<s>
A	O
pair	O
of	O
permutations	O
f0	O
and	O
f1	O
are	O
said	O
to	O
be	O
claw-free	B-Algorithm
if	O
there	O
is	O
no	O
efficient	O
algorithm	O
for	O
computing	O
a	O
claw	B-Algorithm
.	O
</s>
<s>
The	O
terminology	O
claw	B-Algorithm
free	O
was	O
introduced	O
by	O
Goldwasser	O
,	O
Micali	O
,	O
and	O
Rivest	O
in	O
their	O
1984	O
paper	O
,	O
"	O
A	O
Paradoxical	O
Solution	O
to	O
the	O
Signature	O
Problem	O
"	O
(	O
and	O
later	O
in	O
a	O
more	O
complete	O
journal	O
paper	O
)	O
,	O
where	O
they	O
showed	O
that	O
the	O
existence	O
of	O
claw-free	B-Algorithm
pairs	O
of	O
trapdoor	O
permutations	O
implies	O
the	O
existence	O
of	O
digital	O
signature	O
schemes	O
secure	O
against	O
adaptive	O
chosen-message	O
attack	O
.	O
</s>
<s>
The	O
existence	O
of	O
trapdoor	O
permutations	O
does	O
not	O
by	O
itself	O
imply	O
claw-free	B-Algorithm
permutations	I-Algorithm
exist	O
;	O
however	O
,	O
it	O
has	O
been	O
shown	O
that	O
claw-free	B-Algorithm
permutations	I-Algorithm
do	O
exist	O
if	O
factoring	O
is	O
hard	O
.	O
</s>
<s>
Collision	B-Algorithm
Resistant	I-Algorithm
Hash	I-Algorithm
Functions	I-Algorithm
from	O
claw-free	B-Algorithm
permutations	I-Algorithm
.	O
</s>
<s>
The	O
notion	O
of	O
claw-freeness	O
is	O
closely	O
related	O
to	O
that	O
of	O
collision	O
resistance	O
in	O
hash	B-Algorithm
functions	I-Algorithm
.	O
</s>
<s>
The	O
distinction	O
is	O
that	O
claw-free	B-Algorithm
permutations	I-Algorithm
are	O
pairs	O
of	O
functions	O
in	O
which	O
it	O
is	O
hard	O
to	O
create	O
a	O
collision	O
between	O
them	O
,	O
while	O
a	O
collision-resistant	O
hash	B-Algorithm
function	I-Algorithm
is	O
a	O
single	O
function	O
in	O
which	O
it	O
's	O
hard	O
to	O
find	O
a	O
collision	O
,	O
i.e.	O
</s>
<s>
In	O
the	O
hash	B-Algorithm
function	I-Algorithm
literature	O
,	O
this	O
is	O
commonly	O
termed	O
a	O
hash	B-Algorithm
collision	I-Algorithm
.	O
</s>
<s>
A	O
hash	B-Algorithm
function	I-Algorithm
where	O
collisions	O
are	O
difficult	O
to	O
find	O
is	O
said	O
to	O
have	O
collision	O
resistance	O
.	O
</s>
<s>
Given	O
a	O
pair	O
of	O
claw-free	B-Algorithm
permutations	I-Algorithm
f0	O
and	O
f1	O
it	O
is	O
straightforward	O
to	O
create	O
a	O
commitment	O
scheme	O
.	O
</s>
<s>
The	O
sender	O
is	O
bound	O
to	O
his	O
bit	O
because	O
opening	O
a	O
commitment	O
to	O
1b	O
is	O
exactly	O
equivalent	O
to	O
finding	O
a	O
claw	B-Algorithm
.	O
</s>
<s>
Notice	O
that	O
like	O
the	O
construction	O
of	O
Collision	B-Algorithm
Resistant	I-Algorithm
Hash	I-Algorithm
functions	I-Algorithm
,	O
this	O
construction	O
does	O
not	O
require	O
that	O
the	O
claw-free	B-Algorithm
functions	O
have	O
a	O
trapdoor	O
.	O
</s>
