<s>
The	O
generic	B-General_Concept
group	I-General_Concept
model	I-General_Concept
is	O
an	O
idealised	O
cryptographic	O
model	O
,	O
where	O
the	O
adversary	O
is	O
only	O
given	O
access	O
to	O
a	O
randomly	O
chosen	O
encoding	O
of	O
a	O
group	O
,	O
instead	O
of	O
efficient	O
encodings	O
,	O
such	O
as	O
those	O
used	O
by	O
the	O
finite	O
field	O
or	O
elliptic	O
curve	O
groups	O
used	O
in	O
practice	O
.	O
</s>
<s>
If	O
the	O
group	O
should	O
allow	O
for	O
a	O
pairing	B-Protocol
operation	O
this	O
operation	O
would	O
be	O
modeled	O
as	O
an	O
additional	O
oracle	O
.	O
</s>
<s>
One	O
of	O
the	O
main	O
uses	O
of	O
the	O
generic	B-General_Concept
group	I-General_Concept
model	I-General_Concept
is	O
to	O
analyse	O
computational	O
hardness	O
assumptions	O
.	O
</s>
<s>
An	O
analysis	O
in	O
the	O
generic	B-General_Concept
group	I-General_Concept
model	I-General_Concept
can	O
answer	O
the	O
question	O
:	O
"	O
What	O
is	O
the	O
fastest	O
generic	O
algorithm	O
for	O
breaking	O
a	O
cryptographic	O
hardness	O
assumption	O
"	O
.	O
</s>
<s>
This	O
question	O
was	O
answered	O
for	O
the	O
discrete	O
logarithm	O
problem	O
by	O
Victor	O
Shoup	O
using	O
the	O
generic	B-General_Concept
group	I-General_Concept
model	I-General_Concept
.	O
</s>
<s>
Other	O
results	O
in	O
the	O
generic	B-General_Concept
group	I-General_Concept
model	I-General_Concept
are	O
for	O
instance	O
.	O
</s>
<s>
The	O
generic	B-General_Concept
group	I-General_Concept
model	I-General_Concept
suffers	O
from	O
some	O
of	O
the	O
same	O
problems	O
as	O
the	O
random	B-Application
oracle	I-Application
model	I-Application
.	O
</s>
<s>
In	O
particular	O
,	O
it	O
has	O
been	O
shown	O
using	O
a	O
similar	O
argument	O
that	O
there	O
exist	O
cryptographic	O
schemes	O
which	O
are	O
provably	O
secure	O
in	O
the	O
generic	B-General_Concept
group	I-General_Concept
model	I-General_Concept
but	O
which	O
are	O
trivially	O
insecure	O
once	O
the	O
random	O
group	O
encoding	O
is	O
replaced	O
with	O
an	O
efficiently	O
computable	O
instantiation	O
of	O
the	O
encoding	O
function	O
.	O
</s>
