<s>
In	O
cryptography	O
,	O
concrete	B-General_Concept
security	I-General_Concept
or	O
exact	O
security	O
is	O
a	O
practice-oriented	O
approach	O
that	O
aims	O
to	O
give	O
more	O
precise	O
estimates	O
of	O
the	O
computational	O
complexities	O
of	O
adversarial	B-General_Concept
tasks	O
than	O
polynomial	B-Algorithm
equivalence	I-Algorithm
would	O
allow	O
.	O
</s>
<s>
It	O
quantifies	O
the	O
security	O
of	O
a	O
cryptosystem	O
by	O
bounding	O
the	O
probability	O
of	O
success	O
for	O
an	O
adversary	B-General_Concept
running	O
for	O
a	O
fixed	O
amount	O
of	O
time	O
.	O
</s>
<s>
Secure	O
schemes	O
are	O
defined	O
to	O
be	O
those	O
in	O
which	O
the	O
advantage	O
of	O
any	O
computationally	O
bounded	O
adversary	B-General_Concept
is	O
negligible	O
.	O
</s>
<s>
An	O
inefficient	O
reduction	O
results	O
either	O
in	O
the	O
success	O
probability	O
for	O
the	O
adversary	B-General_Concept
or	O
the	O
resource	O
requirement	O
of	O
the	O
scheme	O
being	O
greater	O
than	O
desired	O
.	O
</s>
<s>
Concrete	B-General_Concept
security	I-General_Concept
parametrizes	O
all	O
the	O
resources	O
available	O
to	O
the	O
adversary	B-General_Concept
,	O
such	O
as	O
running	O
time	O
and	O
memory	O
,	O
and	O
other	O
resources	O
specific	O
to	O
the	O
system	O
in	O
question	O
,	O
such	O
as	O
the	O
number	O
of	O
plaintexts	O
it	O
can	O
obtain	O
or	O
the	O
number	O
of	O
queries	O
it	O
can	O
make	O
to	O
any	O
oracles	O
available	O
.	O
</s>
<s>
Then	O
the	O
advantage	O
of	O
the	O
adversary	B-General_Concept
is	O
upper	O
bounded	O
as	O
a	O
function	O
of	O
these	O
resources	O
and	O
of	O
the	O
problem	O
size	O
.	O
</s>
<s>
an	O
adversarial	B-General_Concept
strategy	O
)	O
matching	O
the	O
upper	O
bound	O
,	O
hence	O
the	O
name	O
exact	O
security	O
.	O
</s>
<s>
Concrete	B-General_Concept
security	I-General_Concept
estimates	O
have	O
been	O
applied	O
to	O
cryptographic	O
algorithms	O
:	O
</s>
<s>
In	O
1996	O
,	O
schemes	O
for	O
digital	O
signatures	O
based	O
on	O
the	O
RSA	B-Architecture
and	O
Rabin	B-Algorithm
cryptosystems	I-Algorithm
were	O
proposed	O
,	O
which	O
were	O
shown	O
to	O
be	O
approximately	O
as	O
difficult	O
to	O
break	O
as	O
the	O
original	O
cryptosystems	O
.	O
</s>
<s>
In	O
1997	O
,	O
some	O
notions	O
of	O
concrete	B-General_Concept
security	I-General_Concept
(	O
left-or-right	O
indistinguishability	O
,	O
real-or-random	O
indistinguishability	O
,	O
find-then-guess	O
security	O
,	O
and	O
semantic-security	O
)	O
for	O
symmetric	B-Algorithm
encryption	I-Algorithm
algorithms	O
were	O
proved	O
approximately	O
equivalent	O
in	O
various	O
block	B-Algorithm
cipher	I-Algorithm
modes	I-Algorithm
of	I-Algorithm
operation	I-Algorithm
such	O
as	O
CBC	O
,	O
CTR	O
,	O
and	O
XOR	O
(	O
a	O
stateless	O
variant	O
of	O
CBC	O
)	O
.	O
</s>
<s>
In	O
addition	O
,	O
a	O
software	O
tool	O
named	O
the	O
"	O
Foundational	O
Cryptography	O
Framework	O
"	O
,	O
which	O
embeds	O
into	O
Coq	B-Application
,	O
is	O
able	O
to	O
formally	O
verify	O
proofs	O
of	O
concrete	B-General_Concept
security	I-General_Concept
.	O
</s>
<s>
For	O
example	O
,	O
it	O
is	O
able	O
to	O
verify	O
the	O
concrete	B-General_Concept
security	I-General_Concept
of	O
ElGamal	B-Algorithm
encryption	I-Algorithm
.	O
</s>
