<s>
The	O
Password	B-Protocol
Authenticated	I-Protocol
Key	I-Protocol
Exchange	I-Protocol
by	I-Protocol
Juggling	I-Protocol
(	O
or	O
J-PAKE	B-Protocol
)	O
is	O
a	O
password-authenticated	B-Protocol
key	I-Protocol
agreement	I-Protocol
protocol	O
,	O
proposed	O
by	O
Feng	O
Hao	O
and	O
Peter	O
Ryan	O
.	O
</s>
<s>
This	O
protocol	O
allows	O
two	O
parties	O
to	O
establish	O
private	O
and	O
authenticated	O
communication	O
solely	O
based	O
on	O
their	O
shared	O
(	O
low-entropy	O
)	O
password	O
without	O
requiring	O
a	O
Public	B-Architecture
Key	I-Architecture
Infrastructure	I-Architecture
.	O
</s>
<s>
It	O
provides	O
mutual	O
authentication	O
to	O
the	O
key	O
exchange	O
,	O
a	O
feature	O
that	O
is	O
lacking	O
in	O
the	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
key	I-Protocol
exchange	I-Protocol
protocol	O
.	O
</s>
<s>
Typically	O
a	O
Schnorr	B-Algorithm
group	I-Algorithm
is	O
used	O
.	O
</s>
<s>
In	O
general	O
,	O
J-PAKE	B-Protocol
can	O
use	O
any	O
prime	O
order	O
group	O
that	O
is	O
suitable	O
for	O
public	O
key	O
cryptography	O
,	O
including	O
Elliptic	O
curve	O
cryptography	O
.	O
</s>
<s>
Let	O
be	O
their	O
shared	O
(	O
low-entropy	O
)	O
secret	O
,	O
which	O
can	O
be	O
a	O
password	O
or	O
a	O
hash	B-Algorithm
of	O
a	O
password	O
(	O
)	O
.	O
</s>
<s>
Round	O
1	O
Alice	O
selects	O
,	O
and	O
sends	O
out	O
,	O
together	O
with	O
the	O
Zero-knowledge	B-Protocol
proofs	I-Protocol
(	O
using	O
for	O
example	O
Schnorr	O
non-interactive	O
zero-knowledge	B-Protocol
proof	I-Protocol
as	O
specified	O
in	O
RFC	O
8235	O
)	O
for	O
the	O
proof	O
of	O
the	O
exponents	O
and	O
.	O
</s>
<s>
Similarly	O
,	O
Bob	O
selects	O
,	O
and	O
sends	O
out	O
,	O
together	O
with	O
the	O
Zero-knowledge	B-Protocol
proofs	I-Protocol
for	O
the	O
proof	O
of	O
the	O
exponents	O
and	O
.	O
</s>
<s>
When	O
it	O
finishes	O
,	O
Alice	O
and	O
Bob	O
verify	O
the	O
received	O
Zero-knowledge	B-Protocol
proofs	I-Protocol
and	O
also	O
check	O
.	O
</s>
<s>
Round	O
2	O
Alice	O
sends	O
out	O
and	O
a	O
Zero-knowledge	B-Protocol
proof	I-Protocol
for	O
the	O
proof	O
of	O
the	O
exponent	O
.	O
</s>
<s>
Similarly	O
,	O
Bob	O
sends	O
out	O
and	O
a	O
Zero-knowledge	B-Protocol
proof	I-Protocol
for	O
the	O
proof	O
of	O
the	O
exponent	O
.	O
</s>
<s>
With	O
the	O
same	O
keying	O
material	O
,	O
Alice	O
and	O
Bob	O
can	O
derive	O
a	O
session	O
key	O
using	O
a	O
Cryptographic	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
:	O
.	O
</s>
<s>
The	O
two-round	O
J-PAKE	B-Protocol
protocol	O
is	O
completely	O
symmetric	O
.	O
</s>
<s>
In	O
practice	O
,	O
it	O
is	O
more	O
likely	O
to	O
implement	O
J-PAKE	B-Protocol
in	O
three	O
flows	O
since	O
one	O
party	O
shall	O
normally	O
take	O
the	O
initiative	O
.	O
</s>
<s>
Suppose	O
Alice	O
initiates	O
the	O
communication	O
by	O
sending	O
to	O
Bob	O
:	O
and	O
Zero-knowledge	B-Protocol
proofs	I-Protocol
.	O
</s>
<s>
Then	O
Bob	O
replies	O
with	O
:	O
and	O
Zero-knowledge	B-Protocol
proofs	I-Protocol
.	O
</s>
<s>
Finally	O
,	O
Alice	O
sends	O
to	O
Bob	O
:	O
and	O
a	O
Zero-knowledge	B-Protocol
proof	I-Protocol
.	O
</s>
<s>
A	O
simple	O
method	O
described	O
in	O
SPEKE	B-Protocol
works	O
as	O
follows	O
:	O
Alice	O
sends	O
to	O
Bob	O
,	O
and	O
then	O
Bob	O
replies	O
with	O
.	O
</s>
<s>
EKE	B-Protocol
,	O
Kerberos	B-Protocol
and	O
Needham-Schroeder	B-Protocol
all	O
attempt	O
to	O
provide	O
explicit	O
key	O
confirmation	O
by	O
exactly	O
this	O
method	O
.	O
</s>
<s>
Given	O
that	O
the	O
underlying	O
Schnorr	O
non-interactive	O
zero-knowledge	B-Protocol
proof	I-Protocol
is	O
secure	O
,	O
the	O
J-PAKE	B-Protocol
protocol	O
is	O
proved	O
to	O
satisfy	O
the	O
following	O
properties	O
:	O
</s>
<s>
In	O
2015	O
,	O
Abdalla	O
,	O
Benhamouda	O
and	O
MacKenzie	O
conducted	O
an	O
independent	O
formal	O
analysis	O
of	O
J-PAKE	B-Protocol
to	O
prove	O
its	O
security	O
in	O
a	O
random	O
oracle	O
model	O
assuming	O
algebraic	O
adversaries	O
.	O
</s>
<s>
The	O
J-PAKE	B-Protocol
protocol	O
is	O
designed	O
by	O
combining	O
random	O
public	O
keys	O
in	O
such	O
a	O
structured	O
way	O
to	O
achieve	O
a	O
vanishing	O
effect	O
if	O
both	O
parties	O
supplied	O
exactly	O
the	O
same	O
passwords	O
.	O
</s>
<s>
This	O
is	O
somehow	O
similar	O
to	O
the	O
Anonymous	B-Protocol
veto	I-Protocol
network	I-Protocol
protocol	O
design	O
.	O
</s>
<s>
J-PAKE	B-Protocol
has	O
been	O
implemented	O
in	O
OpenSSL	B-Language
and	O
OpenSSH	B-Language
as	O
an	O
experimental	O
authentication	O
protocol	O
.	O
</s>
<s>
It	O
was	O
removed	O
from	O
the	O
OpenSSH	B-Language
source	O
code	O
at	O
the	O
end	O
of	O
January	O
2014	O
.	O
</s>
<s>
It	O
has	O
also	O
been	O
implemented	O
in	O
Smoke	O
Crypto	O
Chat	O
Messenger	O
,	O
in	O
NSS	B-Protocol
and	O
was	O
used	O
by	O
Firefox	B-Operating_System
Sync	I-Operating_System
version	O
1.1	O
but	O
discontinued	O
in	O
1.5	O
which	O
uses	O
a	O
different	O
key	O
exchange	O
and	O
storage	O
method	O
.	O
</s>
<s>
Mozilla	O
's	O
J-PAKE	B-Protocol
server	O
was	O
shut	O
down	O
along	O
with	O
the	O
Sync	O
1.1	O
storage	O
servers	O
on	O
30	O
September	O
2015	O
.	O
</s>
<s>
Pale	B-Protocol
Moon	I-Protocol
continues	O
to	O
use	O
J-PAKE	B-Protocol
as	O
part	O
of	O
its	O
Sync	O
service	O
.	O
</s>
<s>
Since	O
February	O
2013	O
,	O
J-PAKE	B-Protocol
has	O
been	O
added	O
to	O
the	O
lightweight	O
API	O
in	O
Bouncycastle	B-Language
(	O
1.48	O
and	O
onwards	O
)	O
.	O
</s>
<s>
J-PAKE	B-Protocol
has	O
been	O
included	O
in	O
ISO/IEC	O
11770-4	O
(	O
2017	O
)	O
as	O
an	O
international	O
standard	O
.	O
</s>
