<s>
Inversive	B-Algorithm
congruential	I-Algorithm
generators	I-Algorithm
are	O
a	O
type	O
of	O
nonlinear	O
congruential	O
pseudorandom	B-Algorithm
number	I-Algorithm
generator	I-Algorithm
,	O
which	O
use	O
the	O
modular	O
multiplicative	O
inverse	O
(	O
if	O
it	O
exists	O
)	O
to	O
generate	O
the	O
next	O
number	O
in	O
a	O
sequence	O
.	O
</s>
<s>
The	O
standard	O
formula	O
for	O
an	O
inversive	B-Algorithm
congruential	I-Algorithm
generator	I-Algorithm
,	O
modulo	O
some	O
prime	O
q	O
is	O
:	O
</s>
<s>
Eichenauer-Herrmann	O
,	O
Lehn	O
,	O
Grothe	O
and	O
Niederreiter	O
have	O
shown	O
that	O
inversive	B-Algorithm
congruential	I-Algorithm
generators	I-Algorithm
have	O
good	O
uniformity	O
properties	O
,	O
in	O
particular	O
with	O
regard	O
to	O
lattice	O
structure	O
and	O
serial	O
correlations	O
.	O
</s>
<s>
The	O
construction	O
of	O
a	O
compound	O
inversive	O
generator	O
(	O
CIG	O
)	O
relies	O
on	O
combining	O
two	O
or	O
more	O
inversive	B-Algorithm
congruential	I-Algorithm
generators	I-Algorithm
according	O
to	O
the	O
method	O
described	O
below	O
.	O
</s>
<s>
The	O
compound	O
approach	O
allows	O
combining	O
inversive	B-Algorithm
congruential	I-Algorithm
generators	I-Algorithm
,	O
provided	O
they	O
have	O
full	O
period	O
,	O
in	O
parallel	O
generation	O
systems	O
.	O
</s>
<s>
Thirdly	O
,	O
compound	O
approach	O
has	O
the	O
same	O
properties	O
as	O
single	O
inversive	O
generators	O
,	O
but	O
it	O
also	O
provides	O
period	O
length	O
significantly	O
greater	O
than	O
obtained	O
by	O
a	O
single	O
inversive	B-Algorithm
congruential	I-Algorithm
generator	I-Algorithm
.	O
</s>
<s>
The	O
procedure	O
of	O
designing	O
this	O
complex	O
structure	O
starts	O
with	O
defining	O
finite	O
field	O
of	O
p	O
elements	O
and	O
ends	O
with	O
choosing	O
the	O
parameters	O
a	O
and	O
c	O
for	O
each	O
inversive	B-Algorithm
congruential	I-Algorithm
generator	I-Algorithm
being	O
the	O
component	O
of	O
the	O
compound	O
generator	O
.	O
</s>
<s>
Such	O
a	O
condition	O
is	O
sufficient	O
for	O
maximum	O
period	O
of	O
each	O
inversive	B-Algorithm
congruential	I-Algorithm
generator	I-Algorithm
and	O
finally	O
for	O
maximum	O
period	O
of	O
the	O
compound	O
generator	O
.	O
</s>
<s>
The	O
construction	O
of	O
IMP	O
polynomials	O
is	O
the	O
most	O
efficient	O
approach	O
to	O
find	O
parameters	O
for	O
inversive	B-Algorithm
congruential	I-Algorithm
generator	I-Algorithm
with	O
maximum	O
period	O
length	O
.	O
</s>
<s>
A	O
low	O
discrepancy	O
means	O
that	O
the	O
sequence	O
generated	O
can	O
be	O
used	O
for	O
cryptographic	O
purposes	O
,	O
and	O
the	O
first	O
aim	O
of	O
the	O
inversive	B-Algorithm
congruential	I-Algorithm
generator	I-Algorithm
is	O
to	O
provide	O
pseudorandom	O
numbers	O
.	O
</s>
