<s>
A	O
Byzantine	B-Operating_System
fault	I-Operating_System
(	O
also	O
Byzantine	B-Operating_System
generals	I-Operating_System
problem	I-Operating_System
,	O
interactive	O
consistency	O
,	O
source	O
congruency	O
,	O
error	B-Operating_System
avalanche	I-Operating_System
,	O
Byzantine	B-Operating_System
agreement	I-Operating_System
problem	I-Operating_System
,	O
and	O
Byzantine	B-Operating_System
failure	I-Operating_System
)	O
is	O
a	O
condition	O
of	O
a	O
computer	O
system	O
,	O
particularly	O
distributed	B-Architecture
computing	I-Architecture
systems	O
,	O
where	O
components	O
may	O
fail	O
and	O
there	O
is	O
imperfect	O
information	O
on	O
whether	O
a	O
component	O
has	O
failed	O
.	O
</s>
<s>
The	O
term	O
takes	O
its	O
name	O
from	O
an	O
allegory	B-Algorithm
,	O
the	O
"	O
Byzantine	B-Operating_System
generals	I-Operating_System
problem	I-Operating_System
"	O
,	O
developed	O
to	O
describe	O
a	O
situation	O
in	O
which	O
,	O
in	O
order	O
to	O
avoid	O
catastrophic	O
failure	O
of	O
the	O
system	O
,	O
the	O
system	O
's	O
actors	O
must	O
agree	O
on	O
a	O
concerted	O
strategy	O
,	O
but	O
some	O
of	O
these	O
actors	O
are	O
unreliable	O
.	O
</s>
<s>
In	O
a	O
Byzantine	B-Operating_System
fault	I-Operating_System
,	O
a	O
component	O
such	O
as	O
a	O
server	B-Application
can	O
inconsistently	O
appear	O
both	O
failed	O
and	O
functioning	O
to	O
failure-detection	O
systems	O
,	O
presenting	O
different	O
symptoms	O
to	O
different	O
observers	O
.	O
</s>
<s>
It	O
is	O
difficult	O
for	O
the	O
other	O
components	O
to	O
declare	O
it	O
failed	O
and	O
shut	O
it	O
out	O
of	O
the	O
network	O
,	O
because	O
they	O
need	O
to	O
first	O
reach	O
a	O
consensus	B-Operating_System
regarding	O
which	O
component	O
has	O
failed	O
in	O
the	O
first	O
place	O
.	O
</s>
<s>
Byzantine	B-Operating_System
fault	I-Operating_System
tolerance	I-Operating_System
(	O
BFT	O
)	O
is	O
the	O
resiliency	O
of	O
a	O
fault-tolerant	B-General_Concept
computer	I-General_Concept
system	I-General_Concept
to	O
such	O
conditions	O
.	O
</s>
<s>
Byzantine	B-Operating_System
fault	I-Operating_System
tolerance	I-Operating_System
can	O
be	O
achieved	O
if	O
the	O
loyal	O
(	O
non-faulty	O
)	O
generals	O
have	O
a	O
majority	O
agreement	O
on	O
their	O
strategy	O
.	O
</s>
<s>
For	O
example	O
,	O
missing	O
messages	O
can	O
be	O
given	O
a	O
"	B-Error_Name
null	I-Error_Name
"	I-Error_Name
value	I-Error_Name
.	O
</s>
<s>
Thus	O
,	O
a	O
component	O
may	O
appear	O
functioning	O
to	O
one	O
component	O
and	O
faulty	O
to	O
another	O
,	O
which	O
prevents	O
forming	O
a	O
consensus	B-Operating_System
as	O
to	O
whether	O
the	O
component	O
is	O
faulty	O
or	O
not	O
.	O
</s>
<s>
A	O
Byzantine	B-Operating_System
fault	I-Operating_System
is	O
any	O
fault	O
presenting	O
different	O
symptoms	O
to	O
different	O
observers	O
.	O
</s>
<s>
A	O
Byzantine	B-Operating_System
failure	I-Operating_System
is	O
the	O
loss	O
of	O
a	O
system	O
service	O
due	O
to	O
a	O
Byzantine	B-Operating_System
fault	I-Operating_System
in	O
systems	O
that	O
require	O
consensus	B-Operating_System
among	O
distributed	O
nodes	O
.	O
</s>
<s>
The	O
objective	O
of	O
Byzantine	B-Operating_System
fault	I-Operating_System
tolerance	I-Operating_System
is	O
to	O
be	O
able	O
to	O
defend	O
against	O
failures	O
of	O
system	O
components	O
with	O
or	O
without	O
symptoms	O
that	O
prevent	O
other	O
components	O
of	O
the	O
system	O
from	O
reaching	O
an	O
agreement	O
among	O
themselves	O
,	O
where	O
such	O
an	O
agreement	O
is	O
needed	O
for	O
the	O
correct	O
operation	O
of	O
the	O
system	O
.	O
</s>
<s>
The	O
remaining	O
operationally	O
correct	O
components	O
of	O
a	O
Byzantine	B-Operating_System
fault	I-Operating_System
tolerant	O
system	O
will	O
be	O
able	O
to	O
continue	O
providing	O
the	O
system	O
's	O
service	O
as	O
originally	O
intended	O
,	O
assuming	O
there	O
are	O
a	O
sufficient	O
number	O
of	O
accurately-operating	O
components	O
to	O
maintain	O
the	O
service	O
.	O
</s>
<s>
Byzantine	B-Operating_System
failures	I-Operating_System
are	O
considered	O
the	O
most	O
general	O
and	O
most	O
difficult	O
class	O
of	O
failures	O
among	O
the	O
failure	O
modes	O
.	O
</s>
<s>
Whereas	O
fail-stop	O
failure	O
mode	O
simply	O
means	O
that	O
the	O
only	O
way	O
to	O
fail	O
is	O
a	O
node	B-Data_Structure
crash	O
,	O
detected	O
by	O
other	O
nodes	O
,	O
Byzantine	B-Operating_System
failures	I-Operating_System
imply	O
no	O
restrictions	O
,	O
which	O
means	O
that	O
the	O
failed	O
node	B-Data_Structure
can	O
generate	O
arbitrary	O
data	O
,	O
including	O
data	O
that	O
makes	O
it	O
appear	O
like	O
a	O
functioning	O
node	B-Data_Structure
.	O
</s>
<s>
Thus	O
,	O
Byzantine	B-Operating_System
failures	I-Operating_System
can	O
confuse	O
failure	O
detection	O
systems	O
,	O
which	O
makes	O
fault	B-General_Concept
tolerance	I-General_Concept
difficult	O
.	O
</s>
<s>
Despite	O
the	O
analogy	O
,	O
a	O
Byzantine	B-Operating_System
failure	I-Operating_System
is	O
not	O
necessarily	O
a	O
security	O
problem	O
involving	O
hostile	O
human	O
interference	O
:	O
it	O
can	O
arise	O
purely	O
from	O
electrical	O
or	O
software	O
faults	O
.	O
</s>
<s>
The	O
terms	O
fault	O
and	O
failure	O
are	O
used	O
here	O
according	O
to	O
the	O
standard	O
definitions	O
originally	O
created	O
by	O
a	O
joint	O
committee	O
on	O
"	O
Fundamental	O
Concepts	O
and	O
Terminology	O
"	O
formed	O
by	O
the	O
IEEE	O
Computer	O
Society	O
's	O
Technical	O
Committee	O
on	O
Dependable	O
Computing	O
and	O
Fault-Tolerance	B-General_Concept
and	O
IFIP	O
Working	O
Group	O
10.4	O
on	O
Dependable	O
Computing	O
and	O
Fault	B-General_Concept
Tolerance	I-General_Concept
.	O
</s>
<s>
See	O
also	O
dependability	B-Application
.	O
</s>
<s>
Byzantine	B-Operating_System
fault	I-Operating_System
tolerance	I-Operating_System
is	O
only	O
concerned	O
with	O
broadcast	O
consistency	O
,	O
that	O
is	O
,	O
the	O
property	O
that	O
when	O
one	O
component	O
broadcasts	O
a	O
single	O
consistent	O
value	O
to	O
other	O
components	O
(	O
i.e.	O
,	O
sends	O
the	O
same	O
value	O
to	O
the	O
other	O
components	O
)	O
,	O
they	O
all	O
receive	O
exactly	O
the	O
same	O
value	O
,	O
or	O
in	O
the	O
case	O
that	O
the	O
broadcaster	O
is	O
not	O
consistent	O
,	O
the	O
other	O
components	O
agree	O
on	O
a	O
common	O
value	O
.	O
</s>
<s>
This	O
kind	O
of	O
fault	B-General_Concept
tolerance	I-General_Concept
does	O
not	O
encompass	O
the	O
correctness	O
of	O
the	O
value	O
itself	O
;	O
for	O
example	O
,	O
an	O
adversarial	O
component	O
that	O
deliberately	O
sends	O
an	O
incorrect	O
value	O
,	O
but	O
sends	O
that	O
same	O
value	O
consistently	O
to	O
all	O
components	O
,	O
will	O
not	O
be	O
caught	O
in	O
the	O
Byzantine	B-Operating_System
fault	I-Operating_System
tolerance	I-Operating_System
scheme	O
.	O
</s>
<s>
Property	O
:	O
The	O
system	O
is	O
said	O
to	O
resist	O
Byzantine	B-Operating_System
faults	I-Operating_System
if	O
a	O
component	O
can	O
broadcast	O
a	O
value	O
,	O
and	O
then	O
:	O
</s>
<s>
The	O
problem	O
of	O
obtaining	O
Byzantine	O
consensus	B-Operating_System
was	O
conceived	O
and	O
formalized	O
by	O
Robert	O
Shostak	O
,	O
who	O
dubbed	O
it	O
the	O
interactive	O
consistency	O
problem	O
.	O
</s>
<s>
SIFT	O
(	O
for	O
Software	O
Implemented	O
Fault	B-General_Concept
Tolerance	I-General_Concept
)	O
was	O
the	O
brain	O
child	O
of	O
John	O
Wensley	O
,	O
and	O
was	O
based	O
on	O
the	O
idea	O
of	O
using	O
multiple	O
general-purpose	O
computers	O
that	O
would	O
communicate	O
through	O
pairwise	O
messaging	O
in	O
order	O
to	O
reach	O
a	O
consensus	B-Operating_System
,	O
even	O
if	O
some	O
of	O
the	O
computers	O
were	O
faulty	O
.	O
</s>
<s>
At	O
the	O
beginning	O
of	O
the	O
project	O
,	O
it	O
was	O
not	O
clear	O
how	O
many	O
computers	O
in	O
total	O
were	O
needed	O
to	O
guarantee	O
that	O
a	O
conspiracy	O
of	O
n	O
faulty	O
computers	O
could	O
not	O
"	O
thwart	O
"	O
the	O
efforts	O
of	O
the	O
correctly-operating	O
ones	O
to	O
reach	O
consensus	B-Operating_System
.	O
</s>
<s>
To	O
make	O
the	O
interactive	O
consistency	O
problem	O
easier	O
to	O
understand	O
,	O
Lamport	O
devised	O
a	O
colorful	O
allegory	B-Algorithm
in	O
which	O
a	O
group	O
of	O
army	O
generals	O
formulate	O
a	O
plan	O
for	O
attacking	O
a	O
city	O
.	O
</s>
<s>
This	O
formulation	O
of	O
the	O
problem	O
,	O
together	O
with	O
some	O
additional	O
results	O
,	O
were	O
presented	O
by	O
the	O
same	O
authors	O
in	O
their	O
1982	O
paper	O
,	O
"	O
The	O
Byzantine	B-Operating_System
Generals	I-Operating_System
Problem	I-Operating_System
"	O
.	O
</s>
<s>
Several	O
examples	O
of	O
Byzantine	B-Operating_System
failures	I-Operating_System
that	O
have	O
occurred	O
are	O
given	O
in	O
two	O
equivalent	O
journal	O
papers	O
.	O
</s>
<s>
One	O
example	O
of	O
BFT	O
in	O
use	O
is	O
Bitcoin	B-General_Concept
,	O
a	O
peer-to-peer	O
digital	O
cash	O
system	O
.	O
</s>
<s>
The	O
Bitcoin	B-General_Concept
network	I-General_Concept
works	O
in	O
parallel	O
to	O
generate	O
a	O
blockchain	B-Application
with	O
proof-of-work	O
allowing	O
the	O
system	O
to	O
overcome	O
Byzantine	B-Operating_System
failures	I-Operating_System
and	O
reach	O
a	O
coherent	O
global	O
view	O
of	O
the	O
system	O
's	O
state	O
.	O
</s>
<s>
Some	O
proof	B-Protocol
of	I-Protocol
stake	I-Protocol
blockchains	B-Application
also	O
use	O
BFT	O
algorithms	O
.	O
</s>
<s>
Some	O
aircraft	O
systems	O
,	O
such	O
as	O
the	O
Boeing	O
777	O
Aircraft	B-Device
Information	I-Device
Management	I-Device
System	I-Device
(	O
via	O
its	O
ARINC	O
659	O
SAFEbus	O
network	O
)	O
,	O
</s>
<s>
the	O
Boeing	O
777	O
flight	O
control	O
system	O
,	O
and	O
the	O
Boeing	O
787	O
flight	O
control	O
systems	O
use	O
Byzantine	B-Operating_System
fault	I-Operating_System
tolerance	I-Operating_System
;	O
because	O
these	O
are	O
real-time	O
systems	O
,	O
their	O
Byzantine	B-Operating_System
fault	I-Operating_System
tolerance	I-Operating_System
solutions	O
must	O
have	O
very	O
low	O
latency	O
.	O
</s>
<s>
For	O
example	O
,	O
SAFEbus	O
can	O
achieve	O
Byzantine	B-Operating_System
fault	I-Operating_System
tolerance	I-Operating_System
within	O
the	O
order	O
of	O
a	O
microsecond	O
of	O
added	O
latency	O
.	O
</s>
<s>
The	O
SpaceX	O
Dragon	O
considers	O
Byzantine	B-Operating_System
fault	I-Operating_System
tolerance	I-Operating_System
in	O
its	O
design	O
.	O
</s>
<s>
Byzantine	B-Operating_System
fault	I-Operating_System
tolerance	I-Operating_System
mechanisms	O
use	O
components	O
that	O
repeat	O
an	O
incoming	O
message	O
(	O
or	O
just	O
its	O
signature	O
)	O
to	O
other	O
recipients	O
of	O
that	O
incoming	O
message	O
.	O
</s>
<s>
One	O
solution	O
considers	O
scenarios	O
in	O
which	O
messages	O
may	O
be	O
forged	O
,	O
but	O
which	O
will	O
be	O
Byzantine-fault-tolerant	O
as	O
long	O
as	O
the	O
number	O
of	O
disloyal	O
generals	O
is	O
less	O
than	O
one	O
third	O
of	O
the	O
generals	O
.	O
</s>
<s>
For	O
security-critical	O
systems	O
,	O
digital	O
signatures	O
(	O
in	O
modern	O
computer	O
systems	O
,	O
this	O
may	O
be	O
achieved	O
in	O
practice	O
using	O
public-key	B-Application
cryptography	I-Application
)	O
can	O
provide	O
Byzantine	B-Operating_System
fault	I-Operating_System
tolerance	I-Operating_System
in	O
the	O
presence	O
of	O
an	O
arbitrary	O
number	O
of	O
traitorous	O
generals	O
.	O
</s>
<s>
However	O
,	O
for	O
safety-critical	B-Application
systems	I-Application
(	O
where	O
"	O
security	O
"	O
addresses	O
intelligent	O
threats	O
while	O
"	O
safety	O
"	O
addresses	O
the	O
inherent	O
dangers	O
of	O
an	O
activity	O
or	O
mission	O
)	O
,	O
simple	O
error	O
detecting	O
codes	O
,	O
such	O
as	O
CRCs	O
,	O
provide	O
weaker	O
but	O
often	O
sufficient	O
coverage	O
at	O
a	O
much	O
lower	O
cost	O
.	O
</s>
<s>
Thus	O
,	O
cryptographic	O
digital	O
signature	O
methods	O
are	O
not	O
a	O
good	O
choice	O
for	O
safety-critical	B-Application
systems	I-Application
,	O
unless	O
there	O
is	O
also	O
a	O
specific	O
security	O
threat	O
as	O
well	O
.	O
</s>
<s>
While	O
error	O
detecting	O
codes	O
,	O
such	O
as	O
CRCs	O
,	O
are	O
better	O
than	O
cryptographic	O
techniques	O
,	O
neither	O
provide	O
adequate	O
coverage	O
for	O
active	O
electronics	O
in	O
safety-critical	B-Application
systems	I-Application
.	O
</s>
<s>
Also	O
presented	O
is	O
a	O
variation	O
on	O
the	O
first	O
two	O
solutions	O
allowing	O
Byzantine-fault-tolerant	O
behavior	O
in	O
some	O
situations	O
where	O
not	O
all	O
generals	O
can	O
communicate	O
directly	O
with	O
each	O
other	O
.	O
</s>
<s>
Several	O
system	O
architectures	O
were	O
designed	O
c	O
.	O
1980	O
that	O
implemented	O
Byzantine	B-Operating_System
fault	I-Operating_System
tolerance	I-Operating_System
.	O
</s>
<s>
In	O
1999	O
,	O
Miguel	O
Castro	O
and	O
Barbara	O
Liskov	O
introduced	O
the	O
"	O
Practical	O
Byzantine	B-Operating_System
Fault	I-Operating_System
Tolerance	I-Operating_System
"	O
(	O
PBFT	B-Operating_System
)	O
algorithm	O
,	O
which	O
provides	O
high-performance	O
Byzantine	O
state	O
machine	O
replication	O
,	O
processing	O
thousands	O
of	O
requests	O
per	O
second	O
with	O
sub-millisecond	O
increases	O
in	O
latency	O
.	O
</s>
<s>
After	O
PBFT	B-Operating_System
,	O
several	O
BFT	O
protocols	O
were	O
introduced	O
to	O
improve	O
its	O
robustness	O
and	O
performance	O
.	O
</s>
<s>
Furthermore	O
,	O
BFT	O
protocols	O
were	O
introduced	O
that	O
leverage	O
trusted	O
components	O
to	O
reduce	O
the	O
number	O
of	O
replicas	O
,	O
e.g.	O
,	O
A2M-PBFT-EA	O
and	O
MinBFT	O
.	O
</s>
