<s>
In	O
cryptography	O
,	O
the	O
Rabin	B-Algorithm
signature	I-Algorithm
algorithm	I-Algorithm
is	O
a	O
method	O
of	O
digital	O
signature	O
originally	O
proposed	O
by	O
Michael	O
O	O
.	O
Rabin	O
in	O
1978	O
.	O
</s>
<s>
The	O
Rabin	B-Algorithm
signature	I-Algorithm
algorithm	I-Algorithm
was	O
one	O
of	O
the	O
first	O
digital	O
signature	O
schemes	O
proposed	O
.	O
</s>
<s>
By	O
introducing	O
the	O
use	O
of	O
hashing	B-Algorithm
as	O
an	O
essential	O
step	O
in	O
signing	O
,	O
it	O
was	O
the	O
first	O
design	O
to	O
meet	O
what	O
is	O
now	O
the	O
modern	O
standard	O
of	O
security	O
against	O
forgery	B-General_Concept
,	O
existential	B-General_Concept
unforgeability	I-General_Concept
under	I-General_Concept
chosen-message	I-General_Concept
attack	I-General_Concept
,	O
assuming	O
suitably	O
scaled	O
parameters	O
.	O
</s>
<s>
Rabin	B-Algorithm
signatures	I-Algorithm
resemble	O
RSA	B-Architecture
signatures	I-Architecture
with	O
'	O
exponent	O
'	O
,	O
but	O
this	O
leads	O
to	O
qualitative	O
differences	O
that	O
enable	O
more	O
efficient	O
implementation	O
and	O
a	O
security	O
guarantee	O
relative	O
to	O
the	O
difficulty	O
of	O
integer	O
factorization	O
,	O
which	O
has	O
not	O
been	O
proven	O
for	O
RSA	B-Architecture
.	O
</s>
<s>
However	O
,	O
Rabin	B-Algorithm
signatures	I-Algorithm
have	O
seen	O
relatively	O
little	O
use	O
or	O
standardization	O
outside	O
IEEE	O
P1363	O
in	O
comparison	O
to	O
RSA	B-Architecture
signature	O
schemes	O
such	O
as	O
RSASSA-PKCS1-v1_5	O
and	O
RSASSA-PSS	B-Algorithm
.	O
</s>
<s>
The	O
Rabin	B-Algorithm
signature	I-Algorithm
scheme	O
is	O
parametrized	O
by	O
a	O
randomized	O
hash	B-Algorithm
function	I-Algorithm
of	O
a	O
message	O
and	O
-bit	O
randomization	O
string	O
.	O
</s>
<s>
Square	O
roots	O
are	O
not	O
unique	O
,	O
and	O
different	O
variants	O
of	O
the	O
signature	O
scheme	O
make	O
different	O
choices	O
of	O
square	O
root	O
;	O
in	O
any	O
case	O
,	O
the	O
signer	O
must	O
ensure	O
not	O
to	O
reveal	O
two	O
different	O
roots	O
for	O
the	O
same	O
hash	B-Algorithm
.	O
</s>
<s>
Security	O
against	O
any	O
adversary	O
defined	O
generically	O
in	O
terms	O
of	O
a	O
hash	B-Algorithm
function	I-Algorithm
(	O
i.e.	O
,	O
security	O
in	O
the	O
random	B-Application
oracle	I-Application
model	I-Application
)	O
follows	O
from	O
the	O
difficulty	O
of	O
factoring	O
:	O
</s>
<s>
Any	O
such	O
adversary	O
with	O
high	O
probability	O
of	O
success	O
at	O
forgery	B-General_Concept
can	O
,	O
with	O
nearly	O
as	O
high	O
probability	O
,	O
find	O
two	O
distinct	O
square	O
roots	O
and	O
of	O
a	O
random	O
integer	O
modulo	O
.	O
</s>
<s>
Randomization	O
of	O
the	O
hash	B-Algorithm
function	I-Algorithm
was	O
introduced	O
to	O
allow	O
the	O
signer	O
to	O
find	O
a	O
quadratic	O
residue	O
,	O
but	O
randomized	O
hashing	B-Algorithm
for	O
signatures	O
later	O
became	O
relevant	O
in	O
its	O
own	O
right	O
for	O
tighter	O
security	O
theorems	O
and	O
resilience	O
to	O
collision	O
attacks	O
on	O
fixed	O
hash	B-Algorithm
functions	I-Algorithm
.	O
</s>
<s>
Variants	O
without	O
the	O
hash	B-Algorithm
function	I-Algorithm
have	O
been	O
published	O
in	O
textbooks	O
,	O
crediting	O
Rabin	O
for	O
exponent	O
2	O
but	O
not	O
for	O
the	O
use	O
of	O
a	O
hash	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
In	O
the	O
original	O
paper	O
,	O
the	O
hash	B-Algorithm
function	I-Algorithm
was	O
written	O
with	O
the	O
notation	O
,	O
with	O
C	O
for	O
compression	O
,	O
and	O
using	O
juxtaposition	O
to	O
denote	O
concatenation	O
of	O
and	O
as	O
bit	O
strings	O
:	O
</s>
<s>
The	O
signer	O
now	O
compresses	O
by	O
a	O
hashing	B-Algorithm
function	O
to	O
a	O
word	O
,	O
so	O
that	O
as	O
a	O
binary	O
number	O
…	O
</s>
