<s>
In	O
cryptography	O
,	O
integral	B-General_Concept
cryptanalysis	I-General_Concept
is	O
a	O
cryptanalytic	O
attack	O
that	O
is	O
particularly	O
applicable	O
to	O
block	O
ciphers	O
based	O
on	O
substitution	B-Algorithm
–	I-Algorithm
permutation	I-Algorithm
networks	I-Algorithm
.	O
</s>
<s>
It	O
was	O
originally	O
designed	O
by	O
Lars	O
Knudsen	O
as	O
a	O
dedicated	O
attack	O
against	O
Square	B-Algorithm
,	O
so	O
it	O
is	O
commonly	O
known	O
as	O
the	O
Square	B-General_Concept
attack	I-General_Concept
.	O
</s>
<s>
It	O
was	O
also	O
extended	O
to	O
a	O
few	O
other	O
ciphers	O
related	O
to	O
Square	B-Algorithm
:	O
CRYPTON	B-Algorithm
,	O
Rijndael	B-Algorithm
,	O
and	O
SHARK	B-Algorithm
.	O
</s>
<s>
Stefan	O
Lucks	O
generalized	O
the	O
attack	O
to	O
what	O
he	O
called	O
a	O
saturation	O
attack	O
and	O
used	O
it	O
to	O
attack	O
Twofish	B-Algorithm
,	O
which	O
is	O
not	O
at	O
all	O
similar	O
to	O
Square	B-Algorithm
,	O
having	O
a	O
radically	O
different	O
Feistel	B-Algorithm
network	I-Algorithm
structure	O
.	O
</s>
<s>
Forms	O
of	O
integral	B-General_Concept
cryptanalysis	I-General_Concept
have	O
since	O
been	O
applied	O
to	O
a	O
variety	O
of	O
ciphers	O
,	O
including	O
Hierocrypt	B-Algorithm
,	O
IDEA	B-Algorithm
,	O
Camellia	B-Algorithm
,	O
Skipjack	B-Algorithm
,	O
MISTY1	B-Algorithm
,	O
MISTY2	O
,	O
SAFER++	B-Algorithm
,	O
KHAZAD	B-Algorithm
,	O
and	O
FOX	O
(	O
now	O
called	O
IDEA	B-Algorithm
NXT	I-Algorithm
)	O
.	O
</s>
<s>
Unlike	O
differential	O
cryptanalysis	O
,	O
which	O
uses	O
pairs	O
of	O
chosen	O
plaintexts	O
with	O
a	O
fixed	O
XOR	B-Application
difference	O
,	O
integral	B-General_Concept
cryptanalysis	I-General_Concept
uses	O
sets	O
or	O
even	O
multisets	B-Language
of	O
chosen	O
plaintexts	O
of	O
which	O
part	O
is	O
held	O
constant	O
and	O
another	O
part	O
varies	O
through	O
all	O
possibilities	O
.	O
</s>
<s>
Such	O
a	O
set	O
necessarily	O
has	O
an	O
XOR	B-Application
sum	O
of	O
0	O
,	O
and	O
the	O
XOR	B-Application
sums	O
of	O
the	O
corresponding	O
sets	O
of	O
ciphertexts	O
provide	O
information	O
about	O
the	O
cipher	O
's	O
operation	O
.	O
</s>
<s>
This	O
contrast	O
between	O
the	O
differences	O
of	O
pairs	O
of	O
texts	O
and	O
the	O
sums	O
of	O
larger	O
sets	O
of	O
texts	O
inspired	O
the	O
name	O
"	O
integral	B-General_Concept
cryptanalysis	I-General_Concept
"	O
,	O
borrowing	O
the	O
terminology	O
of	O
calculus	O
.	O
</s>
