<s>
A	O
checksum	B-Algorithm
is	O
a	O
small-sized	O
block	B-General_Concept
of	O
data	O
derived	O
from	O
another	O
block	B-General_Concept
of	O
digital	B-General_Concept
data	I-General_Concept
for	O
the	O
purpose	O
of	O
detecting	B-Error_Name
errors	I-Error_Name
that	O
may	O
have	O
been	O
introduced	O
during	O
its	O
transmission	O
or	O
storage	B-General_Concept
.	O
</s>
<s>
By	O
themselves	O
,	O
checksums	B-Algorithm
are	O
often	O
used	O
to	O
verify	O
data	O
integrity	O
but	O
are	O
not	O
relied	O
upon	O
to	O
verify	O
data	B-Error_Name
authenticity	I-Error_Name
.	O
</s>
<s>
The	O
procedure	O
which	O
generates	O
this	O
checksum	B-Algorithm
is	O
called	O
a	O
checksum	B-Algorithm
function	O
or	O
checksum	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Depending	O
on	O
its	O
design	O
goals	O
,	O
a	O
good	O
checksum	B-Algorithm
algorithm	I-Algorithm
usually	O
outputs	O
a	O
significantly	O
different	O
value	O
,	O
even	O
for	O
small	O
changes	O
made	O
to	O
the	O
input	O
.	O
</s>
<s>
This	O
is	O
especially	O
true	O
of	O
cryptographic	B-Algorithm
hash	I-Algorithm
functions	I-Algorithm
,	O
which	O
may	O
be	O
used	O
to	O
detect	O
many	O
data	O
corruption	O
errors	O
and	O
verify	O
overall	O
data	O
integrity	O
;	O
if	O
the	O
computed	O
checksum	B-Algorithm
for	O
the	O
current	O
data	O
input	O
matches	O
the	O
stored	O
value	O
of	O
a	O
previously	O
computed	O
checksum	B-Algorithm
,	O
there	O
is	O
a	O
very	O
high	O
probability	O
the	O
data	O
has	O
not	O
been	O
accidentally	O
altered	O
or	O
corrupted	O
.	O
</s>
<s>
Checksum	B-Algorithm
functions	O
are	O
related	O
to	O
hash	B-Algorithm
functions	I-Algorithm
,	O
fingerprints	B-Algorithm
,	O
randomization	O
functions	O
,	O
and	O
cryptographic	B-Algorithm
hash	I-Algorithm
functions	I-Algorithm
.	O
</s>
<s>
For	O
instance	O
,	O
a	O
function	O
returning	O
the	O
start	O
of	O
a	O
string	O
can	O
provide	O
a	O
hash	B-Algorithm
appropriate	O
for	O
some	O
applications	O
but	O
will	O
never	O
be	O
a	O
suitable	O
checksum	B-Algorithm
.	O
</s>
<s>
Checksums	B-Algorithm
are	O
used	O
as	O
cryptographic	O
primitives	O
in	O
larger	O
authentication	O
algorithms	O
.	O
</s>
<s>
For	O
cryptographic	O
systems	O
with	O
these	O
two	O
specific	O
design	O
goals	O
,	O
see	O
HMAC	B-Algorithm
.	O
</s>
<s>
Check	B-Error_Name
digits	I-Error_Name
and	O
parity	B-Error_Name
bits	I-Error_Name
are	O
special	O
cases	O
of	O
checksums	B-Algorithm
,	O
appropriate	O
for	O
small	O
blocks	O
of	O
data	O
(	O
such	O
as	O
Social	O
Security	O
numbers	O
,	O
bank	O
account	O
numbers	O
,	O
computer	O
words	O
,	O
single	O
bytes	B-Application
,	O
etc	O
.	O
)	O
.	O
</s>
<s>
Some	O
error-correcting	B-Error_Name
codes	I-Error_Name
are	O
based	O
on	O
special	O
checksums	B-Algorithm
which	O
not	O
only	O
detect	O
common	O
errors	O
but	O
also	O
allow	O
the	O
original	O
data	O
to	O
be	O
recovered	O
in	O
certain	O
cases	O
.	O
</s>
<s>
The	O
simplest	O
checksum	B-Algorithm
algorithm	I-Algorithm
is	O
the	O
so-called	O
longitudinal	B-Error_Name
parity	I-Error_Name
check	I-Error_Name
,	O
which	O
breaks	O
the	O
data	O
into	O
"	O
words	O
"	O
with	O
a	O
fixed	O
number	O
of	O
bits	O
,	O
and	O
then	O
computes	O
the	O
exclusive	O
or	O
(	O
XOR	O
)	O
of	O
all	O
those	O
words	O
.	O
</s>
<s>
To	O
check	O
the	O
integrity	O
of	O
a	O
message	O
,	O
the	O
receiver	O
computes	O
the	O
exclusive	O
or	O
of	O
all	O
its	O
words	O
,	O
including	O
the	O
checksum	B-Algorithm
;	O
if	O
the	O
result	O
is	O
not	O
a	O
word	O
consisting	O
of	O
zeros	O
,	O
the	O
receiver	O
knows	O
a	O
transmission	O
error	O
occurred	O
.	O
</s>
<s>
With	O
this	O
checksum	B-Algorithm
,	O
any	O
transmission	O
error	O
which	O
flips	O
a	O
single	O
bit	O
of	O
the	O
message	O
,	O
or	O
an	O
odd	O
number	O
of	O
bits	O
,	O
will	O
be	O
detected	O
as	O
an	O
incorrect	O
checksum	B-Algorithm
.	O
</s>
<s>
A	O
variant	O
of	O
the	O
previous	O
algorithm	O
is	O
to	O
add	O
all	O
the	O
"	O
words	O
"	O
as	O
unsigned	O
binary	O
numbers	O
,	O
discarding	O
any	O
overflow	O
bits	O
,	O
and	O
append	O
the	O
two	B-General_Concept
's	I-General_Concept
complement	I-General_Concept
of	O
the	O
total	O
as	O
the	O
checksum	B-Algorithm
.	O
</s>
<s>
To	O
validate	O
a	O
message	O
,	O
the	O
receiver	O
adds	O
all	O
the	O
words	O
in	O
the	O
same	O
manner	O
,	O
including	O
the	O
checksum	B-Algorithm
;	O
if	O
the	O
result	O
is	O
not	O
a	O
word	O
full	O
of	O
zeros	O
,	O
an	O
error	O
must	O
have	O
occurred	O
.	O
</s>
<s>
The	O
simple	O
checksums	B-Algorithm
described	O
above	O
fail	O
to	O
detect	O
some	O
common	O
errors	O
which	O
affect	O
many	O
bits	O
at	O
once	O
,	O
such	O
as	O
changing	O
the	O
order	O
of	O
data	O
words	O
,	O
or	O
inserting	O
or	O
deleting	O
words	O
with	O
all	O
bits	O
set	O
to	O
zero	O
.	O
</s>
<s>
The	O
checksum	B-Algorithm
algorithms	I-Algorithm
most	O
used	O
in	O
practice	O
,	O
such	O
as	O
Fletcher	B-Algorithm
's	I-Algorithm
checksum	I-Algorithm
,	O
Adler-32	B-Algorithm
,	O
and	O
cyclic	O
redundancy	O
checks	O
(	O
CRCs	O
)	O
,	O
address	O
these	O
weaknesses	O
by	O
considering	O
not	O
only	O
the	O
value	O
of	O
each	O
word	O
but	O
also	O
its	O
position	O
in	O
the	O
sequence	O
.	O
</s>
<s>
This	O
feature	O
generally	O
increases	O
the	O
cost	B-General_Concept
of	O
computing	O
the	O
checksum	B-Algorithm
.	O
</s>
<s>
The	O
idea	O
of	O
fuzzy	O
checksum	B-Algorithm
was	O
developed	O
for	O
detection	O
of	O
email	O
spam	O
by	O
building	O
up	O
cooperative	O
databases	O
from	O
multiple	O
ISPs	O
of	O
email	O
suspected	O
to	O
be	O
spam	O
.	O
</s>
<s>
By	O
contrast	O
,	O
a	O
"	O
fuzzy	O
checksum	B-Algorithm
"	O
reduces	O
the	O
body	O
text	O
to	O
its	O
characteristic	O
minimum	O
,	O
then	O
generates	O
a	O
checksum	B-Algorithm
in	O
the	O
usual	O
manner	O
.	O
</s>
<s>
This	O
greatly	O
increases	O
the	O
chances	O
of	O
slightly	O
different	O
spam	O
emails	O
producing	O
the	O
same	O
checksum	B-Algorithm
.	O
</s>
<s>
The	O
ISP	O
spam	O
detection	O
software	O
,	O
such	O
as	O
SpamAssassin	B-Language
,	O
of	O
co-operating	O
ISPs	O
,	O
submits	O
checksums	B-Algorithm
of	O
all	O
emails	O
to	O
the	O
centralised	O
service	O
such	O
as	O
DCC	O
.	O
</s>
<s>
If	O
the	O
count	O
of	O
a	O
submitted	O
fuzzy	O
checksum	B-Algorithm
exceeds	O
a	O
certain	O
threshold	O
,	O
the	O
database	O
notes	O
that	O
this	O
probably	O
indicates	O
spam	O
.	O
</s>
<s>
ISP	O
service	O
users	O
similarly	O
generate	O
a	O
fuzzy	O
checksum	B-Algorithm
on	O
each	O
of	O
their	O
emails	O
and	O
request	O
the	O
service	O
for	O
a	O
spam	O
likelihood	O
.	O
</s>
<s>
The	O
effect	O
of	O
a	O
checksum	B-Algorithm
algorithm	I-Algorithm
that	O
yields	O
an	O
-bit	O
checksum	B-Algorithm
is	O
to	O
map	O
each	O
-bit	O
message	O
to	O
a	O
corner	O
of	O
a	O
larger	O
hypercube	O
,	O
with	O
dimension	O
.	O
</s>
<s>
The	O
valid	O
received	O
messages	O
(	O
those	O
that	O
have	O
the	O
correct	O
checksum	B-Algorithm
)	O
comprise	O
a	O
smaller	O
set	O
,	O
with	O
only	O
corners	O
.	O
</s>
<s>
A	O
single-bit	O
transmission	O
error	O
then	O
corresponds	O
to	O
a	O
displacement	O
from	O
a	O
valid	O
corner	O
(	O
the	O
correct	O
message	O
and	O
checksum	B-Algorithm
)	O
to	O
one	O
of	O
the	O
adjacent	O
corners	O
.	O
</s>
<s>
The	O
goal	O
of	O
a	O
good	O
checksum	B-Algorithm
algorithm	I-Algorithm
is	O
to	O
spread	O
the	O
valid	O
corners	O
as	O
far	O
from	O
each	O
other	O
as	O
possible	O
,	O
to	O
increase	O
the	O
likelihood	O
"	O
typical	O
"	O
transmission	O
errors	O
will	O
end	O
up	O
in	O
an	O
invalid	O
corner	O
.	O
</s>
