<s>
In	O
cryptography	O
a	O
universal	B-Algorithm
one-way	I-Algorithm
hash	I-Algorithm
function	I-Algorithm
(	O
UOWHF	B-Algorithm
,	O
often	O
pronounced	O
"	O
woof	O
"	O
)	O
,	O
is	O
a	O
type	O
of	O
universal	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
of	O
particular	O
importance	O
to	O
cryptography	O
.	O
</s>
<s>
UOWHF	B-Algorithm
's	O
are	O
proposed	O
as	O
an	O
alternative	O
to	O
collision-resistant	B-Algorithm
hash	I-Algorithm
functions	I-Algorithm
(	O
CRHFs	B-Algorithm
)	O
.	O
</s>
<s>
CRHFs	B-Algorithm
have	O
a	O
strong	O
collision-resistance	O
property	O
:	O
that	O
it	O
is	O
hard	O
,	O
given	O
randomly	O
chosen	O
hash	B-Algorithm
function	I-Algorithm
parameters	O
,	O
to	O
find	O
any	O
collision	O
of	O
the	O
hash	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
In	O
contrast	O
,	O
UOWHFs	B-Algorithm
require	O
that	O
it	O
be	O
hard	O
to	O
find	O
a	O
collision	O
where	O
one	O
preimage	O
is	O
chosen	O
independently	O
of	O
the	O
hash	B-Algorithm
function	I-Algorithm
parameters	O
.	O
</s>
<s>
The	O
primitive	O
was	O
suggested	O
by	O
Moni	O
Naor	O
and	O
Moti	O
Yung	O
and	O
is	O
also	O
known	O
as	O
"	O
target	O
collision	O
resistant	O
"	O
hash	B-Algorithm
functions	I-Algorithm
;	O
it	O
was	O
employed	O
to	O
construct	O
general	O
digital	O
signature	O
schemes	O
without	O
trapdoor	O
functions	O
,	O
and	O
also	O
within	O
chosen-ciphertext	O
secure	O
public	O
key	O
encryption	O
schemes	O
.	O
</s>
<s>
The	O
security	O
property	O
of	O
a	O
UOWHF	B-Algorithm
is	O
as	O
follows	O
.	O
</s>
<s>
A	O
hash	B-Algorithm
function	I-Algorithm
is	O
chosen	O
randomly	O
from	O
the	O
family	O
.	O
</s>
<s>
UOWHFs	B-Algorithm
are	O
thought	O
to	O
be	O
less	O
computationally	O
expensive	O
than	O
CRHFs	B-Algorithm
,	O
and	O
are	O
most	O
often	O
used	O
for	O
efficiency	O
purposes	O
in	O
schemes	O
where	O
the	O
choice	O
of	O
the	O
hash	B-Algorithm
function	I-Algorithm
happens	O
at	O
some	O
stage	O
of	O
execution	O
,	O
rather	O
than	O
beforehand	O
.	O
</s>
<s>
For	O
instance	O
,	O
the	O
Cramer	B-Algorithm
–	I-Algorithm
Shoup	I-Algorithm
cryptosystem	I-Algorithm
uses	O
a	O
UOWHF	B-Algorithm
as	O
part	O
of	O
the	O
validity	O
check	O
in	O
its	O
ciphertexts	O
.	O
</s>
