<s>
A	O
hash	B-Algorithm
chain	I-Algorithm
is	O
the	O
successive	O
application	O
of	O
a	O
cryptographic	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
to	O
a	O
piece	O
of	O
data	O
.	O
</s>
<s>
In	O
computer	O
security	O
,	O
a	O
hash	B-Algorithm
chain	I-Algorithm
is	O
a	O
method	O
to	O
produce	O
many	O
one-time	O
keys	O
from	O
a	O
single	O
key	O
or	O
password	O
.	O
</s>
<s>
For	O
non-repudiation	O
a	O
hash	B-Algorithm
function	I-Algorithm
can	O
be	O
applied	O
successively	O
to	O
additional	O
pieces	O
of	O
data	O
in	O
order	O
to	O
record	O
the	O
chronology	O
of	O
data	O
's	O
existence	O
.	O
</s>
<s>
A	O
hash	B-Algorithm
chain	I-Algorithm
is	O
a	O
successive	O
application	O
of	O
a	O
cryptographic	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
to	O
a	O
string	O
.	O
</s>
<s>
Leslie	O
Lamport	O
suggested	O
the	O
use	O
of	O
hash	B-Algorithm
chains	I-Algorithm
as	O
a	O
password	O
protection	O
scheme	O
in	O
an	O
insecure	O
environment	O
.	O
</s>
<s>
A	O
server	O
which	O
needs	O
to	O
provide	O
authentication	O
may	O
store	O
a	O
hash	B-Algorithm
chain	I-Algorithm
rather	O
than	O
a	O
plain	O
text	O
password	O
and	O
prevent	O
theft	O
of	O
the	O
password	O
in	O
transmission	O
or	O
theft	O
from	O
the	O
server	O
.	O
</s>
<s>
The	O
server	O
computes	O
and	O
verifies	O
this	O
matches	O
the	O
hash	B-Algorithm
chain	I-Algorithm
it	O
has	O
stored	O
.	O
</s>
<s>
An	O
eavesdropper	O
seeing	O
communicated	O
to	O
the	O
server	O
will	O
be	O
unable	O
to	O
re-transmit	O
the	O
same	O
hash	B-Algorithm
chain	I-Algorithm
to	O
the	O
server	O
for	O
authentication	O
since	O
the	O
server	O
now	O
expects	O
.	O
</s>
<s>
Due	O
to	O
the	O
one-way	O
property	O
of	O
cryptographically	O
secure	B-Algorithm
hash	I-Algorithm
functions	I-Algorithm
,	O
it	O
is	O
infeasible	O
for	O
the	O
eavesdropper	O
to	O
reverse	O
the	O
hash	B-Algorithm
function	I-Algorithm
and	O
obtain	O
an	O
earlier	O
piece	O
of	O
the	O
hash	B-Algorithm
chain	I-Algorithm
.	O
</s>
<s>
In	O
this	O
example	O
,	O
the	O
user	O
could	O
authenticate	O
1000	O
times	O
before	O
the	O
hash	B-Algorithm
chain	I-Algorithm
were	O
exhausted	O
.	O
</s>
<s>
Each	O
time	O
the	O
hash	B-Algorithm
value	O
is	O
different	O
,	O
and	O
thus	O
cannot	O
be	O
duplicated	O
by	O
an	O
attacker	O
.	O
</s>
<s>
Binary	O
hash	B-Algorithm
chains	I-Algorithm
are	O
commonly	O
used	O
in	O
association	O
with	O
a	O
hash	B-Algorithm
tree	I-Algorithm
.	O
</s>
<s>
A	O
binary	O
hash	B-Algorithm
chain	I-Algorithm
takes	O
two	O
hash	B-Algorithm
values	O
as	O
inputs	O
,	O
concatenates	O
them	O
and	O
applies	O
a	O
hash	B-Algorithm
function	I-Algorithm
to	O
the	O
result	O
,	O
thereby	O
producing	O
a	O
third	O
hash	B-Algorithm
value	O
.	O
</s>
<s>
The	O
above	O
diagram	O
shows	O
a	O
hash	B-Algorithm
tree	I-Algorithm
consisting	O
of	O
eight	O
leaf	O
nodes	O
and	O
the	O
hash	B-Algorithm
chain	I-Algorithm
for	O
the	O
third	O
leaf	O
node	O
.	O
</s>
<s>
In	O
addition	O
to	O
the	O
hash	B-Algorithm
values	O
themselves	O
the	O
order	O
of	O
concatenation	O
(	O
right	O
or	O
left	O
1	O
,	O
0	O
)	O
or	O
"	O
order	O
bits	O
"	O
are	O
necessary	O
to	O
complete	O
the	O
hash	B-Algorithm
chain	I-Algorithm
.	O
</s>
<s>
(	O
also	O
known	O
as	O
function	O
chains	O
)	O
are	O
used	O
in	O
hash-based	O
cryptography	O
.	O
</s>
<s>
The	O
chain	O
is	O
parameterized	O
by	O
the	O
w	O
(	O
number	O
of	O
bits	O
in	O
a	O
"	O
digit	O
"	O
d	O
)	O
and	O
security	O
parameter	O
n	O
(	O
number	O
of	O
bits	O
in	O
the	O
hash	B-Algorithm
value	O
,	O
typically	O
double	O
the	O
security	O
strength	O
,	O
256	O
or	O
512	O
)	O
.	O
</s>
<s>
The	O
chain	O
function	O
is	O
typically	O
based	O
on	O
a	O
standard	O
cryptographic	B-Algorithm
hash	I-Algorithm
,	O
but	O
needs	O
to	O
be	O
parameterized	O
(	O
"	O
randomized	O
"	O
)	O
,	O
so	O
it	O
involves	O
few	O
invocations	O
of	O
the	O
underlying	O
hash	B-Algorithm
.	O
</s>
<s>
A	O
hash	B-Algorithm
chain	I-Algorithm
is	O
similar	O
to	O
a	O
blockchain	B-Application
,	O
as	O
they	O
both	O
utilize	O
a	O
cryptographic	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
for	O
creating	O
a	O
link	O
between	O
two	O
nodes	O
.	O
</s>
<s>
However	O
,	O
a	O
blockchain	B-Application
(	O
as	O
used	O
by	O
Bitcoin	B-Protocol
and	O
related	O
systems	O
)	O
is	O
generally	O
intended	O
to	O
support	O
distributed	O
agreement	O
around	O
a	O
public	O
ledger	O
(	O
data	O
)	O
,	O
and	O
incorporates	O
a	O
set	O
of	O
rules	O
for	O
encapsulation	O
of	O
data	O
and	O
associated	O
data	O
permissions	O
.	O
</s>
