<s>
Double-spending	B-Operating_System
is	O
a	O
fundamental	O
flaw	O
in	O
a	O
digital	O
cash	O
protocol	O
in	O
which	O
the	O
same	O
single	O
digital	O
token	O
can	O
be	O
spent	O
more	O
than	O
once	O
.	O
</s>
<s>
As	O
with	O
counterfeit	O
money	O
,	O
such	O
double-spending	B-Operating_System
leads	O
to	O
inflation	O
by	O
creating	O
a	O
new	O
amount	O
of	O
copied	O
currency	O
that	O
did	O
not	O
previously	O
exist	O
.	O
</s>
<s>
Fundamental	O
cryptographic	O
techniques	O
to	O
prevent	O
double-spending	B-Operating_System
,	O
while	O
preserving	O
anonymity	O
in	O
a	O
transaction	O
,	O
are	O
the	O
introduction	O
of	O
an	O
authority	O
(	O
and	O
hence	O
centralization	O
)	O
for	O
blind	O
signatures	O
and	O
,	O
particularly	O
in	O
offline	O
systems	O
,	O
secret	O
splitting	O
.	O
</s>
<s>
Prevention	O
of	O
double-spending	B-Operating_System
is	O
usually	O
implemented	O
using	O
an	O
online	O
central	O
trusted	O
third	O
party	O
that	O
can	O
verify	O
whether	O
a	O
token	O
has	O
been	O
spent	O
.	O
</s>
<s>
This	O
normally	O
represents	O
a	O
single	B-Architecture
point	I-Architecture
of	I-Architecture
failure	I-Architecture
from	O
both	O
availability	O
and	O
trust	O
viewpoints	O
.	O
</s>
<s>
In	O
a	O
decentralized	O
system	O
,	O
the	O
double-spending	B-Operating_System
problem	O
is	O
significantly	O
harder	O
to	O
solve	O
.	O
</s>
<s>
To	O
avoid	O
the	O
need	O
for	O
a	O
trusted	O
third	O
party	O
,	O
many	O
servers	O
must	O
store	O
identical	O
up-to-date	O
copies	O
of	O
a	O
public	O
transaction	O
ledger	B-Language
,	O
but	O
as	O
transactions	O
(	O
requests	O
to	O
spend	O
money	O
)	O
are	O
broadcast	O
,	O
they	O
will	O
arrive	O
at	O
each	O
server	O
at	O
slightly	O
different	O
times	O
.	O
</s>
<s>
Most	O
decentralized	O
systems	O
solve	O
this	O
problem	O
with	O
a	O
consensus	B-Operating_System
algorithm	I-Operating_System
,	O
a	O
way	O
to	O
bring	O
the	O
servers	O
back	O
in	O
sync	O
.	O
</s>
<s>
Two	O
notable	O
types	O
of	O
consensus	B-Operating_System
mechanisms	O
are	O
proof-of-work	O
and	O
proof-of-stake	B-Protocol
.	O
</s>
<s>
By	O
2007	O
,	O
a	O
number	O
of	O
distributed	B-Architecture
systems	I-Architecture
for	O
the	O
prevention	O
of	O
double-spending	B-Operating_System
had	O
been	O
proposed	O
.	O
</s>
<s>
The	O
cryptocurrency	O
Bitcoin	B-Protocol
implemented	O
a	O
solution	O
in	O
early	O
2009	O
.	O
</s>
<s>
Its	O
cryptographic	B-Protocol
protocol	I-Protocol
used	O
a	O
proof-of-work	O
consensus	B-Operating_System
mechanism	O
where	O
transactions	O
are	O
batched	O
into	O
blocks	O
and	O
chained	O
together	O
using	O
a	O
linked	B-Data_Structure
list	I-Data_Structure
of	O
hash	O
pointers	O
(	O
blockchain	B-Application
)	O
.	O
</s>
<s>
Any	O
server	O
can	O
produce	O
a	O
block	O
by	O
solving	O
a	O
computationally	O
difficult	O
puzzle	O
(	O
specifically	O
finding	O
a	O
partial	O
hash	B-Algorithm
collision	I-Algorithm
)	O
called	O
mining	O
.	O
</s>
<s>
The	O
block	O
commits	O
to	O
the	O
entire	O
history	O
of	O
bitcoin	B-Protocol
transactions	O
as	O
well	O
as	O
the	O
new	O
set	O
of	O
incoming	O
transactions	O
.	O
</s>
<s>
The	O
miner	O
is	O
rewarded	O
some	O
bitcoins	B-Protocol
for	O
solving	O
it	O
.	O
</s>
<s>
The	O
double-spending	B-Operating_System
problem	O
persists	O
,	O
however	O
,	O
if	O
two	O
blocks	O
(	O
with	O
conflicting	O
transactions	O
)	O
are	O
mined	O
at	O
the	O
same	O
approximate	O
time	O
.	O
</s>
<s>
Due	O
to	O
the	O
nature	O
of	O
a	O
decentralized	O
blockchain	B-Application
,	O
and	O
in	O
lack	O
of	O
a	O
central	O
authority	O
to	O
do	O
so	O
,	O
the	O
correct	O
succession	O
of	O
transactions	O
is	O
defined	O
only	O
by	O
the	O
dominating	O
consensus	B-Operating_System
.	O
</s>
<s>
This	O
leads	O
to	O
the	O
possibility	O
of	O
one	O
actor	O
gaining	O
majority	O
control	O
over	O
the	O
entities	O
deciding	O
said	O
consensus	B-Operating_System
,	O
to	O
force	O
their	O
own	O
version	O
of	O
events	O
,	O
including	O
alternative	O
and	O
double	O
transactions	O
.	O
</s>
<s>
Larger	O
computational	O
power	O
increases	O
the	O
chance	O
to	O
win	O
the	O
mining	O
reward	O
for	O
each	O
new	O
block	O
mined	O
,	O
which	O
creates	O
an	O
incentive	O
to	O
accumulate	O
clusters	O
of	O
mining	O
nodes	O
,	O
or	O
mining	B-Protocol
pools	I-Protocol
.	O
</s>
<s>
Any	O
pool	O
that	O
achieves	O
51%	O
hashing	O
power	O
can	O
effectively	O
overturn	O
network	O
transactions	O
,	O
resulting	O
in	O
double	B-Operating_System
spending	I-Operating_System
.	O
</s>
<s>
One	O
of	O
the	O
Bitcoin	B-Protocol
forks	O
,	O
Bitcoin	B-Protocol
Gold	I-Protocol
,	O
was	O
hit	O
by	O
such	O
an	O
attack	O
in	O
2018	O
and	O
then	O
again	O
in	O
2020	O
.	O
</s>
<s>
In	O
2014	O
,	O
mining	B-Protocol
pool	I-Protocol
Ghash.io	O
obtained	O
51%	O
hashing	O
power	O
in	O
Bitcoin	B-Protocol
which	O
raised	O
significant	O
controversies	O
about	O
the	O
safety	O
of	O
the	O
network	O
.	O
</s>
