<s>
The	O
Rabin	B-Algorithm
fingerprinting	I-Algorithm
scheme	I-Algorithm
is	O
a	O
method	O
for	O
implementing	O
fingerprints	B-Algorithm
using	O
polynomials	O
over	O
a	O
finite	O
field	O
.	O
</s>
<s>
We	O
then	O
pick	O
a	O
random	O
irreducible	O
polynomial	O
of	O
degree	O
k	O
over	O
GF(2 )	O
,	O
and	O
we	O
define	O
the	O
fingerprint	B-Algorithm
of	O
the	O
message	O
m	O
to	O
be	O
the	O
remainder	O
after	O
division	O
of	O
by	O
over	O
GF(2 )	O
which	O
can	O
be	O
viewed	O
as	O
a	O
polynomial	O
of	O
degree	O
or	O
as	O
a	O
k-bit	O
number	O
.	O
</s>
<s>
Many	O
implementations	O
of	O
the	O
Rabin	B-Algorithm
–	I-Algorithm
Karp	I-Algorithm
algorithm	I-Algorithm
internally	O
use	O
Rabin	B-Algorithm
fingerprints	I-Algorithm
.	O
</s>
<s>
The	O
Low	O
Bandwidth	O
Network	O
Filesystem	O
(	O
LBFS	O
)	O
from	O
MIT	O
uses	O
Rabin	B-Algorithm
fingerprints	I-Algorithm
to	O
implement	O
variable	O
size	O
shift-resistant	O
blocks	O
.	O
</s>
<s>
The	O
basic	O
idea	O
is	O
that	O
the	O
filesystem	O
computes	O
the	O
cryptographic	B-Algorithm
hash	I-Algorithm
of	O
each	O
block	O
in	O
a	O
file	O
.	O
</s>
<s>
LBFS	O
does	O
this	O
by	O
sliding	O
a	O
48	O
byte	O
window	O
over	O
the	O
file	O
and	O
computing	O
the	O
Rabin	B-Algorithm
fingerprint	I-Algorithm
of	O
each	O
window	O
.	O
</s>
<s>
When	O
the	O
low	O
13	O
bits	O
of	O
the	O
fingerprint	B-Algorithm
are	O
zero	O
LBFS	O
calls	O
those	O
48	O
bytes	O
a	O
breakpoint	O
and	O
ends	O
the	O
current	O
block	O
and	O
begins	O
a	O
new	O
one	O
.	O
</s>
<s>
Since	O
the	O
output	O
of	O
Rabin	B-Algorithm
fingerprints	I-Algorithm
are	O
pseudo-random	B-Error_Name
the	O
probability	O
of	O
any	O
given	O
48	O
bytes	O
being	O
a	O
breakpoint	O
is	O
(	O
1	O
in	O
8192	O
)	O
.	O
</s>
<s>
Any	O
hash	B-Algorithm
function	I-Algorithm
could	O
be	O
used	O
to	O
divide	O
a	O
long	O
file	O
into	O
blocks	O
(	O
as	O
long	O
as	O
a	O
cryptographic	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
is	O
then	O
used	O
to	O
find	O
the	O
checksum	O
of	O
each	O
block	O
)	O
:	O
but	O
the	O
Rabin	B-Algorithm
fingerprint	I-Algorithm
is	O
an	O
efficient	O
rolling	B-Error_Name
hash	I-Error_Name
,	O
since	O
the	O
computation	O
of	O
the	O
Rabin	B-Algorithm
fingerprint	I-Algorithm
of	O
region	O
B	O
can	O
reuse	O
some	O
of	O
the	O
computation	O
of	O
the	O
Rabin	B-Algorithm
fingerprint	I-Algorithm
of	O
region	O
A	O
when	O
regions	O
A	O
and	O
B	O
overlap	O
.	O
</s>
<s>
Note	O
that	O
this	O
is	O
a	O
problem	O
similar	O
to	O
that	O
faced	O
by	O
rsync	B-Application
.	O
</s>
