<s>
In	O
cryptography	O
,	O
a	O
product	B-Algorithm
cipher	I-Algorithm
combines	O
two	O
or	O
more	O
transformations	O
in	O
a	O
manner	O
intending	O
that	O
the	O
resulting	O
cipher	O
is	O
more	O
secure	O
than	O
the	O
individual	O
components	O
to	O
make	O
it	O
resistant	O
to	O
cryptanalysis	O
.	O
</s>
<s>
The	O
product	B-Algorithm
cipher	I-Algorithm
combines	O
a	O
sequence	O
of	O
simple	O
transformations	O
such	O
as	O
substitution	O
(	O
S-box	B-Algorithm
)	O
,	O
permutation	B-Algorithm
(	O
P-box	B-Algorithm
)	O
,	O
and	O
modular	O
arithmetic	O
.	O
</s>
<s>
The	O
concept	O
of	O
product	B-Algorithm
ciphers	I-Algorithm
is	O
due	O
to	O
Claude	O
Shannon	O
,	O
who	O
presented	O
the	O
idea	O
in	O
his	O
foundational	O
paper	O
,	O
Communication	O
Theory	O
of	O
Secrecy	O
Systems	O
.	O
</s>
<s>
A	O
particular	O
product	B-Algorithm
cipher	I-Algorithm
design	O
where	O
all	O
the	O
constituting	O
transformation	O
functions	O
have	O
the	O
same	O
structure	O
is	O
called	O
an	O
iterative	O
cipher	O
with	O
the	O
term	O
"	O
rounds	O
"	O
applied	O
to	O
the	O
functions	O
themselves	O
.	O
</s>
<s>
For	O
transformation	O
involving	O
reasonable	O
number	O
of	O
n	O
message	O
symbols	O
,	O
both	O
of	O
the	O
foregoing	O
cipher	O
systems	O
(	O
the	O
S-box	B-Algorithm
and	O
P-box	B-Algorithm
)	O
are	O
by	O
themselves	O
wanting	O
.	O
</s>
<s>
Shannon	O
suggested	O
using	O
a	O
combination	O
of	O
S-box	B-Algorithm
and	O
P-box	B-Algorithm
transformation	O
—	O
a	O
product	B-Algorithm
cipher	I-Algorithm
.	O
</s>
<s>
This	O
approach	O
of	O
alternatively	O
applying	O
substitution	O
and	O
permutation	B-Algorithm
transformation	O
has	O
been	O
used	O
by	O
IBM	O
in	O
the	O
Lucifer	B-Algorithm
cipher	I-Algorithm
system	O
,	O
and	O
has	O
become	O
the	O
standard	O
for	O
national	O
data	B-Algorithm
encryption	I-Algorithm
standards	I-Algorithm
such	O
as	O
the	O
Data	B-Algorithm
Encryption	I-Algorithm
Standard	I-Algorithm
and	O
the	O
Advanced	B-Algorithm
Encryption	I-Algorithm
Standard	I-Algorithm
.	O
</s>
<s>
A	O
product	B-Algorithm
cipher	I-Algorithm
that	O
uses	O
only	O
substitutions	O
and	O
permutations	B-Algorithm
is	O
called	O
a	O
SP-network	B-Algorithm
.	O
</s>
<s>
Feistel	B-Algorithm
ciphers	I-Algorithm
are	O
an	O
important	O
class	O
of	O
product	B-Algorithm
ciphers	I-Algorithm
.	O
</s>
