>
public	B-Application
key	I-Application
representation	O
is	O
changed	O
to	O
NTT	O
domain	O
in	O
order	O
to	O
save	O
the	O
NTT	O
operations	O
.	O
</s>
<s>
The	O
developers	O
have	O
released	O
a	O
reference	O
implementation	O
into	O
the	O
public	O
domain	O
(	O
or	O
under	O
CC0	O
)	O
,	O
which	O
is	O
written	O
in	O
C	B-Language
.	O
The	O
program	B-Library
library	I-Library
liboqs	O
of	O
the	O
Open	O
Quantum	O
Safe	O
(	O
OQS	O
)	O
project	O
contains	O
an	O
implementation	O
based	O
on	O
that	O
.	O
</s>
<s>
OQS	O
also	O
maintains	O
a	O
quantum-safe	O
development	O
branch	O
of	O
OpenSSL	B-Language
,	O
has	O
integrated	O
it	O
into	O
BoringSSL	B-Protocol
,	O
and	O
its	O
code	O
has	O
also	O
been	O
integrated	O
into	O
WolfSSL	B-Protocol
.	O
</s>
<s>
The	O
German	O
Federal	O
Office	O
for	O
Information	O
Security	O
is	O
aiming	O
for	O
implementation	O
in	O
Thunderbird	B-Application
,	O
and	O
in	O
this	O
context	O
also	O
an	O
implementation	O
in	O
the	O
Botan	B-Protocol
program	B-Library
library	I-Library
and	O
corresponding	O
adjustments	O
to	O
the	O
OpenPGP	O
standard	O
.	O
</s>
