<s>
RadioGatún	B-Algorithm
is	O
a	O
cryptographic	B-Algorithm
hash	I-Algorithm
primitive	I-Algorithm
created	O
by	O
Guido	O
Bertoni	O
,	O
Joan	O
Daemen	O
,	O
Michaël	O
Peeters	O
,	O
and	O
Gilles	O
Van	O
Assche	O
.	O
</s>
<s>
It	O
was	O
first	O
publicly	O
presented	O
at	O
the	O
NIST	O
Second	O
Cryptographic	B-Algorithm
Hash	I-Algorithm
Workshop	O
,	O
held	O
in	O
Santa	O
Barbara	O
,	O
California	O
,	O
on	O
August	O
24	O
–	O
25	O
,	O
2006	O
,	O
as	O
part	O
of	O
the	O
NIST	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
competition	I-Algorithm
.	O
</s>
<s>
The	O
same	O
team	O
that	O
developed	O
RadioGatún	B-Algorithm
went	O
on	O
to	O
make	O
considerable	O
revisions	O
to	O
this	O
cryptographic	O
primitive	O
,	O
leading	O
to	O
the	O
Keccak	B-Algorithm
SHA-3	B-Algorithm
algorithm	O
.	O
</s>
<s>
RadioGatún	B-Algorithm
is	O
a	O
family	O
of	O
64	O
different	O
hash	B-Algorithm
functions	I-Algorithm
,	O
distinguished	O
by	O
a	O
single	O
parameter	O
,	O
the	O
word	O
width	O
in	O
bits	O
(	O
w	O
)	O
,	O
adjustable	O
between	O
1	O
and	O
64	O
.	O
</s>
<s>
The	O
only	O
word	O
sizes	O
with	O
official	O
test	O
vectors	O
are	O
the	O
32-bit	O
and	O
64-bit	O
variants	O
of	O
RadioGatún	B-Algorithm
.	O
</s>
<s>
Although	O
RadioGatún	B-Algorithm
is	O
a	O
derivative	O
of	O
Panama	B-Algorithm
,	O
a	O
stream	B-Algorithm
cipher	I-Algorithm
and	O
hash	B-Algorithm
construction	O
from	O
the	O
late	O
1990s	O
whose	O
hash	B-Algorithm
construction	O
has	O
been	O
broken	O
,	O
RadioGatún	B-Algorithm
does	O
not	O
have	O
Panama	B-Algorithm
's	O
weaknesses	O
when	O
used	O
as	O
a	O
hash	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
As	O
of	O
2022	O
,	O
RadioGatún	B-Algorithm
is	O
still	O
a	O
secure	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
;	O
the	O
largest	O
version	O
of	O
RadioGatún	B-Algorithm
that	O
is	O
broken	O
is	O
the	O
one	O
with	O
a	O
word	O
size	O
of	O
two	O
bits	O
.	O
</s>
<s>
RadioGatún	B-Algorithm
has	O
a	O
claimed	O
security	O
strength	O
of	O
304	O
bits	O
for	O
the	O
32-bit	O
version	O
and	O
608	O
bits	O
for	O
the	O
64-bit	O
version	O
.	O
</s>
<s>
RadioGatún	B-Algorithm
can	O
be	O
used	O
either	O
as	O
a	O
hash	B-Algorithm
function	I-Algorithm
or	O
a	O
stream	B-Algorithm
cipher	I-Algorithm
;	O
it	O
can	O
output	O
an	O
arbitrarily	O
long	O
stream	O
of	O
pseudo-random	B-Error_Name
numbers	I-Error_Name
;	O
this	O
kind	O
of	O
hash	B-Algorithm
construction	O
is	O
now	O
known	O
as	O
an	O
"	O
Extendable-Output	O
Function	O
"	O
(	O
XOF	O
)	O
.	O
</s>
<s>
The	O
algorithm	O
's	O
designers	O
,	O
in	O
the	O
original	O
RadioGatún	B-Algorithm
paper	O
,	O
claimed	O
that	O
the	O
first	O
19	O
×	O
w	O
bits	O
(	O
where	O
w	O
is	O
the	O
word	O
width	O
used	O
)	O
of	O
RadioGatún	B-Algorithm
's	O
output	O
is	O
a	O
cryptographically	O
secure	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
.	O
</s>
<s>
Since	O
publishing	O
the	O
paper	O
,	O
the	O
designers	O
revised	O
their	O
security	O
claim	O
,	O
and	O
now	O
claim	O
that	O
RadioGatún	B-Algorithm
has	O
the	O
security	O
of	O
a	O
cryptographic	B-Algorithm
sponge	I-Algorithm
function	O
with	O
a	O
capacity	O
of	O
19w	O
.	O
</s>
<s>
This	O
means	O
that	O
the	O
32-bit	O
version	O
of	O
RadioGatún	B-Algorithm
can	O
be	O
used	O
to	O
make	O
a	O
hash	B-Algorithm
with	O
304	O
bits	O
of	O
security	O
(	O
both	O
from	O
collision	B-Algorithm
attacks	I-Algorithm
and	O
from	O
Preimage	O
attacks	O
)	O
,	O
and	O
the	O
64-bit	O
version	O
offers	O
608	O
bits	O
of	O
security	O
.	O
</s>
<s>
The	O
designers	O
call	O
RadioGatún	B-Algorithm
an	O
"	O
ideal	O
mangling	O
function	O
"	O
.	O
</s>
<s>
RadioGatún	B-Algorithm
uses	O
a	O
"	O
belt	O
"	O
and	O
"	O
mill	O
"	O
to	O
cryptographically	O
process	O
binary	O
data	O
,	O
with	O
the	O
majority	O
of	O
mangling	O
operations	O
performed	O
on	O
the	O
"	O
mill	O
"	O
part	O
of	O
RadioGatún	B-Algorithm
.	O
</s>
<s>
Keccak	B-Algorithm
removed	O
the	O
belt	O
,	O
increased	O
the	O
size	O
of	O
the	O
mill	O
from	O
19	O
words	O
to	O
25	O
words	O
,	O
and	O
made	O
the	O
mill	O
function	O
somewhat	O
more	O
complicated	O
.	O
</s>
<s>
The	O
Wikibooks	O
page	O
on	O
RadioGatún	B-Algorithm
provides	O
full	O
implementation	O
details	O
,	O
and	O
Module:RadioGatun32	O
is	O
an	O
implementation	O
of	O
the	O
32-bit	O
version	O
of	O
RadioGatún	B-Algorithm
.	O
</s>
<s>
In	O
the	O
paper	O
"	O
Two	O
attacks	O
on	O
RadioGatún	B-Algorithm
"	O
,	O
Dmitry	O
Khovratovich	O
presents	O
two	O
attacks	O
that	O
do	O
not	O
break	O
the	O
designers	O
 '	O
security	O
claims	O
,	O
one	O
with	O
a	O
complexity	O
of	O
218w	O
and	O
another	O
with	O
a	O
complexity	O
of	O
223.1w	O
.	O
</s>
<s>
Khovratovich	O
also	O
authored	O
a	O
paper	O
,	O
entitled	O
"	O
Cryptanalysis	O
of	O
hash	B-Algorithm
functions	I-Algorithm
with	O
structures	O
"	O
,	O
which	O
describes	O
an	O
attack	O
with	O
a	O
complexity	O
of	O
218w	O
.	O
</s>
<s>
In	O
the	O
paper	O
"	O
Analysis	O
of	O
the	O
Collision	O
Resistance	O
of	O
RadioGatún	B-Algorithm
using	O
Algebraic	O
Techniques	O
"	O
,	O
Charles	O
Bouillaguet	O
and	O
Pierre-Alain	O
Fouque	O
present	O
a	O
way	O
of	O
generating	O
collisions	O
with	O
the	O
1-bit	O
version	O
of	O
the	O
algorithm	O
using	O
an	O
attack	O
that	O
needs	O
224.5	O
operations	O
.	O
</s>
<s>
This	O
attack	O
is	O
less	O
effective	O
than	O
the	O
other	O
attacks	O
and	O
also	O
does	O
not	O
break	O
RadioGatún	B-Algorithm
's	O
security	O
claim	O
.	O
</s>
<s>
The	O
most	O
effective	O
attack	O
against	O
the	O
algorithm	O
,	O
one	O
with	O
a	O
complexity	O
of	O
211w	O
,	O
is	O
given	O
in	O
the	O
paper	O
"	O
Cryptanalysis	O
of	O
RadioGatun	B-Algorithm
"	O
by	O
Thomas	O
Fuhr	O
and	O
Thomas	O
Peyrin	O
.	O
</s>
<s>
In	O
the	O
paper	O
,	O
they	O
break	O
the	O
2-bit	O
(	O
word	O
size	O
of	O
two	O
)	O
version	O
of	O
RadioGatún	B-Algorithm
.	O
</s>
<s>
The	O
developers	O
of	O
RadioGatún	B-Algorithm
have	O
stated	O
that	O
their	O
"	O
own	O
experiments	O
did	O
not	O
inspire	O
confidence	O
in	O
RadioGatún	B-Algorithm
"	O
.	O
</s>
<s>
The	O
only	O
RadioGatún	B-Algorithm
variants	O
that	O
the	O
designers	O
supplied	O
test	O
vectors	O
(	O
published	O
hash	B-Algorithm
values	O
for	O
sample	O
inputs	O
so	O
programmers	O
can	O
verify	O
they	O
are	O
correctly	O
implementing	O
the	O
algorithm	O
)	O
for	O
are	O
the	O
32-bit	O
and	O
64-bit	O
versions	O
.	O
</s>
<s>
These	O
test	O
vectors	O
,	O
generated	O
using	O
the	O
32-bit	O
version	O
of	O
RadioGatún	B-Algorithm
,	O
only	O
show	O
the	O
first	O
256	O
bits	O
of	O
RadioGatún[32]'s	O
arbitrarily	O
long	O
output	O
stream	O
:	O
</s>
<s>
Here	O
are	O
hashes	B-Algorithm
for	O
the	O
64-bit	O
version	O
:	O
</s>
