<s>
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
key	I-Protocol
exchange	I-Protocol
is	O
a	O
mathematical	O
method	B-Protocol
of	O
securely	O
exchanging	O
cryptographic	O
keys	O
over	O
a	O
public	O
channel	O
and	O
was	O
one	O
of	O
the	O
first	O
public-key	B-Application
protocols	I-Application
as	O
conceived	O
by	O
Ralph	O
Merkle	O
and	O
named	O
after	O
Whitfield	O
Diffie	O
and	O
Martin	O
Hellman	O
.	O
</s>
<s>
DH	O
is	O
one	O
of	O
the	O
earliest	O
practical	O
examples	O
of	O
public	B-Application
key	I-Application
exchange	O
implemented	O
within	O
the	O
field	O
of	O
cryptography	O
.	O
</s>
<s>
Published	O
in	O
1976	O
by	O
Diffie	O
and	O
Hellman	O
,	O
this	O
is	O
the	O
earliest	O
publicly	O
known	O
work	O
that	O
proposed	O
the	O
idea	O
of	O
a	O
private	B-Application
key	I-Application
and	O
a	O
corresponding	O
public	B-Application
key	I-Application
.	O
</s>
<s>
Traditionally	O
,	O
secure	O
encrypted	O
communication	O
between	O
two	O
parties	O
required	O
that	O
they	O
first	O
exchange	O
keys	O
by	O
some	O
secure	O
physical	O
means	O
,	O
such	O
as	O
paper	O
key	O
lists	O
transported	O
by	O
a	O
trusted	O
courier	B-Protocol
.	O
</s>
<s>
The	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
key	I-Protocol
exchange	I-Protocol
method	B-Protocol
allows	O
two	O
parties	O
that	O
have	O
no	O
prior	O
knowledge	O
of	O
each	O
other	O
to	O
jointly	O
establish	O
a	O
shared	O
secret	O
key	O
over	O
an	O
insecure	O
channel	O
.	O
</s>
<s>
This	O
key	O
can	O
then	O
be	O
used	O
to	O
encrypt	O
subsequent	O
communications	O
using	O
a	O
symmetric-key	B-Algorithm
cipher	I-Algorithm
.	O
</s>
<s>
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
is	O
used	O
to	O
secure	O
a	O
variety	O
of	O
Internet	O
services	O
.	O
</s>
<s>
The	O
scheme	O
was	O
published	O
by	O
Whitfield	O
Diffie	O
and	O
Martin	O
Hellman	O
in	O
1976	O
,	O
but	O
in	O
1997	O
it	O
was	O
revealed	O
that	O
James	O
H	O
.	O
Ellis	O
,	O
Clifford	O
Cocks	O
,	O
and	O
Malcolm	O
J	O
.	O
Williamson	O
of	O
GCHQ	O
,	O
the	O
British	O
signals	O
intelligence	O
agency	O
,	O
had	O
previously	O
shown	O
in	O
1969	O
how	O
public-key	B-Application
cryptography	I-Application
could	O
be	O
achieved	O
.	O
</s>
<s>
Although	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
key	B-Protocol
agreement	I-Protocol
itself	O
is	O
a	O
non-authenticated	O
key-agreement	B-Protocol
protocol	I-Protocol
,	O
it	O
provides	O
the	O
basis	O
for	O
a	O
variety	O
of	O
authenticated	O
protocols	O
,	O
and	O
is	O
used	O
to	O
provide	O
forward	O
secrecy	O
in	O
Transport	B-Protocol
Layer	I-Protocol
Security	I-Protocol
's	O
ephemeral	B-General_Concept
modes	O
(	O
referred	O
to	O
as	O
EDH	O
or	O
DHE	O
depending	O
on	O
the	O
cipher	B-Protocol
suite	I-Protocol
)	O
.	O
</s>
<s>
The	O
method	B-Protocol
was	O
followed	O
shortly	O
afterwards	O
by	O
RSA	B-Architecture
,	O
an	O
implementation	O
of	O
public-key	B-Application
cryptography	I-Application
using	O
asymmetric	B-Application
algorithms	I-Application
.	O
</s>
<s>
In	O
2002	O
,	O
Hellman	O
suggested	O
the	O
algorithm	O
be	O
called	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
–	I-Protocol
Merkle	I-Protocol
key	I-Protocol
exchange	I-Protocol
in	O
recognition	O
of	O
Ralph	O
Merkle	O
's	O
contribution	O
to	O
the	O
invention	O
of	O
public-key	B-Application
cryptography	I-Application
(	O
Hellman	O
,	O
2002	O
)	O
,	O
writing	O
:	O
</s>
<s>
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
key	I-Protocol
exchange	I-Protocol
establishes	O
a	O
shared	O
secret	O
between	O
two	O
parties	O
that	O
can	O
be	O
used	O
for	O
secret	O
communication	O
for	O
exchanging	O
data	O
over	O
a	O
public	O
network	O
.	O
</s>
<s>
An	O
analogy	O
illustrates	O
the	O
concept	O
of	O
public	B-Application
key	I-Application
exchange	O
by	O
using	O
colors	O
instead	O
of	O
very	O
large	O
numbers	O
:	O
</s>
<s>
It	O
is	O
impossible	O
to	O
compute	O
in	O
a	O
practical	O
amount	O
of	O
time	O
even	O
for	O
modern	O
supercomputers	B-Architecture
.	O
</s>
<s>
a	O
=	O
Alice	O
's	O
private	B-Application
key	I-Application
,	O
known	O
only	O
to	O
Alice	O
.	O
</s>
<s>
b	O
=	O
Bob	O
's	O
private	B-Application
key	I-Application
known	O
only	O
to	O
Bob	O
.	O
</s>
<s>
A	O
=	O
Alice	O
's	O
public	B-Application
key	I-Application
,	O
known	O
to	O
Alice	O
,	O
Bob	O
,	O
and	O
Eve	O
.	O
</s>
<s>
B	O
=	O
Bob	O
's	O
public	B-Application
key	I-Application
,	O
known	O
to	O
Alice	O
,	O
Bob	O
,	O
and	O
Eve	O
.	O
</s>
<s>
Note	O
:	O
It	O
should	O
be	O
difficult	O
for	O
Alice	O
to	O
solve	O
for	O
Bob	O
's	O
private	B-Application
key	I-Application
or	O
for	O
Bob	O
to	O
solve	O
for	O
Alice	O
's	O
private	B-Application
key	I-Application
.	O
</s>
<s>
If	O
it	O
is	O
not	O
difficult	O
for	O
Alice	O
to	O
solve	O
for	O
Bob	O
's	O
private	B-Application
key	I-Application
(	O
or	O
vice	O
versa	O
)	O
,	O
Eve	O
may	O
simply	O
substitute	O
her	O
own	O
private	O
/	O
public	B-Application
key	I-Application
pair	I-Application
,	O
plug	O
Bob	O
's	O
public	B-Application
key	I-Application
into	O
her	O
private	B-Application
key	I-Application
,	O
produce	O
a	O
fake	O
shared	O
secret	O
key	O
,	O
and	O
solve	O
for	O
Bob	O
's	O
private	B-Application
key	I-Application
(	O
and	O
use	O
that	O
to	O
solve	O
for	O
the	O
shared	O
secret	O
key	O
.	O
</s>
<s>
Eve	O
may	O
attempt	O
to	O
choose	O
a	O
public	O
/	O
private	B-Application
key	I-Application
pair	O
that	O
will	O
make	O
it	O
easy	O
for	O
her	O
to	O
solve	O
for	O
Bob	O
's	O
private	B-Application
key	I-Application
)	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
elliptic	B-Protocol
curve	I-Protocol
Diffie	I-Protocol
–	I-Protocol
Hellman	I-Protocol
protocol	O
is	O
a	O
variant	O
that	O
represents	O
an	O
element	O
of	O
G	O
as	O
a	O
point	O
on	O
an	O
elliptic	O
curve	O
instead	O
of	O
as	O
an	O
integer	O
modulo	O
n.Variants	O
using	O
hyperelliptic	O
curves	O
have	O
also	O
been	O
proposed	O
.	O
</s>
<s>
The	O
supersingular	B-Algorithm
isogeny	I-Algorithm
key	I-Algorithm
exchange	I-Algorithm
is	O
a	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
variant	O
that	O
was	O
designed	O
to	O
be	O
secure	O
against	O
quantum	B-Architecture
computers	I-Architecture
,	O
but	O
it	O
was	O
broken	O
in	O
July	O
2022	O
.	O
</s>
<s>
The	O
used	O
keys	O
can	O
either	O
be	O
ephemeral	B-General_Concept
or	O
static	O
(	O
long	O
term	O
)	O
key	O
,	O
but	O
could	O
even	O
be	O
mixed	O
,	O
so	O
called	O
semi-static	O
DH	O
.	O
</s>
<s>
ephemeral	B-General_Concept
,	O
ephemeral	B-General_Concept
:	O
Usually	O
used	O
for	O
key	B-Protocol
agreement	I-Protocol
.	O
</s>
<s>
ephemeral	B-General_Concept
,	O
static	O
:	O
For	O
example	O
used	O
in	O
ElGamal	B-Algorithm
encryption	I-Algorithm
or	O
Integrated	B-Protocol
Encryption	I-Protocol
Scheme	I-Protocol
(	O
IES	O
)	O
.	O
</s>
<s>
If	O
used	O
in	O
key	B-Protocol
agreement	I-Protocol
it	O
could	O
provide	O
implicit	O
one-sided	O
authenticity	O
(	O
the	O
ephemeral	B-General_Concept
side	O
could	O
verify	O
the	O
authenticity	O
of	O
the	O
static	O
side	O
)	O
.	O
</s>
<s>
It	O
is	O
possible	O
to	O
use	O
ephemeral	B-General_Concept
and	O
static	O
keys	O
in	O
one	O
key	B-Protocol
agreement	I-Protocol
to	O
provide	O
more	O
security	O
as	O
for	O
example	O
shown	O
in	O
NIST	O
SP	O
800-56A	O
,	O
but	O
it	O
is	O
also	O
possible	O
to	O
combine	O
those	O
in	O
a	O
single	O
DH	B-Protocol
key	I-Protocol
exchange	I-Protocol
,	O
which	O
is	O
then	O
called	O
triple	O
DH	O
(	O
3-DH	O
)	O
.	O
</s>
<s>
In	O
1997	O
a	O
kind	O
of	O
triple	O
DH	O
was	O
proposed	O
by	O
Simon	O
Blake-Wilson	O
,	O
Don	O
Johnson	O
,	O
Alfred	O
Menezes	O
in	O
"	O
Key	B-Protocol
Agreement	I-Protocol
Protocols	I-Protocol
and	O
their	O
Security	O
Analysis	O
(	O
1997	O
)	O
"	O
,	O
which	O
was	O
improved	O
by	O
C	O
.	O
Kudla	O
and	O
K	O
.	O
G	O
.	O
Paterson	O
in	O
“	O
Modular	O
Security	O
Proofs	O
for	O
Key	B-Protocol
Agreement	I-Protocol
Protocols	I-Protocol
(	O
2005	O
)	O
”	O
and	O
shown	O
to	O
be	O
secure	O
.	O
</s>
<s>
The	O
long	O
term	O
secret	O
keys	O
of	O
Alice	O
and	O
Bob	O
are	O
denoted	O
by	O
a	O
and	O
b	O
respectively	O
,	O
with	O
public	B-Application
keys	I-Application
A	O
and	O
B	O
,	O
as	O
well	O
as	O
the	O
ephemeral	B-General_Concept
key	I-General_Concept
pairs	O
x	O
,	O
X	O
and	O
y	O
,	O
Y	O
.	O
</s>
<s>
The	O
long	O
term	O
public	B-Application
keys	I-Application
need	O
to	O
be	O
transferred	O
somehow	O
.	O
</s>
<s>
That	O
can	O
be	O
done	O
beforehand	O
in	O
a	O
separate	O
,	O
trusted	O
channel	O
,	O
or	O
the	O
public	B-Application
keys	I-Application
can	O
be	O
encrypted	O
using	O
some	O
partial	O
key	B-Protocol
agreement	I-Protocol
to	O
preserve	O
anonymity	O
.	O
</s>
<s>
For	O
more	O
of	O
such	O
details	O
as	O
well	O
as	O
other	O
improvements	O
like	O
side	O
channel	O
protection	O
or	O
explicit	O
key	O
confirmation	O
,	O
as	O
well	O
as	O
early	O
messages	O
and	O
additional	O
password	B-Protocol
authentication	I-Protocol
,	O
one	O
could	O
e.g.	O
</s>
<s>
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
key	B-Protocol
agreement	I-Protocol
is	O
not	O
limited	O
to	O
negotiating	O
a	O
key	O
shared	O
by	O
only	O
two	O
participants	O
.	O
</s>
<s>
For	O
example	O
,	O
Alice	O
,	O
Bob	O
,	O
and	O
Carol	O
could	O
participate	O
in	O
a	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
agreement	O
as	O
follows	O
,	O
with	O
all	O
operations	O
taken	O
to	O
be	O
modulo	O
p	O
:	O
</s>
<s>
The	O
parties	O
generate	O
their	O
private	B-Application
keys	I-Application
,	O
named	O
a	O
,	O
b	O
,	O
and	O
c	O
.	O
</s>
<s>
Starting	O
with	O
an	O
"	O
empty	O
"	O
key	O
consisting	O
only	O
of	O
g	O
,	O
the	O
secret	O
is	O
made	O
by	O
raising	O
the	O
current	O
value	O
to	O
every	O
participant	O
's	O
private	O
exponent	O
once	O
,	O
in	O
any	O
order	O
(	O
the	O
first	O
such	O
exponentiation	O
yields	O
the	O
participant	O
's	O
own	O
public	B-Application
key	I-Application
)	O
.	O
</s>
<s>
Thus	O
,	O
each	O
user	O
must	O
obtain	O
their	O
copy	O
of	O
the	O
secret	O
by	O
applying	O
their	O
own	O
private	B-Application
key	I-Application
last	O
(	O
otherwise	O
there	O
would	O
be	O
no	O
way	O
for	O
the	O
last	O
contributor	O
to	O
communicate	O
the	O
final	O
key	O
to	O
its	O
recipient	O
,	O
as	O
that	O
last	O
contributor	O
would	O
have	O
turned	O
the	O
key	O
into	O
the	O
very	O
secret	O
the	O
group	O
wished	O
to	O
protect	O
)	O
.	O
</s>
<s>
By	O
choosing	O
a	O
more	O
optimal	O
order	O
,	O
and	O
relying	O
on	O
the	O
fact	O
that	O
keys	O
can	O
be	O
duplicated	O
,	O
it	O
is	O
possible	O
to	O
reduce	O
the	O
number	O
of	O
modular	O
exponentiations	O
performed	O
by	O
each	O
participant	O
to	O
using	O
a	O
divide-and-conquer-style	B-Algorithm
approach	O
,	O
given	O
here	O
for	O
eight	O
participants	O
:	O
</s>
<s>
The	O
eavesdropper	O
has	O
to	O
solve	O
the	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
problem	O
to	O
obtain	O
gab	O
.	O
</s>
<s>
An	O
efficient	O
algorithm	O
to	O
solve	O
the	O
discrete	O
logarithm	O
problem	O
would	O
make	O
it	O
easy	O
to	O
compute	O
a	O
or	O
b	O
and	O
solve	O
the	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
problem	O
,	O
making	O
this	O
and	O
many	O
other	O
public	B-Application
key	I-Application
cryptosystems	I-Application
insecure	O
.	O
</s>
<s>
A	O
protocol	O
using	O
such	O
a	O
choice	O
is	O
for	O
example	O
IKEv2	B-Protocol
.	O
</s>
<s>
In	O
the	O
original	O
description	O
,	O
the	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
exchange	O
by	O
itself	O
does	O
not	O
provide	O
authentication	O
of	O
the	O
communicating	O
parties	O
and	O
is	O
thus	O
vulnerable	O
to	O
a	O
man-in-the-middle	O
attack	O
.	O
</s>
<s>
In	O
most	O
cases	O
it	O
will	O
not	O
help	O
them	O
get	O
Mallory	O
's	O
private	B-Application
key	I-Application
,	O
even	O
if	O
she	O
used	O
the	O
same	O
key	O
for	O
both	O
exchanges	O
.	O
</s>
<s>
A	O
method	B-Protocol
to	O
authenticate	O
the	O
communicating	O
parties	O
to	O
each	O
other	O
is	O
generally	O
needed	O
to	O
prevent	O
this	O
type	O
of	O
attack	O
.	O
</s>
<s>
Variants	O
of	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
,	O
such	O
as	O
STS	B-Protocol
protocol	I-Protocol
,	O
may	O
be	O
used	O
instead	O
to	O
avoid	O
these	O
types	O
of	O
attacks	O
.	O
</s>
<s>
The	O
number	B-Algorithm
field	I-Algorithm
sieve	I-Algorithm
algorithm	O
,	O
which	O
is	O
generally	O
the	O
most	O
effective	O
in	O
solving	O
the	O
discrete	O
logarithm	O
problem	O
,	O
consists	O
of	O
four	O
computational	O
steps	O
.	O
</s>
<s>
By	O
precomputing	O
the	O
first	O
three	O
steps	O
of	O
the	O
number	B-Algorithm
field	I-Algorithm
sieve	I-Algorithm
for	O
the	O
most	O
common	O
groups	O
,	O
an	O
attacker	O
need	O
only	O
carry	O
out	O
the	O
last	O
step	O
,	O
which	O
is	O
much	O
less	O
computationally	O
expensive	O
than	O
the	O
first	O
three	O
steps	O
,	O
to	O
obtain	O
a	O
specific	O
logarithm	O
.	O
</s>
<s>
The	O
Logjam	B-Protocol
attack	I-Protocol
used	O
this	O
vulnerability	O
to	O
compromise	O
a	O
variety	O
of	O
Internet	O
services	O
that	O
allowed	O
the	O
use	O
of	O
groups	O
whose	O
order	O
was	O
a	O
512-bit	O
prime	O
number	O
,	O
so	O
called	O
export	O
grade	O
.	O
</s>
<s>
As	O
estimated	O
by	O
the	O
authors	O
behind	O
the	O
Logjam	B-Protocol
attack	I-Protocol
,	O
the	O
much	O
more	O
difficult	O
precomputation	O
needed	O
to	O
solve	O
the	O
discrete	O
log	O
problem	O
for	O
a	O
1024-bit	O
prime	O
would	O
cost	O
on	O
the	O
order	O
of	O
$100	O
million	O
,	O
well	O
within	O
the	O
budget	O
of	O
a	O
large	O
national	O
intelligence	O
agency	O
such	O
as	O
the	O
U.S.	O
National	O
Security	O
Agency	O
(	O
NSA	O
)	O
.	O
</s>
<s>
The	O
Logjam	B-Protocol
authors	O
speculate	O
that	O
precomputation	O
against	O
widely	O
reused	O
1024-bit	O
DH	O
primes	O
is	O
behind	O
claims	O
in	O
leaked	O
NSA	O
documents	O
that	O
NSA	O
is	O
able	O
to	O
break	O
much	O
of	O
current	O
cryptography	O
.	O
</s>
<s>
To	O
avoid	O
these	O
vulnerabilities	O
,	O
the	O
Logjam	B-Protocol
authors	O
recommend	O
use	O
of	O
elliptic	O
curve	O
cryptography	O
,	O
for	O
which	O
no	O
similar	O
attack	O
is	O
known	O
.	O
</s>
<s>
Failing	O
that	O
,	O
they	O
recommend	O
that	O
the	O
order	O
,	O
p	O
,	O
of	O
the	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
group	O
should	O
be	O
at	O
least	O
2048bits	O
.	O
</s>
<s>
Public	B-Application
key	I-Application
encryption	I-Application
schemes	O
based	O
on	O
the	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
key	I-Protocol
exchange	I-Protocol
have	O
been	O
proposed	O
.	O
</s>
<s>
The	O
first	O
such	O
scheme	O
is	O
the	O
ElGamal	B-Algorithm
encryption	I-Algorithm
.	O
</s>
<s>
A	O
more	O
modern	O
variant	O
is	O
the	O
Integrated	B-Protocol
Encryption	I-Protocol
Scheme	I-Protocol
.	O
</s>
<s>
Protocols	O
that	O
achieve	O
forward	O
secrecy	O
generate	O
new	O
key	B-Application
pairs	I-Application
for	O
each	O
session	B-Protocol
and	O
discard	O
them	O
at	O
the	O
end	O
of	O
the	O
session	B-Protocol
.	O
</s>
<s>
The	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
key	I-Protocol
exchange	I-Protocol
is	O
a	O
frequent	O
choice	O
for	O
such	O
protocols	O
,	O
because	O
of	O
its	O
fast	O
key	O
generation	O
.	O
</s>
<s>
When	O
Alice	O
and	O
Bob	O
share	O
a	O
password	O
,	O
they	O
may	O
use	O
a	O
password-authenticated	B-Protocol
key	I-Protocol
agreement	I-Protocol
(	O
PK	O
)	O
form	O
of	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
to	O
prevent	O
man-in-the-middle	O
attacks	O
.	O
</s>
<s>
One	O
simple	O
scheme	O
is	O
to	O
compare	O
the	O
hash	B-Algorithm
of	O
s	O
concatenated	O
with	O
the	O
password	O
calculated	O
independently	O
on	O
both	O
ends	O
of	O
channel	O
.	O
</s>
<s>
This	O
approach	O
is	O
described	O
in	O
ITU-T	O
Recommendation	O
X.1035	B-Protocol
,	O
which	O
is	O
used	O
by	O
the	O
G.hn	B-General_Concept
home	O
networking	O
standard	O
.	O
</s>
<s>
An	O
example	O
of	O
such	O
a	O
protocol	O
is	O
the	O
Secure	B-Protocol
Remote	I-Protocol
Password	I-Protocol
protocol	I-Protocol
.	O
</s>
<s>
It	O
is	O
also	O
possible	O
to	O
use	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
as	O
part	O
of	O
a	O
public	B-Architecture
key	I-Architecture
infrastructure	I-Architecture
,	O
allowing	O
Bob	O
to	O
encrypt	O
a	O
message	O
so	O
that	O
only	O
Alice	O
will	O
be	O
able	O
to	O
decrypt	O
it	O
,	O
with	O
no	O
prior	O
communication	O
between	O
them	O
other	O
than	O
Bob	O
having	O
trusted	O
knowledge	O
of	O
Alice	O
's	O
public	B-Application
key	I-Application
.	O
</s>
<s>
Alice	O
's	O
public	B-Application
key	I-Application
is	O
.	O
</s>
<s>
To	O
send	O
her	O
a	O
message	O
,	O
Bob	O
chooses	O
a	O
random	O
b	O
and	O
then	O
sends	O
Alice	O
(	O
unencrypted	O
)	O
together	O
with	O
the	O
message	O
encrypted	O
with	O
symmetric	B-Algorithm
key	I-Algorithm
.	O
</s>
<s>
Only	O
Alice	O
can	O
determine	O
the	O
symmetric	B-Algorithm
key	I-Algorithm
and	O
hence	O
decrypt	O
the	O
message	O
because	O
only	O
she	O
has	O
a	O
(	O
the	O
private	B-Application
key	I-Application
)	O
.	O
</s>
<s>
A	O
pre-shared	O
public	B-Application
key	I-Application
also	O
prevents	O
man-in-the-middle	O
attacks	O
.	O
</s>
<s>
In	O
practice	O
,	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
is	O
not	O
used	O
in	O
this	O
way	O
,	O
with	O
RSA	B-Architecture
being	O
the	O
dominant	O
public	B-Application
key	I-Application
algorithm	I-Application
.	O
</s>
<s>
This	O
is	O
largely	O
for	O
historical	O
and	O
commercial	O
reasons	O
,	O
namely	O
that	O
RSA	B-Architecture
Security	O
created	O
a	O
certificate	O
authority	O
for	O
key	O
signing	O
that	O
became	O
Verisign	B-Application
.	O
</s>
<s>
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
,	O
as	O
elaborated	O
above	O
,	O
cannot	O
directly	O
be	O
used	O
to	O
sign	O
certificates	O
.	O
</s>
<s>
However	O
,	O
the	O
ElGamal	B-Algorithm
and	O
DSA	O
signature	O
algorithms	O
are	O
mathematically	O
related	O
to	O
it	O
,	O
as	O
well	O
as	O
MQV	B-Protocol
,	O
STS	B-Protocol
and	O
the	O
IKE	B-Protocol
component	O
of	O
the	O
IPsec	B-Protocol
protocol	O
suite	O
for	O
securing	O
Internet	B-Protocol
Protocol	I-Protocol
communications	O
.	O
</s>
