<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
a	O
hash	B-Algorithm
collision	I-Algorithm
or	O
hash	B-Algorithm
clash	O
is	O
when	O
two	O
pieces	O
of	O
data	O
in	O
a	O
hash	B-Algorithm
table	I-Algorithm
share	O
the	O
same	O
hash	B-Error_Name
value	I-Error_Name
.	O
</s>
<s>
The	O
hash	B-Error_Name
value	I-Error_Name
in	O
this	O
case	O
is	O
derived	O
from	O
a	O
hash	B-Algorithm
function	I-Algorithm
which	O
takes	O
a	O
data	O
input	O
and	O
returns	O
a	O
fixed	O
length	O
of	O
bits	O
.	O
</s>
<s>
Although	O
hash	B-Error_Name
algorithms	I-Error_Name
have	O
been	O
created	O
with	O
the	O
intent	O
of	O
being	O
collision	O
resistant	O
,	O
they	O
can	O
still	O
sometimes	O
map	O
different	O
data	O
to	O
the	O
same	O
hash	B-Algorithm
(	O
by	O
virtue	O
of	O
the	O
pigeonhole	O
principle	O
)	O
.	O
</s>
<s>
Due	O
to	O
the	O
possible	O
negative	O
applications	O
of	O
hash	B-Algorithm
collisions	I-Algorithm
in	O
data	B-General_Concept
management	I-General_Concept
and	O
computer	O
security	O
(	O
in	O
particular	O
,	O
cryptographic	B-Algorithm
hash	I-Algorithm
functions	I-Algorithm
)	O
,	O
collision	O
avoidance	O
has	O
become	O
an	O
important	O
topic	O
in	O
computer	O
security	O
.	O
</s>
<s>
Hash	B-Algorithm
collisions	I-Algorithm
can	O
be	O
unavoidable	O
depending	O
on	O
the	O
number	O
of	O
objects	O
in	O
a	O
set	O
and	O
whether	O
or	O
not	O
the	O
bit	O
string	O
they	O
are	O
mapped	O
to	O
is	O
long	O
enough	O
in	O
length	O
.	O
</s>
<s>
When	O
there	O
is	O
a	O
set	O
of	O
n	O
objects	O
,	O
if	O
n	O
is	O
greater	O
than	O
|R|	O
,	O
which	O
in	O
this	O
case	O
R	O
is	O
the	O
range	O
of	O
the	O
hash	B-Error_Name
value	I-Error_Name
,	O
the	O
probability	O
that	O
there	O
will	O
be	O
a	O
hash	B-Algorithm
collision	I-Algorithm
is	O
1	O
,	O
meaning	O
it	O
is	O
guaranteed	O
to	O
occur	O
.	O
</s>
<s>
Another	O
reason	O
hash	B-Algorithm
collisions	I-Algorithm
are	O
likely	O
at	O
some	O
point	O
in	O
time	O
stems	O
from	O
the	O
idea	O
of	O
the	O
birthday	O
paradox	O
in	O
mathematics	O
.	O
</s>
<s>
Bad	O
actors	O
can	O
use	O
this	O
approach	O
to	O
make	O
it	O
simpler	O
for	O
them	O
to	O
find	O
hash	B-Error_Name
values	I-Error_Name
that	O
collide	O
with	O
any	O
other	O
hash	B-Error_Name
value	I-Error_Name
–	O
rather	O
than	O
searching	O
for	O
a	O
specific	O
value	O
.	O
</s>
<s>
When	O
hash	B-Algorithm
functions	I-Algorithm
and	O
fingerprints	O
are	O
used	O
to	O
identify	O
similar	O
data	O
,	O
such	O
as	O
homologous	O
DNA	O
sequences	O
or	O
similar	O
audio	O
files	O
,	O
the	O
functions	O
are	O
designed	O
so	O
as	O
to	O
maximize	O
the	O
probability	O
of	O
collision	O
between	O
distinct	O
but	O
similar	O
data	O
,	O
using	O
techniques	O
like	O
locality-sensitive	B-Algorithm
hashing	I-Algorithm
.	O
</s>
<s>
Checksums	B-Algorithm
,	O
on	O
the	O
other	O
hand	O
,	O
are	O
designed	O
to	O
minimize	O
the	O
probability	O
of	O
collisions	O
between	O
similar	O
inputs	O
,	O
without	O
regard	O
for	O
collisions	O
between	O
very	O
different	O
inputs	O
.	O
</s>
<s>
Instances	O
where	O
bad	O
actors	O
attempt	O
to	O
create	O
or	O
find	O
hash	B-Algorithm
collisions	I-Algorithm
are	O
known	O
as	O
collision	B-Algorithm
attacks	I-Algorithm
.	I-Algorithm
</s>
<s>
In	O
practice	O
,	O
security-related	O
applications	O
use	O
cryptographic	B-Algorithm
hash	I-Algorithm
algorithms	O
,	O
which	O
are	O
designed	O
to	O
be	O
long	O
enough	O
for	O
random	O
matches	O
to	O
be	O
unlikely	O
,	O
fast	O
enough	O
that	O
they	O
can	O
be	O
used	O
anywhere	O
,	O
and	O
safe	O
enough	O
that	O
it	O
would	O
be	O
extremely	O
hard	O
to	O
find	O
collisions	O
.	O
</s>
<s>
Hash	B-Algorithm
collisions	I-Algorithm
can	O
occur	O
by	O
chance	O
and	O
can	O
be	O
intentionally	O
created	O
for	O
many	O
hash	B-Error_Name
algorithms	I-Error_Name
.	O
</s>
<s>
The	O
probability	O
of	O
a	O
hash	B-Algorithm
collision	I-Algorithm
thus	O
depends	O
on	O
the	O
size	O
of	O
the	O
algorithm	O
,	O
the	O
distribution	O
of	O
hash	B-Error_Name
values	I-Error_Name
,	O
and	O
whether	O
or	O
not	O
it	O
is	O
both	O
mathematically	O
known	O
and	O
computationally	O
feasible	O
to	O
create	O
specific	O
collisions	O
.	O
</s>
<s>
Take	O
into	O
account	O
the	O
following	O
hash	B-Error_Name
algorithms	I-Error_Name
–	O
CRC-32	O
,	O
MD5	B-Algorithm
,	O
and	O
SHA-1	B-Algorithm
.	O
</s>
<s>
These	O
are	O
common	O
hash	B-Error_Name
algorithms	I-Error_Name
with	O
varying	O
levels	O
of	O
collision	O
risk	O
.	O
</s>
<s>
CRC-32	O
poses	O
the	O
highest	O
risk	O
for	O
hash	B-Algorithm
collisions	I-Algorithm
.	O
</s>
<s>
This	O
hash	B-Algorithm
function	I-Algorithm
is	O
generally	O
not	O
recommended	O
for	O
use	O
.	O
</s>
<s>
If	O
a	O
hub	O
were	O
to	O
contain	O
77,163	O
hash	B-Error_Name
values	I-Error_Name
,	O
the	O
chance	O
of	O
a	O
hash	B-Algorithm
collision	I-Algorithm
occurring	O
is	O
50%	O
,	O
which	O
is	O
extremely	O
high	O
compared	O
to	O
other	O
methods	O
.	O
</s>
<s>
MD5	B-Algorithm
is	O
the	O
most	O
commonly	O
used	O
and	O
when	O
compared	O
to	O
the	O
other	O
two	O
hash	B-Algorithm
functions	I-Algorithm
,	O
it	O
represents	O
the	O
middle	O
ground	O
in	O
terms	O
of	O
hash	B-Algorithm
collision	I-Algorithm
risk	O
.	O
</s>
<s>
SHA-1	B-Algorithm
offers	O
the	O
lowest	O
risk	O
for	O
hash	B-Algorithm
collisions	I-Algorithm
.	O
</s>
<s>
For	O
a	O
SHA-1	B-Algorithm
function	O
to	O
have	O
a	O
50%	O
chance	O
of	O
a	O
hash	B-Algorithm
collision	I-Algorithm
occurring	O
,	O
there	O
would	O
have	O
to	O
be	O
1.42	O
×	O
10	O
records	O
in	O
the	O
hub	O
.	O
</s>
<s>
Having	O
a	O
hub	O
with	O
a	O
smaller	O
number	O
of	O
records	O
could	O
decrease	O
the	O
probability	O
of	O
a	O
hash	B-Algorithm
collision	I-Algorithm
in	O
all	O
of	O
these	O
hash	B-Algorithm
functions	I-Algorithm
,	O
although	O
there	O
will	O
always	O
be	O
a	O
minor	O
risk	O
present	O
,	O
which	O
is	O
inevitable	O
,	O
unless	O
collision	O
resolution	O
techniques	O
are	O
used	O
.	O
</s>
<s>
Since	O
hash	B-Algorithm
collisions	I-Algorithm
are	O
inevitable	O
,	O
hash	B-Algorithm
tables	I-Algorithm
have	O
mechanisms	O
of	O
dealing	O
with	O
them	O
,	O
known	O
as	O
collision	O
resolutions	O
.	O
</s>
<s>
Two	O
of	O
the	O
most	O
common	O
strategies	O
are	O
open	B-Algorithm
addressing	I-Algorithm
and	O
separate	O
chaining	O
.	O
</s>
<s>
The	O
cache-conscious	O
collision	O
resolution	O
is	O
another	O
strategy	O
that	O
has	O
been	O
discussed	O
in	O
the	O
past	O
for	O
string	O
hash	B-Algorithm
tables	I-Algorithm
.	O
</s>
<s>
Cells	O
in	O
the	O
hash	B-Algorithm
table	I-Algorithm
are	O
assigned	O
one	O
of	O
three	O
states	O
in	O
this	O
method	O
–	O
occupied	O
,	O
empty	O
,	O
or	O
deleted	O
.	O
</s>
<s>
If	O
a	O
hash	B-Algorithm
collision	I-Algorithm
occurs	O
,	O
the	O
table	O
will	O
be	O
probed	O
to	O
move	O
the	O
record	O
to	O
an	O
alternate	O
cell	O
that	O
is	O
stated	O
as	O
empty	O
.	O
</s>
<s>
There	O
are	O
different	O
types	O
of	O
probing	O
that	O
take	O
place	O
when	O
a	O
hash	B-Algorithm
collision	I-Algorithm
happens	O
and	O
this	O
method	O
is	O
implemented	O
.	O
</s>
<s>
Some	O
types	O
of	O
probing	O
are	O
linear	B-Algorithm
probing	I-Algorithm
,	O
double	B-Algorithm
hashing	I-Algorithm
,	O
and	O
quadratic	B-Algorithm
probing	I-Algorithm
.	O
</s>
<s>
Open	B-Algorithm
Addressing	I-Algorithm
is	O
also	O
known	O
as	O
closed	B-Algorithm
hashing	I-Algorithm
.	O
</s>
<s>
This	O
strategy	O
allows	O
more	O
than	O
one	O
record	O
to	O
be	O
"	O
chained	O
"	O
to	O
the	O
cells	O
of	O
a	O
hash	B-Algorithm
table	I-Algorithm
.	O
</s>
<s>
This	O
efficiently	O
prevents	O
a	O
hash	B-Algorithm
collision	I-Algorithm
from	O
occurring	O
since	O
records	O
with	O
the	O
same	O
hash	B-Error_Name
values	I-Error_Name
can	O
go	O
into	O
the	O
same	O
cell	O
,	O
but	O
it	O
has	O
its	O
disadvantages	O
.	O
</s>
<s>
Although	O
much	O
less	O
used	O
than	O
the	O
previous	O
two	O
,	O
has	O
proposed	O
the	O
cache-conscious	O
collision	O
resolution	O
method	O
in	O
2005	O
.	O
</s>
<s>
In	O
this	O
case	O
,	O
instead	O
of	O
chained	O
lists	O
,	O
the	O
hash	B-Error_Name
values	I-Error_Name
are	O
represented	O
in	O
a	O
contiguous	O
list	O
of	O
items	O
.	O
</s>
<s>
This	O
is	O
better	O
suited	O
for	O
string	O
hash	B-Algorithm
tables	I-Algorithm
and	O
the	O
use	O
for	O
numeric	O
values	O
is	O
still	O
unknown	O
.	O
</s>
