<s>
SPEKE	B-Protocol
(	O
Simple	B-Protocol
Password	I-Protocol
Exponential	I-Protocol
Key	I-Protocol
Exchange	I-Protocol
)	O
is	O
a	O
cryptographic	O
method	O
for	O
password-authenticated	B-Protocol
key	I-Protocol
agreement	I-Protocol
.	O
</s>
<s>
The	O
protocol	O
consists	O
of	O
little	O
more	O
than	O
a	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
key	I-Protocol
exchange	I-Protocol
where	O
the	O
Diffie-Hellman	B-Protocol
generator	O
g	O
is	O
created	O
from	O
a	O
hash	B-Algorithm
of	O
the	O
password	O
.	O
</s>
<s>
Here	O
is	O
one	O
simple	O
form	O
of	O
SPEKE	B-Protocol
:	O
</s>
<s>
Alice	O
and	O
Bob	O
agree	O
to	O
use	O
an	O
appropriately	O
large	O
and	O
randomly	O
selected	O
safe	O
prime	O
p	O
,	O
as	O
well	O
as	O
a	O
hash	B-Algorithm
function	I-Algorithm
H( )	O
.	O
</s>
<s>
Unlike	O
unauthenticated	O
Diffie-Hellman	B-Protocol
,	O
SPEKE	B-Protocol
prevents	O
man-in-the-middle	O
attack	O
by	O
the	O
incorporation	O
of	O
the	O
password	O
.	O
</s>
<s>
In	O
general	O
,	O
SPEKE	B-Protocol
can	O
use	O
any	O
prime	O
order	O
group	O
that	O
is	O
suitable	O
for	O
public	O
key	O
cryptography	O
,	O
including	O
elliptic-curve	O
cryptography	O
.	O
</s>
<s>
However	O
,	O
when	O
SPEKE	B-Protocol
is	O
realized	O
by	O
using	O
Elliptic-curve	O
cryptography	O
,	O
the	O
protocol	O
is	O
essentially	O
changed	O
by	O
requiring	O
an	O
additional	O
primitive	O
that	O
must	O
securely	O
map	O
a	O
password	O
onto	O
a	O
random	O
point	O
on	O
the	O
designated	O
elliptic	O
curve	O
.	O
</s>
<s>
SPEKE	B-Protocol
is	O
one	O
of	O
the	O
older	O
and	O
well-known	O
protocols	O
in	O
the	O
relatively	O
new	O
field	O
of	O
password-authenticated	B-Protocol
key	I-Protocol
exchange	I-Protocol
.	O
</s>
<s>
In	O
1997	O
Jablon	O
refined	O
and	O
enhanced	O
SPEKE	B-Protocol
with	O
additional	O
variations	O
,	O
including	O
an	O
augmented	O
password-authenticated	B-Protocol
key	I-Protocol
agreement	I-Protocol
method	O
called	O
B-SPEKE	O
.	O
</s>
<s>
A	O
paper	O
published	O
by	O
MacKenzie	O
in	O
2001	O
presents	O
a	O
proof	O
in	O
the	O
random	O
oracle	O
model	O
that	O
SPEKE	B-Protocol
is	O
a	O
secure	O
PAKE	B-Protocol
protocol	O
(	O
using	O
a	O
somewhat	O
relaxed	O
definition	O
)	O
based	O
on	O
a	O
variation	O
of	O
the	O
Decision	O
Diffie-Hellman	B-Protocol
assumption	O
.	O
</s>
<s>
However	O
,	O
the	O
proof	O
treats	O
the	O
key	O
confirmation	O
function	O
in	O
SPEKE	B-Protocol
as	O
mandatory	O
,	O
which	O
is	O
not	O
how	O
SPEKE	B-Protocol
is	O
specified	O
in	O
the	O
IEEE	O
P1363.2	O
and	O
ISO/IEC	O
11770-4	O
standards	O
.	O
</s>
<s>
In	O
2014	O
,	O
two	O
attacks	O
are	O
identified	O
against	O
the	O
SPEKE	B-Protocol
protocol	O
as	O
specified	O
in	O
the	O
original	O
Jablon	O
's	O
1996	O
paper	O
and	O
in	O
the	O
IEEE	O
P1363.2	O
(	O
D26	O
)	O
and	O
ISO/IEC	O
11770-4	O
(	O
2006	O
)	O
standards	O
.	O
</s>
<s>
The	O
first	O
attack	O
indicates	O
a	O
practical	O
weakness	O
of	O
the	O
protocol	O
while	O
the	O
second	O
attack	O
has	O
theoretical	O
implications	O
on	O
security	O
proofs	O
of	O
SPEKE	B-Protocol
.	O
</s>
<s>
During	O
the	O
ISO/IEC	O
JTC	O
1/SC	O
27	O
meeting	O
in	O
Mexico	O
City	O
in	O
October	O
2014	O
,	O
the	O
two	O
attacks	O
were	O
discussed	O
by	O
the	O
technical	O
committee	O
in	O
ISO/IEC	O
SC	O
27/Work	O
Group	O
2	O
,	O
and	O
it	O
had	O
been	O
agreed	O
that	O
the	O
SPEKE	B-Protocol
specification	O
in	O
ISO/IEC	O
11770-4	O
(	O
2006	O
)	O
should	O
be	O
revised	O
to	O
address	O
the	O
identified	O
issues	O
.	O
</s>
<s>
The	O
patched	O
SPEKE	B-Protocol
has	O
been	O
published	O
in	O
ISO/IEC	O
11770-4	O
(	O
2017	O
)	O
.	O
</s>
<s>
However	O
,	O
the	O
SPEKE	B-Protocol
specification	O
in	O
IEEE	O
P1363.2	O
remains	O
unpatched	O
.	O
</s>
<s>
Standards	O
that	O
describe	O
SPEKE	B-Protocol
include	O
IEEE	O
P1363.2	O
and	O
ISO/IEC	O
11770-4	O
.	O
</s>
<s>
In	O
the	O
latest	O
ISO/IEC	O
11770-4	O
(	O
2017	O
)	O
standard	O
,	O
the	O
SPEKE	B-Protocol
specification	O
is	O
revised	O
from	O
the	O
previous	O
one	O
in	O
ISO/IEC	O
11770-4	O
(	O
2006	O
)	O
to	O
address	O
the	O
two	O
attacks	O
reported	O
by	O
Hao	O
and	O
Shahandashti	O
in	O
2014	O
.	O
</s>
