<s>
Public-key	B-Application
cryptography	I-Application
,	O
or	O
asymmetric	B-Application
cryptography	I-Application
,	O
is	O
the	O
field	O
of	O
cryptographic	B-General_Concept
systems	I-General_Concept
that	O
use	O
pairs	O
of	O
related	O
keys	O
.	O
</s>
<s>
Each	O
key	B-Application
pair	I-Application
consists	O
of	O
a	O
public	B-Application
key	I-Application
and	O
a	O
corresponding	O
private	B-Application
key	I-Application
.	O
</s>
<s>
Key	B-Application
pairs	I-Application
are	O
generated	O
with	O
cryptographic	O
algorithms	O
based	O
on	O
mathematical	O
problems	O
termed	O
one-way	O
functions	O
.	O
</s>
<s>
Security	O
of	O
public-key	B-Application
cryptography	I-Application
depends	O
on	O
keeping	O
the	O
private	B-Application
key	I-Application
secret	O
;	O
the	O
public	B-Application
key	I-Application
can	O
be	O
openly	O
distributed	O
without	O
compromising	O
security	O
.	O
</s>
<s>
In	O
a	O
public-key	B-Application
encryption	I-Application
system	O
,	O
anyone	O
with	O
a	O
public	B-Application
key	I-Application
can	O
encrypt	O
a	O
message	O
,	O
yielding	O
a	O
ciphertext	O
,	O
but	O
only	O
those	O
who	O
know	O
the	O
corresponding	O
private	B-Application
key	I-Application
can	O
decrypt	O
the	O
ciphertext	O
to	O
obtain	O
the	O
original	O
message	O
.	O
</s>
<s>
For	O
example	O
,	O
a	O
journalist	O
can	O
publish	O
the	O
public	B-Application
key	I-Application
of	O
an	O
encryption	O
key	B-Application
pair	I-Application
on	O
a	O
web	O
site	O
so	O
that	O
sources	O
can	O
send	O
secret	O
messages	O
to	O
the	O
news	O
organization	O
in	O
ciphertext	O
.	O
</s>
<s>
Only	O
the	O
journalist	O
who	O
knows	O
the	O
corresponding	O
private	B-Application
key	I-Application
can	O
decrypt	O
the	O
ciphertexts	O
to	O
obtain	O
the	O
sources	O
 '	O
messagesan	O
eavesdropper	O
reading	O
email	O
on	O
its	O
way	O
to	O
the	O
journalist	O
cannot	O
decrypt	O
the	O
ciphertexts	O
.	O
</s>
<s>
However	O
,	O
public-key	B-Application
encryption	I-Application
does	O
not	O
conceal	O
metadata	O
like	O
what	O
computer	O
a	O
source	O
used	O
to	O
send	O
a	O
message	O
,	O
when	O
they	O
sent	O
it	O
,	O
or	O
how	O
long	O
it	O
is	O
.	O
</s>
<s>
Public-key	B-Application
encryption	I-Application
on	O
its	O
own	O
also	O
does	O
not	O
tell	O
the	O
recipient	O
anything	O
about	O
who	O
sent	O
a	O
messageit	O
just	O
conceals	O
the	O
content	O
of	O
a	O
message	O
in	O
a	O
ciphertext	O
that	O
can	O
only	O
be	O
decrypted	O
with	O
the	O
private	B-Application
key	I-Application
.	O
</s>
<s>
In	O
a	O
digital	O
signature	O
system	O
,	O
a	O
sender	O
can	O
use	O
a	O
private	B-Application
key	I-Application
together	O
with	O
a	O
message	O
to	O
create	O
a	O
signature	O
.	O
</s>
<s>
Anyone	O
with	O
the	O
corresponding	O
public	B-Application
key	I-Application
can	O
verify	O
whether	O
the	O
signature	O
matches	O
the	O
message	O
,	O
but	O
a	O
forger	O
who	O
does	O
not	O
know	O
the	O
private	B-Application
key	I-Application
cannot	O
find	O
any	O
message/signature	O
pair	O
that	O
will	O
pass	O
verification	O
with	O
the	O
public	B-Application
key	I-Application
.	O
</s>
<s>
For	O
example	O
,	O
a	O
software	O
publisher	O
can	O
create	O
a	O
signature	O
key	B-Application
pair	I-Application
and	O
include	O
the	O
public	B-Application
key	I-Application
in	O
software	O
installed	O
on	O
computers	O
.	O
</s>
<s>
Later	O
,	O
the	O
publisher	O
can	O
distribute	O
an	O
update	O
to	O
the	O
software	O
signed	O
using	O
the	O
private	B-Application
key	I-Application
,	O
and	O
any	O
computer	O
receiving	O
an	O
update	O
can	O
confirm	O
it	O
is	O
genuine	O
by	O
verifying	O
the	O
signature	O
using	O
the	O
public	B-Application
key	I-Application
.	O
</s>
<s>
As	O
long	O
as	O
the	O
software	O
publisher	O
keeps	O
the	O
private	B-Application
key	I-Application
secret	O
,	O
even	O
if	O
a	O
forger	O
can	O
distribute	O
malicious	O
updates	O
to	O
computers	O
,	O
they	O
cannot	O
convince	O
the	O
computers	O
that	O
any	O
malicious	O
updates	O
are	O
genuine	O
.	O
</s>
<s>
Public	B-Application
key	I-Application
algorithms	I-Application
are	O
fundamental	O
security	O
primitives	O
in	O
modern	O
cryptosystems	B-General_Concept
,	O
including	O
applications	O
and	O
protocols	O
which	O
offer	O
assurance	O
of	O
the	O
confidentiality	O
,	O
authenticity	O
and	O
non-repudiability	O
of	O
electronic	O
communications	O
and	O
data	O
storage	O
.	O
</s>
<s>
They	O
underpin	O
numerous	O
Internet	O
standards	O
,	O
such	O
as	O
Transport	B-Protocol
Layer	I-Protocol
Security	I-Protocol
(	O
TLS	B-Protocol
)	O
,	O
SSH	B-Protocol
,	O
S/MIME	B-Protocol
and	O
PGP	B-Application
.	O
</s>
<s>
Some	O
public	B-Application
key	I-Application
algorithms	I-Application
provide	O
key	B-General_Concept
distribution	I-General_Concept
and	O
secrecy	O
(	O
e.g.	O
,	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
key	I-Protocol
exchange	I-Protocol
)	O
,	O
some	O
provide	O
digital	O
signatures	O
(	O
e.g.	O
,	O
Digital	O
Signature	O
Algorithm	O
)	O
,	O
and	O
some	O
provide	O
both	O
(	O
e.g.	O
,	O
RSA	B-Architecture
)	O
.	O
</s>
<s>
Compared	O
to	O
symmetric	B-Algorithm
encryption	I-Algorithm
,	O
asymmetric	B-Application
encryption	I-Application
is	O
rather	O
slower	O
than	O
good	O
symmetric	B-Algorithm
encryption	I-Algorithm
,	O
too	O
slow	O
for	O
many	O
purposes	O
.	O
</s>
<s>
Today	O
's	O
cryptosystems	B-General_Concept
(	O
such	O
as	O
TLS	B-Protocol
,	O
Secure	B-Protocol
Shell	I-Protocol
)	O
use	O
both	O
symmetric	B-Algorithm
encryption	I-Algorithm
and	O
asymmetric	B-Application
encryption	I-Application
,	O
often	O
by	O
using	O
asymmetric	B-Application
encryption	I-Application
to	O
securely	O
exchange	O
a	O
secret	O
key	O
which	O
is	O
then	O
used	O
for	O
symmetric	B-Algorithm
encryption	I-Algorithm
.	O
</s>
<s>
Before	O
the	O
mid-1970s	O
,	O
all	O
cipher	O
systems	O
used	O
symmetric	B-Algorithm
key	I-Algorithm
algorithms	I-Algorithm
,	O
in	O
which	O
the	O
same	O
cryptographic	O
key	O
is	O
used	O
with	O
the	O
underlying	O
algorithm	O
by	O
both	O
the	O
sender	O
and	O
the	O
recipient	O
,	O
who	O
must	O
both	O
keep	O
it	O
secret	O
.	O
</s>
<s>
By	O
contrast	O
,	O
in	O
a	O
public	B-Application
key	I-Application
system	O
,	O
the	O
public	B-Application
keys	I-Application
can	O
be	O
disseminated	O
widely	O
and	O
openly	O
,	O
and	O
only	O
the	O
corresponding	O
private	B-Application
keys	I-Application
need	O
be	O
kept	O
secret	O
by	O
its	O
owner	O
.	O
</s>
<s>
Two	O
of	O
the	O
best-known	O
uses	O
of	O
public	B-Application
key	I-Application
cryptography	I-Application
are	O
:	O
</s>
<s>
Public	B-Application
key	I-Application
encryption	I-Application
,	O
in	O
which	O
a	O
message	O
is	O
encrypted	O
with	O
the	O
intended	O
recipient	O
's	O
public	B-Application
key	I-Application
.	O
</s>
<s>
For	O
properly	O
chosen	O
and	O
used	O
algorithms	O
,	O
messages	O
cannot	O
in	O
practice	O
be	O
decrypted	O
by	O
anyone	O
who	O
does	O
not	O
possess	O
the	O
matching	O
private	B-Application
key	I-Application
,	O
who	O
is	O
thus	O
presumed	O
to	O
be	O
the	O
owner	O
of	O
that	O
key	O
and	O
so	O
the	O
person	O
associated	O
with	O
the	O
public	B-Application
key	I-Application
.	O
</s>
<s>
Digital	O
signatures	O
,	O
in	O
which	O
a	O
message	O
is	O
signed	O
with	O
the	O
sender	O
's	O
private	B-Application
key	I-Application
and	O
can	O
be	O
verified	O
by	O
anyone	O
who	O
has	O
access	O
to	O
the	O
sender	O
's	O
public	B-Application
key	I-Application
.	O
</s>
<s>
This	O
verification	O
proves	O
that	O
the	O
sender	O
had	O
access	O
to	O
the	O
private	B-Application
key	I-Application
,	O
and	O
therefore	O
is	O
very	O
likely	O
to	O
be	O
the	O
person	O
associated	O
with	O
the	O
public	B-Application
key	I-Application
.	O
</s>
<s>
It	O
also	O
proves	O
that	O
the	O
signature	O
was	O
prepared	O
for	O
that	O
exact	O
message	O
,	O
since	O
verification	O
will	O
fail	O
for	O
any	O
other	O
message	O
one	O
could	O
devise	O
without	O
using	O
the	O
private	B-Application
key	I-Application
.	O
</s>
<s>
One	O
important	O
issue	O
is	O
confidence/proof	O
that	O
a	O
particular	O
public	B-Application
key	I-Application
is	O
authentic	O
,	O
i.e.	O
</s>
<s>
A	O
public	B-Architecture
key	I-Architecture
infrastructure	I-Architecture
(	O
PKI	O
)	O
,	O
in	O
which	O
one	O
or	O
more	O
third	O
parties	O
–	O
known	O
as	O
certificate	B-Architecture
authorities	I-Architecture
–	O
certify	O
ownership	O
of	O
key	B-Application
pairs	I-Application
.	O
</s>
<s>
TLS	B-Protocol
relies	O
upon	O
this	O
.	O
</s>
<s>
A	O
"	O
web	O
of	O
trust	O
"	O
which	O
decentralizes	O
authentication	O
by	O
using	O
individual	O
endorsements	O
of	O
links	O
between	O
a	O
user	O
and	O
the	O
public	B-Application
key	I-Application
belonging	O
to	O
that	O
user	O
.	O
</s>
<s>
PGP	B-Application
uses	O
this	O
approach	O
,	O
in	O
addition	O
to	O
lookup	O
in	O
the	O
domain	B-Protocol
name	I-Protocol
system	I-Protocol
(	O
DNS	B-Protocol
)	O
.	O
</s>
<s>
The	O
DKIM	B-Protocol
system	O
for	O
digitally	O
signing	O
emails	O
also	O
uses	O
this	O
approach	O
.	O
</s>
<s>
The	O
most	O
obvious	O
application	O
of	O
a	O
public	B-Application
key	I-Application
encryption	I-Application
system	O
is	O
for	O
encrypting	O
communication	O
to	O
provide	O
confidentiality	O
–	O
a	O
message	O
that	O
a	O
sender	O
encrypts	O
using	O
the	O
recipient	O
's	O
public	B-Application
key	I-Application
which	O
can	O
be	O
decrypted	O
only	O
by	O
the	O
recipient	O
's	O
paired	O
private	B-Application
key	I-Application
.	O
</s>
<s>
Another	O
application	O
in	O
public	B-Application
key	I-Application
cryptography	I-Application
is	O
the	O
digital	O
signature	O
.	O
</s>
<s>
Further	O
applications	O
built	O
on	O
this	O
foundation	O
include	O
:	O
digital	O
cash	O
,	O
password-authenticated	B-Protocol
key	I-Protocol
agreement	I-Protocol
,	O
time-stamping	O
services	O
and	O
non-repudiation	O
protocols	O
.	O
</s>
<s>
Because	O
asymmetric	B-Application
key	I-Application
algorithms	I-Application
are	O
nearly	O
always	O
much	O
more	O
computationally	O
intensive	O
than	O
symmetric	O
ones	O
,	O
it	O
is	O
common	O
to	O
use	O
a	O
public/private	O
asymmetric	O
key-exchange	O
algorithm	O
to	O
encrypt	O
and	O
exchange	O
a	O
symmetric	B-Algorithm
key	I-Algorithm
,	O
which	O
is	O
then	O
used	O
by	O
symmetric-key	B-Algorithm
cryptography	I-Algorithm
to	O
transmit	O
data	O
using	O
the	O
now-shared	O
symmetric	B-Algorithm
key	I-Algorithm
for	O
a	O
symmetric	B-Algorithm
key	I-Algorithm
encryption	I-Algorithm
algorithm	O
.	O
</s>
<s>
PGP	B-Application
,	O
SSH	B-Protocol
,	O
and	O
the	O
SSL/TLS	B-Protocol
family	O
of	O
schemes	O
use	O
this	O
procedure	O
;	O
they	O
are	O
thus	O
called	O
hybrid	O
cryptosystems	B-General_Concept
.	O
</s>
<s>
The	O
initial	O
asymmetric	O
cryptography-based	O
key	O
exchange	O
to	O
share	O
a	O
server-generated	O
symmetric	B-Algorithm
key	I-Algorithm
from	O
the	O
server	O
to	O
client	O
has	O
the	O
advantage	O
of	O
not	O
requiring	O
that	O
a	O
symmetric	B-Algorithm
key	I-Algorithm
be	O
pre-shared	O
manually	O
,	O
such	O
as	O
on	O
printed	O
paper	O
or	O
discs	O
transported	O
by	O
a	O
courier	O
,	O
while	O
providing	O
the	O
higher	O
data	O
throughput	O
of	O
symmetric	B-Algorithm
key	I-Algorithm
cryptography	I-Algorithm
over	O
asymmetric	B-Application
key	I-Application
cryptography	I-Application
for	O
the	O
remainder	O
of	O
the	O
shared	O
connection	O
.	O
</s>
<s>
Aside	O
from	O
poor	O
choice	O
of	O
an	O
asymmetric	B-Application
key	I-Application
algorithm	I-Application
(	O
there	O
are	O
few	O
which	O
are	O
widely	O
regarded	O
as	O
satisfactory	O
)	O
or	O
too	O
short	O
a	O
key	O
length	O
,	O
the	O
chief	O
security	O
risk	O
is	O
that	O
the	O
private	B-Application
key	I-Application
of	O
a	O
pair	O
becomes	O
known	O
.	O
</s>
<s>
All	O
public	B-Application
key	I-Application
schemes	O
are	O
in	O
theory	O
susceptible	O
to	O
a	O
"	O
brute-force	O
key	O
search	O
attack	O
"	O
.	O
</s>
<s>
Some	O
special	O
and	O
specific	O
algorithms	O
have	O
been	O
developed	O
to	O
aid	O
in	O
attacking	O
some	O
public	B-Application
key	I-Application
encryption	I-Application
algorithms	O
;	O
both	O
RSA	B-Architecture
and	O
ElGamal	B-Algorithm
encryption	I-Algorithm
have	O
known	O
attacks	O
that	O
are	O
much	O
faster	O
than	O
the	O
brute-force	O
approach	O
.	O
</s>
<s>
Major	O
weaknesses	O
have	O
been	O
found	O
for	O
several	O
formerly	O
promising	O
asymmetric	B-Application
key	I-Application
algorithms	I-Application
.	O
</s>
<s>
The	O
"	B-Algorithm
knapsack	I-Algorithm
packing	I-Algorithm
"	I-Algorithm
algorithm	I-Algorithm
was	O
found	O
to	O
be	O
insecure	O
after	O
the	O
development	O
of	O
a	O
new	O
attack	O
.	O
</s>
<s>
As	O
with	O
all	O
cryptographic	O
functions	O
,	O
public-key	B-Application
implementations	O
may	O
be	O
vulnerable	O
to	O
side-channel	O
attacks	O
that	O
exploit	O
information	O
leakage	O
to	O
simplify	O
the	O
search	O
for	O
a	O
secret	O
key	O
.	O
</s>
<s>
Another	O
potential	O
security	O
vulnerability	O
in	O
using	O
asymmetric	B-Application
keys	I-Application
is	O
the	O
possibility	O
of	O
a	O
"	O
man-in-the-middle	O
"	O
attack	O
,	O
in	O
which	O
the	O
communication	O
of	O
public	B-Application
keys	I-Application
is	O
intercepted	O
by	O
a	O
third	O
party	O
(	O
the	O
"	O
man	O
in	O
the	O
middle	O
"	O
)	O
and	O
then	O
modified	O
to	O
provide	O
different	O
public	B-Application
keys	I-Application
instead	O
.	O
</s>
<s>
Encrypted	O
messages	O
and	O
responses	O
must	O
,	O
in	O
all	O
instances	O
,	O
be	O
intercepted	O
,	O
decrypted	O
,	O
and	O
re-encrypted	O
by	O
the	O
attacker	O
using	O
the	O
correct	O
public	B-Application
keys	I-Application
for	O
the	O
different	O
communication	O
segments	O
so	O
as	O
to	O
avoid	O
suspicion	O
.	O
</s>
<s>
Capturing	O
the	O
public	B-Application
key	I-Application
would	O
only	O
require	O
searching	O
for	O
the	O
key	O
as	O
it	O
gets	O
sent	O
through	O
the	O
ISP	O
's	O
communications	O
hardware	O
;	O
in	O
properly	O
implemented	O
asymmetric	B-Application
key	I-Application
schemes	O
,	O
this	O
is	O
not	O
a	O
significant	O
risk	O
.	O
</s>
<s>
In	O
summation	O
,	O
public	B-Application
keys	I-Application
are	O
easier	O
to	O
alter	O
when	O
the	O
communications	O
hardware	O
used	O
by	O
a	O
sender	O
is	O
controlled	O
by	O
an	O
attacker	O
.	O
</s>
<s>
One	O
approach	O
to	O
prevent	O
such	O
attacks	O
involves	O
the	O
use	O
of	O
a	O
public	B-Architecture
key	I-Architecture
infrastructure	I-Architecture
(	O
PKI	O
)	O
;	O
a	O
set	O
of	O
roles	O
,	O
policies	O
,	O
and	O
procedures	O
needed	O
to	O
create	O
,	O
manage	O
,	O
distribute	O
,	O
use	O
,	O
store	O
and	O
revoke	B-Protocol
digital	O
certificates	O
and	O
manage	O
public-key	B-Application
encryption	I-Application
.	O
</s>
<s>
For	O
example	O
,	O
the	O
certificate	B-Architecture
authority	I-Architecture
issuing	O
the	O
certificate	O
must	O
be	O
trusted	O
by	O
all	O
participating	O
parties	O
to	O
have	O
properly	O
checked	O
the	O
identity	O
of	O
the	O
key-holder	O
,	O
to	O
have	O
ensured	O
the	O
correctness	O
of	O
the	O
public	B-Application
key	I-Application
when	O
it	O
issues	O
a	O
certificate	O
,	O
to	O
be	O
secure	O
from	O
computer	O
piracy	O
,	O
and	O
to	O
have	O
made	O
arrangements	O
with	O
all	O
participants	O
to	O
check	O
all	O
their	O
certificates	O
before	O
protected	O
communications	O
can	O
begin	O
.	O
</s>
<s>
Web	B-Application
browsers	I-Application
,	O
for	O
instance	O
,	O
are	O
supplied	O
with	O
a	O
long	O
list	O
of	O
"	O
self-signed	O
identity	O
certificates	O
"	O
from	O
PKI	O
providers	O
–	O
these	O
are	O
used	O
to	O
check	O
the	O
bona	O
fides	O
of	O
the	O
certificate	B-Architecture
authority	I-Architecture
and	O
then	O
,	O
in	O
a	O
second	O
step	O
,	O
the	O
certificates	O
of	O
potential	O
communicators	O
.	O
</s>
<s>
An	O
attacker	O
who	O
could	O
subvert	O
one	O
of	O
those	O
certificate	B-Architecture
authorities	I-Architecture
into	O
issuing	O
a	O
certificate	O
for	O
a	O
bogus	O
public	B-Application
key	I-Application
could	O
then	O
mount	O
a	O
"	O
man-in-the-middle	O
"	O
attack	O
as	O
easily	O
as	O
if	O
the	O
certificate	O
scheme	O
were	O
not	O
used	O
at	O
all	O
.	O
</s>
<s>
Examples	O
include	O
TLS	B-Protocol
and	O
its	O
predecessor	O
SSL	O
,	O
which	O
are	O
commonly	O
used	O
to	O
provide	O
security	O
for	O
web	B-Application
browser	I-Application
transactions	O
(	O
for	O
example	O
,	O
to	O
securely	O
send	O
credit	O
card	O
details	O
to	O
an	O
online	O
store	O
)	O
.	O
</s>
<s>
Aside	O
from	O
the	O
resistance	O
to	O
attack	O
of	O
a	O
particular	O
key	B-Application
pair	I-Application
,	O
the	O
security	O
of	O
the	O
certification	O
hierarchy	O
must	O
be	O
considered	O
when	O
deploying	O
public	B-Application
key	I-Application
systems	O
.	O
</s>
<s>
Some	O
certificate	B-Architecture
authority	I-Architecture
–	O
usually	O
a	O
purpose-built	O
program	O
running	O
on	O
a	O
server	O
computer	O
–	O
vouches	O
for	O
the	O
identities	O
assigned	O
to	O
specific	O
private	B-Application
keys	I-Application
by	O
producing	O
a	O
digital	O
certificate	O
.	O
</s>
<s>
Public	B-Application
key	I-Application
digital	O
certificates	O
are	O
typically	O
valid	O
for	O
several	O
years	O
at	O
a	O
time	O
,	O
so	O
the	O
associated	O
private	B-Application
keys	I-Application
must	O
be	O
held	O
securely	O
over	O
that	O
time	O
.	O
</s>
<s>
When	O
a	O
private	B-Application
key	I-Application
used	O
for	O
certificate	O
creation	O
higher	O
in	O
the	O
PKI	O
server	O
hierarchy	O
is	O
compromised	O
,	O
or	O
accidentally	O
disclosed	O
,	O
then	O
a	O
"	O
man-in-the-middle	O
attack	O
"	O
is	O
possible	O
,	O
making	O
any	O
subordinate	O
certificate	O
wholly	O
insecure	O
.	O
</s>
<s>
Examples	O
of	O
well-regarded	O
asymmetric	B-Application
key	I-Application
techniques	O
for	O
varied	O
purposes	O
include	O
:	O
</s>
<s>
Examples	O
of	O
asymmetric	B-Application
key	I-Application
algorithms	I-Application
not	O
yet	O
widely	O
adopted	O
include	O
:	O
</s>
<s>
Examples	O
of	O
notable	O
–	O
yet	O
insecure	O
–	O
asymmetric	B-Application
key	I-Application
algorithms	I-Application
include	O
:	O
</s>
<s>
Examples	O
of	O
protocols	O
using	O
asymmetric	B-Application
key	I-Application
algorithms	I-Application
include	O
:	O
</s>
<s>
A	O
number	O
of	O
significant	O
practical	O
difficulties	O
arise	O
with	O
this	O
approach	O
to	O
distributing	B-General_Concept
keys	I-General_Concept
.	O
</s>
<s>
In	O
July	O
1996	O
,	O
mathematician	O
Solomon	O
W	O
.	O
Golomb	O
said	O
:	O
"	O
Jevons	O
anticipated	O
a	O
key	O
feature	O
of	O
the	O
RSA	B-Architecture
Algorithm	I-Architecture
for	O
public	B-Application
key	I-Application
cryptography	I-Application
,	O
although	O
he	O
certainly	O
did	O
not	O
invent	O
the	O
concept	O
of	O
public	O
key	O
cryptography.	O
"	O
</s>
<s>
In	O
1970	O
,	O
James	O
H	O
.	O
Ellis	O
,	O
a	O
British	O
cryptographer	O
at	O
the	O
UK	O
Government	O
Communications	O
Headquarters	O
(	O
GCHQ	O
)	O
,	O
conceived	O
of	O
the	O
possibility	O
of	O
"	O
non-secret	O
encryption	O
"	O
,	O
(	O
now	O
called	O
public	B-Application
key	I-Application
cryptography	I-Application
)	O
,	O
but	O
could	O
see	O
no	O
way	O
to	O
implement	O
it	O
.	O
</s>
<s>
In	O
1973	O
,	O
his	O
colleague	O
Clifford	O
Cocks	O
implemented	O
what	O
has	O
become	O
known	O
as	O
the	O
RSA	B-Architecture
encryption	I-Architecture
algorithm	I-Architecture
,	O
giving	O
a	O
practical	O
method	O
of	O
"	O
non-secret	O
encryption	O
"	O
,	O
and	O
in	O
1974	O
another	O
GCHQ	O
mathematician	O
and	O
cryptographer	O
,	O
Malcolm	O
J	O
.	O
Williamson	O
,	O
developed	O
what	O
is	O
now	O
known	O
as	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
key	I-Protocol
exchange	I-Protocol
.	O
</s>
<s>
Both	O
organisations	O
had	O
a	O
military	O
focus	O
and	O
only	O
limited	O
computing	O
power	O
was	O
available	O
in	O
any	O
case	O
;	O
the	O
potential	O
of	O
public	B-Application
key	I-Application
cryptography	I-Application
remained	O
unrealised	O
by	O
either	O
organization	O
:	O
</s>
<s>
Only	O
at	O
the	O
end	O
of	O
the	O
evolution	O
from	O
Berners-Lee	O
designing	O
an	O
open	O
internet	O
architecture	O
for	O
CERN	O
,	O
its	O
adaptation	O
and	O
adoption	O
for	O
the	O
Arpanet	O
...	O
did	O
public	B-Application
key	I-Application
cryptography	I-Application
realise	O
its	O
full	O
potential	O
.	O
</s>
<s>
In	O
1976	O
,	O
an	O
asymmetric	B-Application
key	I-Application
cryptosystem	B-General_Concept
was	O
published	O
by	O
Whitfield	O
Diffie	O
and	O
Martin	O
Hellman	O
who	O
,	O
influenced	O
by	O
Ralph	O
Merkle	O
's	O
work	O
on	O
public	B-Application
key	I-Application
distribution	O
,	O
disclosed	O
a	O
method	O
of	O
public	B-Application
key	I-Application
agreement	O
.	O
</s>
<s>
This	O
method	O
of	O
key	O
exchange	O
,	O
which	O
uses	O
exponentiation	O
in	O
a	O
finite	O
field	O
,	O
came	O
to	O
be	O
known	O
as	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
key	I-Protocol
exchange	I-Protocol
.	O
</s>
<s>
This	O
was	O
the	O
first	O
published	O
practical	O
method	O
for	O
establishing	O
a	O
shared	O
secret-key	B-Application
over	O
an	O
authenticated	O
(	O
but	O
not	O
confidential	O
)	O
communications	O
channel	O
without	O
using	O
a	O
prior	O
shared	O
secret	O
.	O
</s>
<s>
Merkle	O
's	O
"	O
public	O
key-agreement	O
technique	O
"	O
became	O
known	O
as	O
Merkle	B-Protocol
's	I-Protocol
Puzzles	I-Protocol
,	O
and	O
was	O
invented	O
in	O
1974	O
and	O
only	O
published	O
in	O
1978	O
.	O
</s>
<s>
This	O
makes	O
asymmetric	B-Application
encryption	I-Application
a	O
rather	O
new	O
field	O
in	O
cryptography	O
although	O
cryptography	O
itself	O
dates	O
back	O
more	O
than	O
2,000	O
years	O
.	O
</s>
<s>
The	O
latter	O
authors	O
published	O
their	O
work	O
in	O
1978	O
in	O
Martin	O
Gardner	O
's	O
Scientific	O
American	O
column	O
,	O
and	O
the	O
algorithm	O
came	O
to	O
be	O
known	O
as	O
RSA	B-Architecture
,	O
from	O
their	O
initials	O
.	O
</s>
<s>
RSA	B-Architecture
uses	O
exponentiation	O
modulo	O
a	O
product	O
of	O
two	O
very	O
large	O
primes	O
,	O
to	O
encrypt	O
and	O
decrypt	O
,	O
performing	O
both	O
public	B-Application
key	I-Application
encryption	I-Application
and	O
public	B-Application
key	I-Application
digital	O
signatures	O
.	O
</s>
<s>
Since	O
the	O
1970s	O
,	O
a	O
large	O
number	O
and	O
variety	O
of	O
encryption	O
,	O
digital	O
signature	O
,	O
key	B-Protocol
agreement	I-Protocol
,	O
and	O
other	O
techniques	O
have	O
been	O
developed	O
,	O
including	O
the	O
Rabin	B-Algorithm
cryptosystem	I-Algorithm
,	O
ElGamal	B-Algorithm
encryption	I-Algorithm
,	O
DSA	O
-	O
and	O
elliptic	O
curve	O
cryptography	O
.	O
</s>
