<s>
In	O
cryptography	O
,	O
a	O
three-pass	B-Algorithm
protocol	I-Algorithm
for	O
sending	O
messages	O
is	O
a	O
framework	O
which	O
allows	O
one	O
party	O
to	O
securely	O
send	O
a	O
message	O
to	O
a	O
second	O
party	O
without	O
the	O
need	O
to	O
exchange	O
or	O
distribute	O
encryption	O
keys	O
.	O
</s>
<s>
It	O
is	O
called	O
a	O
three-pass	B-Algorithm
protocol	I-Algorithm
because	O
the	O
sender	O
and	O
the	O
receiver	O
exchange	O
three	O
encrypted	O
messages	O
.	O
</s>
<s>
The	O
first	O
three-pass	B-Algorithm
protocol	I-Algorithm
was	O
developed	O
by	O
Adi	O
Shamir	O
circa	O
1980	O
,	O
and	O
is	O
described	O
in	O
more	O
detail	O
in	O
a	O
later	O
section	O
.	O
</s>
<s>
The	O
basic	O
concept	O
of	O
the	O
three-pass	B-Algorithm
protocol	I-Algorithm
is	O
that	O
each	O
party	O
has	O
a	O
private	O
encryption	O
key	O
and	O
a	O
private	O
decryption	O
key	O
.	O
</s>
<s>
In	O
order	O
for	O
the	O
encryption	O
function	O
and	O
decryption	O
function	O
to	O
be	O
suitable	O
for	O
the	O
three-pass	B-Algorithm
protocol	I-Algorithm
they	O
must	O
have	O
the	O
property	O
that	O
for	O
any	O
message	O
m	O
,	O
any	O
encryption	O
key	O
e	O
with	O
corresponding	O
decryption	O
key	O
d	O
and	O
any	O
independent	O
encryption	O
key	O
k	O
,	O
.	O
</s>
<s>
The	O
three-pass	B-Algorithm
protocol	I-Algorithm
works	O
as	O
follows	O
:	O
</s>
<s>
The	O
first	O
three-pass	B-Algorithm
protocol	I-Algorithm
was	O
the	O
Shamir	B-Algorithm
three-pass	I-Algorithm
protocol	I-Algorithm
developed	O
circa	O
in	O
1980	O
.	O
</s>
<s>
It	O
is	O
also	O
called	O
the	O
Shamir	B-Algorithm
No-Key	I-Algorithm
Protocol	I-Algorithm
because	O
the	O
sender	O
and	O
the	O
receiver	O
do	O
not	O
exchange	O
any	O
keys	O
,	O
however	O
the	O
protocol	O
requires	O
the	O
sender	O
and	O
receiver	O
to	O
have	O
two	O
private	O
keys	O
for	O
encrypting	O
and	O
decrypting	O
messages	O
.	O
</s>
<s>
The	O
Massey	B-Algorithm
–	I-Algorithm
Omura	I-Algorithm
Cryptosystem	I-Algorithm
was	O
proposed	O
by	O
James	O
Massey	O
and	O
Jim	O
K	O
.	O
Omura	O
in	O
1982	O
as	O
a	O
possible	O
improvement	O
over	O
the	O
Shamir	O
protocol	O
.	O
</s>
<s>
By	O
using	O
this	O
representation	O
,	O
exponentiations	O
by	O
powers	O
of	O
2	O
can	O
be	O
accomplished	O
by	O
cyclic	B-Algorithm
shifts	I-Algorithm
.	O
</s>
<s>
K	O
.	O
Sakurai	O
and	O
H	O
.	O
Shizuya	O
show	O
that	O
under	O
certain	O
assumptions	O
breaking	O
Massey	B-Algorithm
–	I-Algorithm
Omura	I-Algorithm
cryptosystem	I-Algorithm
is	O
equivalent	O
to	O
the	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
assumption	O
.	O
</s>
<s>
The	O
three-pass	B-Algorithm
protocol	I-Algorithm
as	O
described	O
above	O
does	O
not	O
provide	O
any	O
authentication	O
.	O
</s>
