<s>
In	O
cryptography	O
,	O
a	O
password-authenticated	B-Protocol
key	I-Protocol
agreement	I-Protocol
method	O
is	O
an	O
interactive	O
method	O
for	O
two	O
or	O
more	O
parties	O
to	O
establish	O
cryptographic	O
keys	O
based	O
on	O
one	O
or	O
more	O
party	O
's	O
knowledge	O
of	O
a	O
password	O
.	O
</s>
<s>
Password-authenticated	B-Protocol
key	I-Protocol
agreement	I-Protocol
generally	O
encompasses	O
methods	O
such	O
as	O
:	O
</s>
<s>
Password-authenticated	B-Protocol
key	I-Protocol
exchange	I-Protocol
(	O
PAKE	B-Protocol
)	O
is	O
a	O
method	O
in	O
which	O
two	O
or	O
more	O
parties	O
,	O
based	O
only	O
on	O
their	O
knowledge	O
of	O
a	O
shared	O
password	O
,	O
establish	O
a	O
cryptographic	O
key	O
using	O
an	O
exchange	O
of	O
messages	O
,	O
such	O
that	O
an	O
unauthorized	O
party	O
(	O
one	O
who	O
controls	O
the	O
communication	O
channel	O
but	O
does	O
not	O
possess	O
the	O
password	O
)	O
cannot	O
participate	O
in	O
the	O
method	O
and	O
is	O
constrained	O
as	O
much	O
as	O
possible	O
from	O
brute-force	O
guessing	O
the	O
password	O
.	O
</s>
<s>
Two	O
forms	O
of	O
PAKE	B-Protocol
are	O
balanced	O
and	O
augmented	O
methods	O
.	O
</s>
<s>
Balanced	O
PAKE	B-Protocol
assumes	O
the	O
two	O
parties	O
in	O
either	O
a	O
client-client	O
or	O
client-server	O
situation	O
use	O
the	O
same	O
secret	O
password	O
to	O
negotiate	O
and	O
authenticate	O
a	O
shared	O
key	O
.	O
</s>
<s>
Elliptic	O
Curve	O
based	O
Secure	B-Protocol
Remote	I-Protocol
Password	I-Protocol
protocol	I-Protocol
(	O
EC-SRP	O
or	O
SRP5	O
)	O
There	O
is	O
a	O
free	O
Java	O
card	O
implementation	O
.	O
</s>
<s>
Augmented	O
PAKE	B-Protocol
is	O
a	O
variation	O
applicable	O
to	O
client/server	O
scenarios	O
,	O
in	O
which	O
the	O
server	O
does	O
not	O
store	O
password-equivalent	O
data	O
.	O
</s>
<s>
Some	O
augmented	O
PAKE	B-Protocol
systems	O
use	O
an	O
oblivious	O
pseudorandom	O
function	O
to	O
mix	O
the	O
user	O
's	O
secret	O
password	O
with	O
the	O
server	O
's	O
secret	O
salt	O
value	O
,	O
so	O
that	O
the	O
user	O
never	O
learns	O
the	O
server	O
's	O
secret	O
salt	O
value	O
and	O
the	O
server	O
never	O
learns	O
the	O
user	O
's	O
password	O
(	O
or	O
password-equivalent	O
value	O
)	O
or	O
the	O
final	O
key	O
.	O
</s>
<s>
The	O
first	O
successful	O
password-authenticated	B-Protocol
key	I-Protocol
agreement	I-Protocol
methods	O
were	O
Encrypted	B-Protocol
Key	I-Protocol
Exchange	I-Protocol
methods	O
described	O
by	O
Steven	O
M	O
.	O
Bellovin	O
and	O
Michael	O
Merritt	O
in	O
1992	O
.	O
</s>
<s>
The	O
first	O
provably-secure	O
PAKE	B-Protocol
protocols	O
were	O
given	O
in	O
work	O
by	O
M	O
.	O
Bellare	O
,	O
D	O
.	O
Pointcheval	O
,	O
and	O
P	O
.	O
Rogaway	O
(	O
Eurocrypt	O
2000	O
)	O
and	O
V	O
.	O
Boyko	O
,	O
P	O
.	O
MacKenzie	O
,	O
and	O
S	O
.	O
Patel	O
(	O
Eurocrypt	O
2000	O
)	O
.	O
</s>
<s>
These	O
protocols	O
were	O
proven	O
secure	O
in	O
the	O
so-called	O
random	B-Application
oracle	I-Application
model	I-Application
(	O
or	O
even	O
stronger	O
variants	O
)	O
,	O
and	O
the	O
first	O
protocols	O
proven	O
secure	O
under	O
standard	O
assumptions	O
were	O
those	O
of	O
O	O
.	O
Goldreich	O
and	O
Y	O
.	O
Lindell	O
(	O
Crypto	O
2001	O
)	O
which	O
serves	O
as	O
a	O
plausibility	O
proof	O
but	O
is	O
not	O
efficient	O
,	O
and	O
J	O
.	O
Katz	O
,	O
R	O
.	O
Ostrovsky	O
,	O
and	O
M	O
.	O
Yung	O
(	O
Eurocrypt	O
2001	O
)	O
which	O
is	O
practical	O
.	O
</s>
<s>
A	O
considerable	O
number	O
of	O
alternative	O
,	O
secure	O
PAKE	B-Protocol
protocols	O
were	O
given	O
in	O
work	O
by	O
M	O
.	O
Bellare	O
,	O
D	O
.	O
Pointcheval	O
,	O
and	O
P	O
.	O
Rogaway	O
,	O
variations	O
,	O
and	O
security	O
proofs	O
have	O
been	O
proposed	O
in	O
this	O
growing	O
class	O
of	O
password-authenticated	B-Protocol
key	I-Protocol
agreement	I-Protocol
methods	O
.	O
</s>
<s>
Current	O
standards	O
for	O
these	O
methods	O
include	O
IETF	O
RFC	O
2945	O
,	O
RFC	O
5054	O
,	O
RFC	O
5931	O
,	O
RFC	O
5998	O
,	O
RFC	O
6124	O
,	O
RFC	O
6617	O
,	O
RFC	O
6628	O
and	O
RFC	O
6631	O
,	O
IEEE	O
Std	O
1363.2-2008	O
,	O
ITU-T	O
X.1035	B-Protocol
and	O
ISO-IEC	O
11770-4:2006	O
.	O
</s>
<s>
On	O
request	O
of	O
the	O
internet	O
engineering	O
task	O
force	O
IETF	O
,	O
a	O
PAKE	B-Protocol
selection	O
process	O
has	O
been	O
carried	O
out	O
in	O
2018	O
and	O
2019	O
by	O
the	O
IRTF	O
crypto	O
forum	O
research	O
group	O
(	O
CFRG	O
)	O
.	O
</s>
<s>
In	O
the	O
final	O
round	O
in	O
2019	O
four	O
finalists	O
AuCPace	O
,	O
OPAQUE	O
(	O
augmented	O
cases	O
)	O
and	O
CPace	O
,	O
SPAKE2	O
(	O
balanced	O
PAKE	B-Protocol
)	O
prevailed	O
.	O
</s>
