<s>
The	O
Benaloh	B-Algorithm
Cryptosystem	I-Algorithm
is	O
an	O
extension	O
of	O
the	O
Goldwasser-Micali	B-Algorithm
cryptosystem	I-Algorithm
(	O
GM	O
)	O
created	O
in	O
1985	O
by	O
Josh	O
(	O
Cohen	O
)	O
Benaloh	O
.	O
</s>
<s>
The	O
main	O
improvement	O
of	O
the	O
Benaloh	B-Algorithm
Cryptosystem	I-Algorithm
over	O
GM	O
is	O
that	O
longer	O
blocks	O
of	O
data	O
can	O
be	O
encrypted	O
at	O
once	O
,	O
whereas	O
in	O
GM	O
each	O
bit	O
is	O
encrypted	O
individually	O
.	O
</s>
<s>
Like	O
many	O
public	B-Application
key	I-Application
cryptosystems	I-Application
,	O
this	O
scheme	O
works	O
in	O
the	O
group	O
where	O
n	O
is	O
a	O
product	O
of	O
two	O
large	O
primes	O
.	O
</s>
<s>
The	O
public	B-Application
key	I-Application
is	O
then	O
,	O
and	O
the	O
private	B-Application
key	I-Application
is	O
.	O
</s>
<s>
For	O
larger	O
values	O
of	O
r	O
,	O
the	O
Baby-step	B-Language
giant-step	I-Language
algorithm	O
can	O
be	O
used	O
to	O
recover	O
m	O
in	O
time	O
and	O
space	O
.	O
</s>
