<s>
The	O
Goldreich	O
–	O
Goldwasser	O
–	O
Halevi	O
(	O
GGH	O
)	O
lattice-based	O
cryptosystem	B-General_Concept
is	O
an	O
asymmetric	B-Application
cryptosystem	I-Application
based	O
on	O
lattices	O
.	O
</s>
<s>
There	O
is	O
also	O
a	O
GGH	B-Algorithm
signature	I-Algorithm
scheme	I-Algorithm
.	O
</s>
<s>
The	O
Goldreich	O
–	O
Goldwasser	O
–	O
Halevi	O
(	O
GGH	O
)	O
cryptosystem	B-General_Concept
makes	O
use	O
of	O
the	O
fact	O
that	O
the	O
closest	O
vector	O
problem	O
can	O
be	O
a	O
hard	O
problem	O
.	O
</s>
<s>
The	O
GGH	B-Algorithm
encryption	I-Algorithm
scheme	I-Algorithm
was	O
cryptanalyzed	O
(	O
broken	O
)	O
in	O
1999	O
by	O
.	O
</s>
<s>
Nguyen	O
and	O
Oded	O
Regev	O
had	O
cryptanalyzed	O
the	O
related	O
GGH	B-Algorithm
signature	I-Algorithm
scheme	I-Algorithm
in	O
2006	O
.	O
</s>
<s>
GGH	O
involves	O
a	O
private	B-Application
key	I-Application
and	O
a	O
public	B-Application
key	I-Application
.	O
</s>
<s>
The	O
private	B-Application
key	I-Application
is	O
a	O
basis	O
of	O
a	O
lattice	O
with	O
good	O
properties	O
(	O
such	O
as	O
short	O
nearly	O
orthogonal	O
vectors	O
)	O
and	O
a	O
unimodular	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
The	O
public	B-Application
key	I-Application
is	O
another	O
basis	O
of	O
the	O
lattice	O
of	O
the	O
form	O
.	O
</s>
<s>
In	O
1999	O
,	O
Nguyen	O
showed	O
that	O
the	O
GGH	B-Algorithm
encryption	I-Algorithm
scheme	I-Algorithm
has	O
a	O
flaw	O
in	O
the	O
design	O
.	O
</s>
