<s>
Shabal	B-Error_Name
is	O
a	O
cryptographic	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
submitted	O
by	O
the	O
France-funded	O
research	O
project	O
Saphir	O
to	O
NIST	B-Algorithm
's	I-Algorithm
international	I-Algorithm
competition	I-Algorithm
on	I-Algorithm
hash	I-Algorithm
functions	I-Algorithm
.	O
</s>
<s>
The	O
research	O
partners	O
of	O
Saphir	O
(	O
with	O
the	O
exception	O
of	O
LIENS	O
)	O
initiated	O
the	O
conception	O
of	O
Shabal	B-Error_Name
and	O
were	O
later	O
joined	O
by	O
partners	O
of	O
the	O
research	O
project	O
Saphir2	O
who	O
actively	O
contributed	O
to	O
the	O
final	O
design	O
of	O
Shabal	B-Error_Name
.	O
</s>
<s>
Saphir	O
(	O
Security	O
and	O
Analysis	O
of	O
Hash	B-Algorithm
Primitives	O
)	O
is	O
an	O
ANR	O
funded	O
project	O
on	O
hash	B-Algorithm
functions	I-Algorithm
.	O
</s>
<s>
Shabal	B-Error_Name
was	O
an	O
entry	O
in	O
the	O
NIST	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
competition	I-Algorithm
,	O
where	O
it	O
passed	O
to	O
the	O
second	O
round	O
,	O
but	O
failed	O
to	O
enter	O
the	O
final	O
round	O
.	O
</s>
<s>
Shabal	B-Error_Name
was	O
not	O
selected	O
as	O
a	O
finalist	O
mainly	O
due	O
to	O
security	O
concerns	O
.	O
</s>
<s>
Although	O
the	O
security	O
of	O
the	O
full	O
hash	B-Algorithm
algorithm	O
was	O
not	O
compromised	O
,	O
the	O
discovery	O
of	O
non-randomness	O
properties	O
with	O
low	O
time	O
complexities	O
raised	O
concerns	O
among	O
NIST	O
's	O
cryptographers	O
about	O
the	O
possibility	O
of	O
more	O
powerful	O
attacks	O
in	O
the	O
future	O
.	O
</s>
<s>
Shabal	B-Error_Name
uses	O
a	O
mode	O
of	O
operation	O
that	O
can	O
be	O
considered	O
as	O
a	O
variant	O
of	O
a	O
wide-pipe	O
,	O
Merkle	O
–	O
Damgård	O
hash	B-Algorithm
construction	O
.	O
</s>
<s>
The	O
internal	O
state	O
of	O
Shabal	B-Error_Name
consists	O
of	O
three	O
parts	O
,	O
denoted	O
as	O
A	O
,	O
B	O
and	O
C	O
.	O
The	O
keyed	O
permutation	O
of	O
Shabal	B-Error_Name
updates	O
A	O
and	O
B	O
using	O
nonlinear	O
feedback	O
shift	O
registers	O
that	O
interact	O
with	O
each	O
other	O
.	O
</s>
<s>
The	O
chaining	O
mode	O
of	O
Shabal	B-Error_Name
works	O
as	O
follows	O
:	O
</s>
<s>
Two	O
tunable	O
parameters	O
(	O
p	O
,	O
r	O
)	O
are	O
defined	O
for	O
Shabal	B-Error_Name
,	O
where	O
p	O
is	O
the	O
number	O
of	O
loops	O
performed	O
within	O
the	O
key	O
permutation	O
,	O
and	O
r	O
is	O
the	O
size	O
of	O
A	O
.	O
</s>
<s>
Additionally	O
,	O
p	O
and	O
r	O
should	O
satisfy	O
16p	O
≡	O
0	O
mod	O
r	O
.	O
The	O
same	O
internal	O
function	O
is	O
used	O
for	O
all	O
output	O
sizes	O
of	O
Shabal	B-Error_Name
.	O
</s>
<s>
Output	O
sizes	O
of	O
Shabal	B-Error_Name
,	O
based	O
on	O
length	O
of	O
the	O
digest	O
are	O
:	O
</s>
<s>
Example	O
Shabal	B-Error_Name
hashes	B-Algorithm
:	O
</s>
<s>
Various	O
distinguishers	O
have	O
been	O
proposed	O
for	O
the	O
permutation	O
of	O
Shabal	B-Error_Name
.	O
</s>
<s>
Using	O
cube	O
testers	O
,	O
a	O
statistical	O
non-randomness	O
property	O
of	O
Shabal	B-Error_Name
's	O
key	O
permutation	O
was	O
described	O
with	O
time	O
complexity	O
2300	O
.	O
</s>
<s>
A	O
rotational	O
distinguisher	O
to	O
the	O
keyed	O
permutation	O
of	O
Shabal	B-Error_Name
using	O
2171	O
calls	O
was	O
presented	O
.	O
</s>
<s>
However	O
,	O
the	O
attack	O
cannot	O
be	O
extended	O
to	O
the	O
hash	B-Algorithm
algorithm	O
,	O
due	O
to	O
the	O
non-symmetric	O
IV	O
,	O
the	O
addition	O
of	O
the	O
block	O
counter	O
and	O
the	O
existence	O
of	O
the	O
finalization	O
rounds	O
.	O
</s>
<s>
The	O
authors	O
also	O
presented	O
a	O
method	O
to	O
find	O
pseudo-collisions	O
and	O
pseudosecond-preimages	O
for	O
a	O
variant	O
of	O
Shabal	B-Error_Name
in	O
which	O
the	O
number	O
of	O
iterations	O
in	O
the	O
finalization	O
is	O
24N	O
(	O
N	O
≥	O
2	O
)	O
,	O
instead	O
of	O
36	O
.	O
</s>
<s>
However	O
,	O
this	O
attack	O
does	O
not	O
work	O
for	O
the	O
original	O
Shabal	B-Error_Name
,	O
since	O
it	O
is	O
not	O
possible	O
to	O
cancel	O
out	O
the	O
differences	O
when	O
the	O
number	O
of	O
iterations	O
is	O
36	O
.	O
</s>
<s>
A	O
low	O
weight	O
(	O
45-bit	O
)	O
pseudo-collision	O
attack	O
on	O
the	O
Shabal	B-Error_Name
compression	O
function	O
with	O
time	O
complexity	O
284	O
was	O
presented	O
.	O
</s>
<s>
A	O
preimage	O
attack	O
with	O
2497	O
time	O
and	O
2400	O
memory	O
complexity	O
for	O
Shabal	B-Error_Name
512	O
using	O
security	O
parameters	O
(	O
2	O
,	O
12	O
)	O
.	O
</s>
<s>
None	O
of	O
the	O
distinguishers	O
directly	O
threatens	O
the	O
claimed	O
security	O
of	O
the	O
hash	B-Algorithm
algorithm	O
.	O
</s>
