<s>
The	O
Texas	B-Architecture
Instruments	I-Architecture
signing	I-Architecture
key	I-Architecture
controversy	I-Architecture
resulted	O
from	O
Texas	O
Instruments	O
 '	O
(	O
TI	O
)	O
response	O
to	O
a	O
project	O
to	O
factorize	O
the	O
512-bit	O
RSA	B-Architecture
cryptographic	O
keys	O
needed	O
to	O
write	O
custom	O
firmware	B-Application
to	O
TI	O
devices	O
.	O
</s>
<s>
In	O
July	O
2009	O
,	O
Benjamin	O
Moody	O
,	O
a	O
United-TI	O
forum	B-Application
user	O
,	O
published	O
the	O
factors	O
of	O
a	O
512-bit	O
RSA	B-Architecture
key	O
used	O
to	O
sign	O
the	O
TI-83	B-Device
+	I-Device
series	I-Device
graphing	O
calculator	O
.	O
</s>
<s>
The	O
discovery	O
of	O
the	O
private	O
key	O
would	O
allow	O
end	O
users	O
to	O
flash	B-Device
their	O
own	O
operating	B-General_Concept
systems	I-General_Concept
onto	O
the	O
device	O
without	O
having	O
to	O
use	O
any	O
special	O
software	O
.	O
</s>
<s>
Moody	O
used	O
two	O
free	O
implementations	O
of	O
the	O
general	B-Algorithm
number	I-Algorithm
field	I-Algorithm
sieve	I-Algorithm
,	O
msieve	O
and	O
ggnfs	O
;	O
the	O
computation	O
took	O
73	O
days	O
on	O
a	O
1.9GHz	O
dual-core	O
processor	O
.	O
</s>
<s>
This	O
demonstrates	O
the	O
progress	O
of	O
hardware	O
development	O
:	O
the	O
factorization	O
of	O
the	O
similar	O
512-bit	O
RSA-155	O
in	O
1999	O
using	O
the	O
same	O
algorithm	O
required	O
a	O
large	O
dedicated	O
research	O
group	O
,	O
8000	O
MIPS-years	O
of	O
computing	O
time	O
,	O
and	O
a	O
Cray	B-Device
C916	I-Device
supercomputer	O
.	O
</s>
<s>
In	O
response	O
,	O
members	O
of	O
the	O
wider	O
TI	O
graphing	O
calculators	O
community	O
(	O
at	O
yAronet	O
)	O
set	O
up	O
a	O
BOINC-based	O
distributed	B-Architecture
computing	I-Architecture
project	O
,	O
RSA	B-Architecture
Lattice	O
Siever	O
(	O
RSALS	O
for	O
short	O
)	O
,	O
that	O
quickly	O
factored	O
the	O
other	O
keys	O
.	O
</s>
<s>
RSA	B-Architecture
Lattice	O
Siever	O
remained	O
active	O
for	O
nearly	O
three	O
years	O
after	O
outliving	O
its	O
initial	O
purpose	O
,	O
by	O
factoring	O
other	O
integers	O
for	O
the	O
mathematical	O
community	O
.	O
</s>
<s>
Texas	O
Instruments	O
began	O
by	O
sending	O
out	O
two	O
initial	O
Digital	O
Millennium	O
Copyright	O
Act	O
(	O
DMCA	O
)	O
take-down	O
requests	O
to	O
the	O
hackers	O
,	O
referring	O
to	O
sites	O
or	O
forum	B-Application
posts	O
that	O
they	O
controlled	O
.	O
</s>
<s>
TI	O
then	O
sent	O
further	O
DMCA	O
notices	O
to	O
a	O
variety	O
of	O
websites	O
displaying	O
the	O
keys	O
,	O
including	O
United-TI	O
,	O
Reddit	B-Application
,	O
and	O
Wikipedia	O
.	O
</s>
<s>
The	O
public	O
RSA	B-Architecture
parameters	O
of	O
the	O
original	O
TI-83	B-Device
+	I-Device
/	O
TI-83	B-Device
+	I-Device
Silver	O
Edition	O
OS	O
signing	O
key	O
factored	O
by	O
Benjamin	O
Moody	O
are	O
the	O
following	O
512-bit	O
modulus	O
n	O
and	O
public	O
(	O
or	O
encryption	O
)	O
exponent	O
e	O
(	O
specified	O
in	O
hexadecimal	O
)	O
:	O
</s>
<s>
The	O
keys	O
factored	O
by	O
RSA	B-Architecture
Lattice	O
Siever	O
(	O
the	O
TI-92	O
+	O
,	O
TI-73	B-Device
,	O
TI-89	B-Device
,	O
Voyage	O
200	O
,	O
TI-89	B-Device
Titanium	O
,	O
TI-84	B-Device
+	I-Device
/	O
TI-84	B-Device
Silver	O
Edition	O
OS	O
signing	O
and	O
date-stamp	O
signing	O
keys	O
)	O
are	O
similar	O
but	O
with	O
different	O
values	O
of	O
n	O
,	O
p	O
,	O
q	O
,	O
and	O
d	O
.	O
A	O
single	O
date-stamp	O
signing	O
key	O
is	O
shared	O
by	O
all	O
models	O
.	O
</s>
