<s>
In	O
cryptography	O
,	O
a	O
padded	B-Algorithm
uniform	O
random	O
blob	O
or	O
PURB	B-Algorithm
is	O
a	O
discipline	O
for	O
encrypted	O
data	O
formats	O
designed	O
to	O
minimize	O
unintended	O
information	O
leakage	O
either	O
from	O
its	O
encryption	O
format	O
metadata	O
or	O
from	O
its	O
total	O
length	O
.	O
</s>
<s>
When	O
properly	O
created	O
,	O
a	O
PURB	B-Algorithm
's	O
content	O
is	O
indistinguishable	O
from	O
a	O
uniform	O
random	O
bit	O
string	O
to	O
any	O
observer	O
without	O
a	O
relevant	O
decryption	O
key	O
.	O
</s>
<s>
A	O
PURB	B-Algorithm
therefore	O
leaks	O
no	O
information	O
through	O
headers	O
or	O
other	O
cleartext	O
metadata	O
associated	O
with	O
the	O
encrypted	O
data	O
format	O
.	O
</s>
<s>
This	O
leakage	O
minimization	O
"	O
hygiene	O
"	O
practice	O
contrasts	O
with	O
traditional	O
encrypted	O
data	O
formats	O
such	O
as	O
Pretty	B-Application
Good	I-Application
Privacy	I-Application
,	O
which	O
include	O
cleartext	O
metadata	O
encoding	O
information	O
such	O
as	O
the	O
application	O
that	O
created	O
the	O
data	O
,	O
the	O
data	O
format	O
version	O
,	O
the	O
number	O
of	O
recipients	O
the	O
data	O
is	O
encrypted	O
for	O
,	O
the	O
identities	O
or	O
public	B-Application
keys	I-Application
of	O
the	O
recipients	O
,	O
and	O
the	O
ciphers	O
or	O
suites	O
that	O
were	O
used	O
to	O
encrypt	O
the	O
data	O
.	O
</s>
<s>
While	O
such	O
encryption	O
metadata	O
was	O
considered	O
non-sensitive	O
when	O
these	O
encrypted	O
formats	O
were	O
designed	O
,	O
modern	O
attack	O
techniques	O
have	O
found	O
numerous	O
ways	O
to	O
employ	O
such	O
incidentally-leaked	O
metadata	O
in	O
facilitating	O
attacks	O
,	O
such	O
as	O
by	O
identifying	O
data	O
encrypted	O
with	O
weak	O
ciphers	O
or	O
obsolete	O
algorithms	O
,	O
fingerprinting	O
applications	O
to	O
track	O
users	O
or	O
identify	O
software	O
versions	O
with	O
known	O
vulnerabilities	O
,	O
or	O
traffic	O
analysis	O
techniques	O
such	O
as	O
identifying	O
all	O
users	O
,	O
groups	O
,	O
and	O
associated	O
public	B-Application
keys	I-Application
involved	O
in	O
a	O
conversation	O
from	O
an	O
encrypted	O
message	O
observed	O
between	O
only	O
two	O
of	O
them	O
.	O
</s>
<s>
In	O
addition	O
,	O
a	O
PURB	B-Algorithm
is	O
padded	B-Algorithm
to	O
a	O
constrained	O
set	O
of	O
possible	O
lengths	O
,	O
in	O
order	O
to	O
minimize	O
the	O
amount	O
of	O
information	O
the	O
encrypted	O
data	O
could	O
potentially	O
leak	O
to	O
observers	O
via	O
its	O
total	O
length	O
.	O
</s>
<s>
Without	O
padding	B-Algorithm
,	O
encrypted	O
objects	O
such	O
as	O
files	O
or	O
bit	O
strings	O
up	O
to	O
bits	O
in	O
length	O
can	O
leak	O
up	O
to	O
bits	O
of	O
information	O
to	O
an	O
observer	O
-	O
namely	O
the	O
number	O
of	O
bits	O
required	O
to	O
represent	O
the	O
length	O
exactly	O
.	O
</s>
<s>
A	O
PURB	B-Algorithm
is	O
padded	B-Algorithm
to	O
a	O
length	O
representable	O
in	O
a	O
floating	O
point	O
number	O
whose	O
mantissa	O
is	O
no	O
longer	O
(	O
i.e.	O
,	O
contains	O
no	O
more	O
significant	O
bits	O
)	O
than	O
its	O
exponent	O
.	O
</s>
<s>
This	O
constraint	O
limits	O
the	O
maximum	O
amount	O
of	O
information	O
a	O
PURB	B-Algorithm
's	O
total	O
length	O
can	O
leak	O
to	O
bits	O
,	O
a	O
significant	O
asymptotic	O
reduction	O
and	O
the	O
best	O
achievable	O
in	O
general	O
for	O
variable-length	O
encrypted	O
formats	O
whose	O
multiplicative	O
overhead	O
is	O
limited	O
to	O
a	O
constant	O
factor	O
of	O
the	O
unpadded	O
payload	O
size	O
.	O
</s>
<s>
This	O
asymptotic	O
leakage	O
is	O
the	O
same	O
as	O
one	O
would	O
obtain	O
by	O
padding	B-Algorithm
encrypted	O
objects	O
to	O
a	O
power	O
of	O
some	O
base	O
,	O
such	O
as	O
to	O
a	O
power	O
of	O
two	O
.	O
</s>
<s>
Allowing	O
some	O
significant	O
mantissa	O
bits	O
in	O
the	O
length	O
's	O
representation	O
rather	O
than	O
just	O
an	O
exponent	O
,	O
however	O
,	O
significantly	O
reduces	O
the	O
overhead	O
of	O
padding	B-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
padding	B-Algorithm
to	O
the	O
next	O
power	O
of	O
two	O
can	O
impose	O
up	O
to	O
100%	O
overhead	O
by	O
nearly	O
doubling	O
the	O
object	O
's	O
size	O
,	O
while	O
a	O
PURB	B-Algorithm
's	O
padding	B-Algorithm
imposes	O
overhead	O
of	O
at	O
most	O
12%	O
for	O
small	O
strings	O
and	O
decreasing	O
gradually	O
(	O
to	O
6%	O
,	O
3%	O
,	O
etc	O
.	O
)	O
</s>
<s>
Experimental	O
evidence	O
indicate	O
that	O
on	O
data	O
sets	O
comprising	O
objects	O
such	O
as	O
files	O
,	O
software	O
packages	O
,	O
and	O
online	O
videos	O
,	O
leaving	O
objects	O
unpadded	O
or	O
padding	B-Algorithm
to	O
a	O
constant	O
block	O
size	O
often	O
leaves	O
them	O
uniquely	O
identifiable	O
by	O
total	O
length	O
alone	O
.	O
</s>
<s>
Padding	B-Algorithm
objects	O
to	O
a	O
power	O
of	O
two	O
or	O
to	O
a	O
PURB	B-Algorithm
length	O
,	O
in	O
contrast	O
,	O
ensures	O
that	O
most	O
objects	O
are	O
indistinguishable	O
from	O
at	O
least	O
some	O
other	O
objects	O
and	O
thus	O
have	O
a	O
nontrivial	O
anonymity	O
set	O
.	O
</s>
<s>
Because	O
a	O
PURB	B-Algorithm
is	O
a	O
discipline	O
for	O
designing	O
encrypted	O
formats	O
and	O
not	O
a	O
particular	O
encrypted	O
format	O
,	O
there	O
is	O
no	O
single	O
prescribed	O
method	O
for	O
encoding	O
or	O
decoding	O
PURBs	B-Algorithm
.	O
</s>
<s>
Applications	O
may	O
use	O
any	O
encryption	O
and	O
encoding	O
scheme	O
provided	O
it	O
produces	O
a	O
bit	O
string	O
that	O
appears	O
uniformly	O
random	O
to	O
an	O
observer	O
without	O
an	O
appropriate	O
key	O
,	O
provided	O
the	O
appropriate	O
hardness	O
assumptions	O
are	O
satisfied	O
of	O
course	O
,	O
and	O
provided	O
the	O
PURB	B-Algorithm
is	O
padded	B-Algorithm
to	O
one	O
of	O
the	O
allowed	O
lengths	O
.	O
</s>
<s>
Correctly-encoded	O
PURBs	B-Algorithm
therefore	O
do	O
not	O
identify	O
the	O
application	O
that	O
created	O
them	O
in	O
their	O
ciphertext	O
.	O
</s>
<s>
A	O
decoding	O
application	O
,	O
therefore	O
,	O
cannot	O
readily	O
tell	O
before	O
decryption	O
whether	O
a	O
PURB	B-Algorithm
was	O
encrypted	O
for	O
that	O
application	O
or	O
its	O
user	O
,	O
other	O
than	O
by	O
trying	O
to	O
decrypt	O
it	O
with	O
any	O
available	O
decryption	O
keys	O
.	O
</s>
<s>
Encoding	O
and	O
decoding	O
a	O
PURB	B-Algorithm
presents	O
technical	O
efficiency	O
challenges	O
,	O
in	O
that	O
traditional	O
parsing	B-Language
techniques	O
are	O
not	O
applicable	O
because	O
a	O
PURB	B-Algorithm
by	O
definition	O
has	O
no	O
metadata	O
markers	O
that	O
a	O
traditional	O
parser	O
could	O
use	O
to	O
discern	O
the	O
PURB	B-Algorithm
's	O
structure	O
before	O
decrypting	O
it	O
.	O
</s>
<s>
Instead	O
,	O
a	O
PURB	B-Algorithm
must	O
be	O
decrypted	O
first	O
obliviously	O
to	O
its	O
internal	O
structure	O
,	O
and	O
then	O
parsed	B-Language
only	O
after	O
the	O
decoder	O
has	O
used	O
an	O
appropriate	O
decryption	O
key	O
to	O
find	O
a	O
suitable	O
cryptographic	O
entrypoint	O
into	O
the	O
PURB	B-Algorithm
.	O
</s>
<s>
Encoding	O
and	O
decoding	O
PURBs	B-Algorithm
intended	O
to	O
be	O
decrypted	O
by	O
several	O
different	O
recipients	O
,	O
public	B-Application
keys	I-Application
,	O
and/or	O
ciphers	O
presents	O
the	O
additional	O
technical	O
challenge	O
that	O
each	O
recipient	O
must	O
find	O
a	O
different	O
entrypoint	O
at	O
a	O
distinct	O
location	O
in	O
the	O
PURB	B-Algorithm
non-overlapping	O
with	O
those	O
of	O
the	O
other	O
recipients	O
,	O
but	O
the	O
PURB	B-Algorithm
presents	O
no	O
cleartext	O
metadata	O
indicating	O
the	O
positions	O
of	O
those	O
entrypoints	O
or	O
even	O
the	O
total	O
number	O
of	O
them	O
.	O
</s>
<s>
The	O
paper	O
that	O
proposed	O
PURBs	B-Algorithm
also	O
included	O
algorithms	O
for	O
encrypting	O
objects	O
to	O
multiple	O
recipients	O
using	O
multiple	O
cipher	O
suites	O
.	O
</s>
<s>
With	O
these	O
algorithms	O
,	O
recipients	O
can	O
find	O
their	O
respective	O
entrypoints	O
into	O
the	O
PURB	B-Algorithm
with	O
only	O
a	O
logarithmic	O
number	O
of	O
trial	O
decryptions	O
using	O
symmetric-key	B-Algorithm
cryptography	I-Algorithm
and	O
only	O
one	O
expensive	O
public-key	B-Application
operation	O
per	O
cipher	O
suite	O
.	O
</s>
<s>
A	O
third	O
technical	O
challenge	O
is	O
representing	O
the	O
public-key	B-Application
cryptographic	O
material	O
that	O
needs	O
to	O
be	O
encoded	O
into	O
each	O
entrypoint	O
in	O
a	O
PURB	B-Algorithm
,	O
such	O
as	O
the	O
ephemeral	B-Protocol
Diffie-Hellman	I-Protocol
public	B-Application
key	I-Application
a	O
recipient	O
needs	O
to	O
derive	O
the	O
shared	O
secret	O
,	O
in	O
an	O
encoding	O
indistinguishable	O
from	O
uniformly	O
random	O
bits	O
.	O
</s>
<s>
The	O
primary	O
privacy	O
advantage	O
that	O
PURBs	B-Algorithm
offer	O
is	O
a	O
strong	O
assurance	O
that	O
correctly-encrypted	O
data	O
leaks	O
nothing	O
incidental	O
via	O
internal	O
metadata	O
that	O
observers	O
might	O
readily	O
use	O
to	O
identify	O
weaknesses	O
in	O
the	O
data	O
or	O
software	O
used	O
to	O
produce	O
it	O
,	O
or	O
to	O
fingerprint	O
the	O
application	O
or	O
user	O
that	O
created	O
the	O
PURB	B-Algorithm
.	O
</s>
<s>
A	O
primary	O
disadvantage	O
of	O
the	O
PURB	B-Algorithm
encryption	O
discipline	O
is	O
the	O
complexity	O
of	O
encoding	O
and	O
decoding	O
,	O
because	O
the	O
decoder	O
cannot	O
rely	O
on	O
conventional	O
parsing	B-Language
techniques	O
before	O
decryption	O
.	O
</s>
<s>
A	O
secondary	O
disadvantage	O
is	O
the	O
overhead	O
that	O
padding	B-Algorithm
adds	O
,	O
although	O
the	O
padding	B-Algorithm
scheme	O
proposed	O
for	O
PURBs	B-Algorithm
incurs	O
at	O
most	O
only	O
a	O
few	O
percent	O
overhead	O
for	O
objects	O
of	O
significant	O
size	O
.	O
</s>
<s>
The	O
Padme	O
padding	B-Algorithm
proposed	O
in	O
the	O
PURB	B-Algorithm
paper	O
only	O
creates	O
files	O
of	O
specific	O
very	O
distinct	O
sizes	O
.	O
</s>
<s>
Thus	O
,	O
an	O
encrypted	O
file	O
may	O
often	O
be	O
identified	O
as	O
PURB	B-Algorithm
encrypted	O
with	O
high	O
confidence	O
,	O
as	O
the	O
probability	O
of	O
any	O
other	O
file	O
having	O
exactly	O
one	O
of	O
those	O
padded	B-Algorithm
sizes	O
is	O
very	O
low	O
.	O
</s>
<s>
Another	O
padding	B-Algorithm
problem	O
occurs	O
with	O
very	O
short	O
messages	O
,	O
where	O
the	O
padding	B-Algorithm
does	O
not	O
effectively	O
hide	O
the	O
size	O
of	O
the	O
content	O
.	O
</s>
<s>
One	O
critique	O
of	O
incurring	O
the	O
complexity	O
and	O
overhead	O
costs	O
of	O
PURB	B-Algorithm
encryption	O
is	O
that	O
the	O
context	O
in	O
which	O
a	O
PURB	B-Algorithm
is	O
stored	O
or	O
transmitted	O
may	O
often	O
leak	O
metadata	O
about	O
the	O
encrypted	O
content	O
anyway	O
,	O
and	O
such	O
metadata	O
is	O
outside	O
of	O
the	O
encryption	O
format	O
's	O
purview	O
or	O
control	O
and	O
thus	O
cannot	O
be	O
addressed	O
by	O
the	O
encryption	O
format	O
alone	O
.	O
</s>
<s>
For	O
example	O
,	O
an	O
application	O
's	O
or	O
user	O
's	O
choice	O
of	O
filename	O
and	O
directory	O
in	O
which	O
to	O
store	O
a	O
PURB	B-Algorithm
on	O
disk	O
may	O
indicate	O
allow	O
an	O
observer	O
to	O
infer	O
the	O
application	O
that	O
likely	O
created	O
it	O
and	O
to	O
what	O
purpose	O
,	O
even	O
if	O
the	O
PURB	B-Algorithm
's	O
data	O
content	O
itself	O
does	O
not	O
.	O
</s>
<s>
Similarly	O
,	O
encrypting	O
an	O
E-mail	O
'	O
s	O
body	O
as	O
a	O
PURB	B-Algorithm
instead	O
of	O
with	O
traditional	O
PGP	B-Application
or	O
S/MIME	B-Protocol
format	O
may	O
eliminate	O
the	O
encryption	O
format	O
's	O
metadata	O
leakage	O
,	O
but	O
cannot	O
prevent	O
information	O
leakage	O
from	O
the	O
cleartext	O
E-mail	O
headers	O
,	O
or	O
from	O
the	O
endpoint	O
hosts	O
and	O
E-mail	O
servers	O
involved	O
in	O
the	O
exchange	O
.	O
</s>
<s>
Nevertheless	O
,	O
separate	O
but	O
complementary	O
disciplines	O
are	O
typically	O
available	O
to	O
limit	O
such	O
contextual	O
metadata	O
leakage	O
,	O
such	O
as	O
appropriate	O
file	O
naming	O
conventions	O
or	O
use	O
of	O
pseudonymous	B-Protocol
E-mail	I-Protocol
addresses	I-Protocol
for	O
sensitive	O
communications	O
.	O
</s>
