<s>
The	O
Naccache	B-Algorithm
–	I-Algorithm
Stern	I-Algorithm
cryptosystem	I-Algorithm
is	O
a	O
homomorphic	O
public-key	B-Application
cryptosystem	I-Application
whose	O
security	O
rests	O
on	O
the	O
higher	O
residuosity	O
problem	O
.	O
</s>
<s>
The	O
Naccache	B-Algorithm
–	I-Algorithm
Stern	I-Algorithm
cryptosystem	I-Algorithm
was	O
discovered	O
by	O
David	O
Naccache	O
and	O
Jacques	O
Stern	O
in	O
1998	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
the	O
numbers	O
σ	O
,	O
n	O
,	O
g	O
and	O
the	O
private	B-Application
key	I-Application
is	O
the	O
pair	O
p	O
,	O
q	O
.	O
</s>
<s>
When	O
k	O
=	O
1	O
this	O
is	O
essentially	O
the	O
Benaloh	B-Algorithm
cryptosystem	I-Algorithm
.	O
</s>
<s>
The	O
semantic	O
security	O
of	O
the	O
Naccache	B-Algorithm
–	I-Algorithm
Stern	I-Algorithm
cryptosystem	I-Algorithm
rests	O
on	O
an	O
extension	O
of	O
the	O
quadratic	O
residuosity	O
problem	O
known	O
as	O
the	O
higher	O
residuosity	O
problem	O
.	O
</s>
