<s>
MQV	B-Protocol
(	O
Menezes	B-Protocol
–	I-Protocol
Qu	I-Protocol
–	I-Protocol
Vanstone	I-Protocol
)	O
is	O
an	O
authenticated	O
protocol	B-Protocol
for	O
key	B-Protocol
agreement	I-Protocol
based	O
on	O
the	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
scheme	O
.	O
</s>
<s>
Like	O
other	O
authenticated	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
schemes	O
,	O
MQV	B-Protocol
provides	O
protection	O
against	O
an	O
active	O
attacker	O
.	O
</s>
<s>
The	O
protocol	B-Protocol
can	O
be	O
modified	O
to	O
work	O
in	O
an	O
arbitrary	O
finite	O
group	O
,	O
and	O
,	O
in	O
particular	O
,	O
elliptic	O
curve	O
groups	O
,	O
where	O
it	O
is	O
known	O
as	O
elliptic	O
curve	O
MQV	B-Protocol
(	O
ECMQV	B-Protocol
)	O
.	O
</s>
<s>
MQV	B-Protocol
was	O
initially	O
proposed	O
by	O
Alfred	O
Menezes	O
,	O
Minghua	O
Qu	O
and	O
Scott	O
Vanstone	O
in	O
1995	O
.	O
</s>
<s>
MQV	B-Protocol
is	O
incorporated	O
in	O
the	O
public-key	O
standard	O
IEEE	O
P1363	O
and	O
NIST	O
's	O
SP800-56A	O
standard	O
.	O
</s>
<s>
Some	O
variants	O
of	O
MQV	B-Protocol
are	O
claimed	O
in	O
patents	O
assigned	O
to	O
Certicom	O
.	O
</s>
<s>
ECMQV	B-Protocol
has	O
been	O
dropped	O
from	O
the	O
National	O
Security	O
Agency	O
's	O
Suite	O
B	O
set	O
of	O
cryptographic	O
standards	O
.	O
</s>
<s>
A	O
key	O
for	O
a	O
symmetric-key	B-Algorithm
algorithm	I-Algorithm
can	O
be	O
derived	O
from	O
.	O
</s>
<s>
The	O
original	O
MQV	B-Protocol
protocol	B-Protocol
does	O
not	O
include	O
user	O
identities	O
of	O
the	O
communicating	O
parties	O
in	O
the	O
key	O
exchange	O
flows	O
.	O
</s>
<s>
However	O
,	O
explicit	O
key	O
confirmation	O
is	O
optional	O
in	O
MQV	B-Protocol
(	O
and	O
in	O
the	O
IEEE	O
P1363	O
specification	O
)	O
.	O
</s>
<s>
In	O
2001	O
,	O
Kaliski	O
presented	O
an	O
unknown	O
key-share	O
attack	O
that	O
exploited	O
the	O
missing	O
identities	O
in	O
the	O
MQV	B-Protocol
key	O
exchange	O
protocol	B-Protocol
.	O
</s>
<s>
The	O
attack	O
works	O
against	O
implicitly	O
authenticated	O
MQV	B-Protocol
that	O
does	O
not	O
have	O
explicit	O
key	O
confirmation	O
.	O
</s>
<s>
In	O
2006	O
,	O
Menezes	O
and	O
Ustaoglu	O
proposed	O
to	O
address	O
this	O
attack	O
by	O
including	O
user	O
identities	O
in	O
the	O
key	O
derivation	O
function	O
at	O
the	O
end	O
of	O
the	O
MQV	B-Protocol
key	O
exchange	O
.	O
</s>
<s>
In	O
2005	O
,	O
Krawczyk	O
proposed	O
a	O
hash	O
variant	O
of	O
MQV	B-Protocol
,	O
called	O
HMQV	O
.	O
</s>
<s>
The	O
HMQV	O
protocol	B-Protocol
was	O
designed	O
to	O
address	O
Kaliski	O
's	O
attack	O
(	O
without	O
mandating	O
explicit	O
key	O
confirmation	O
)	O
,	O
with	O
the	O
additional	O
goals	O
of	O
achieving	O
provable	O
security	O
and	O
better	O
efficiency	O
.	O
</s>
<s>
HMQV	O
made	O
three	O
changes	O
to	O
MQV	B-Protocol
:	O
</s>
<s>
Removing	O
the	O
mandatory	O
requirement	O
in	O
MQV	B-Protocol
that	O
a	O
certificate	O
authority	O
(	O
CA	O
)	O
must	O
verify	O
the	O
proof-of-possession	O
of	O
the	O
user	O
's	O
private	O
key	O
during	O
the	O
public	O
key	O
registration	O
.	O
</s>
<s>
Removing	O
the	O
mandatory	O
requirement	O
in	O
MQV	B-Protocol
that	O
a	O
user	O
must	O
verify	O
whether	O
the	O
received	O
ephemeral	O
public	O
key	O
is	O
a	O
valid	O
public	O
key	O
(	O
known	O
as	O
public	O
key	O
validation	O
)	O
.	O
</s>
<s>
HMQV	O
claims	O
to	O
be	O
superior	O
to	O
MQV	B-Protocol
in	O
performance	O
because	O
it	O
dispenses	O
with	O
the	O
operations	O
in	O
2	O
)	O
and	O
3	O
)	O
above	O
,	O
which	O
are	O
mandatory	O
in	O
MQV	B-Protocol
.	O
</s>
<s>
It	O
shows	O
that	O
when	O
engaged	O
with	O
an	O
active	O
attacker	O
,	O
the	O
HMQV	O
protocol	B-Protocol
leaks	O
information	O
about	O
the	O
user	O
's	O
long-term	O
private	O
key	O
,	O
and	O
depending	O
on	O
the	O
underlying	O
cryptographic	O
group	O
setting	O
,	O
the	O
entire	O
private	O
key	O
may	O
be	O
recovered	O
by	O
the	O
attacker	O
.	O
</s>
<s>
The	O
revised	O
HMQV	O
could	O
still	O
claim	O
to	O
be	O
more	O
efficient	O
than	O
MQV	B-Protocol
.	O
</s>
<s>
This	O
contradicts	O
the	O
common	O
understanding	O
that	O
"	O
authentication	O
"	O
in	O
an	O
authenticated	O
key	O
exchange	O
protocol	B-Protocol
is	O
defined	O
based	O
on	O
proving	O
the	O
knowledge	O
of	O
a	O
private	O
key	O
.	O
</s>
<s>
This	O
issue	O
is	O
not	O
applicable	O
to	O
MQV	B-Protocol
.	O
</s>
<s>
However	O
,	O
this	O
change	O
would	O
diminish	O
the	O
efficiency	O
advantages	O
of	O
HMQV	O
over	O
MQV	B-Protocol
.	O
</s>
