<s>
CEILIDH	B-Protocol
is	O
a	O
public	B-Application
key	I-Application
cryptosystem	I-Application
based	O
on	O
the	O
discrete	O
logarithm	O
problem	O
in	O
algebraic	O
torus	O
.	O
</s>
<s>
This	O
idea	O
was	O
first	O
introduced	O
by	O
Alice	O
Silverberg	O
and	O
Karl	O
Rubin	O
in	O
2003	O
;	O
Silverberg	O
named	O
CEILIDH	B-Protocol
after	O
her	O
cat	O
.	O
</s>
<s>
This	O
Scheme	O
is	O
based	O
on	O
the	O
Diffie-Hellman	B-Protocol
key	I-Protocol
agreement	I-Protocol
.	O
</s>
<s>
This	O
scheme	O
is	O
based	O
on	O
the	O
ElGamal	B-Algorithm
encryption	I-Algorithm
.	O
</s>
<s>
Alice	O
chooses	O
a	O
random	O
number	O
as	O
her	O
private	B-Application
key	I-Application
.	O
</s>
<s>
The	O
resulting	O
public	B-Application
key	I-Application
is	O
.	O
</s>
<s>
The	O
CEILIDH	B-Protocol
scheme	O
is	O
based	O
on	O
the	O
ElGamal	B-Algorithm
scheme	O
and	O
thus	O
has	O
similar	O
security	O
properties	O
.	O
</s>
<s>
If	O
the	O
computational	O
Diffie-Hellman	B-Protocol
assumption	O
holds	O
the	O
underlying	O
cyclic	O
group	O
,	O
then	O
the	O
encryption	O
function	O
is	O
one-way	O
.	O
</s>
<s>
If	O
the	O
decisional	O
Diffie-Hellman	B-Protocol
assumption	O
(	O
DDH	O
)	O
holds	O
in	O
,	O
then	O
CEILIDH	B-Protocol
achieves	O
semantic	O
security	O
.	O
</s>
<s>
Semantic	O
security	O
is	O
not	O
implied	O
by	O
the	O
computational	O
Diffie-Hellman	B-Protocol
assumption	O
alone	O
.	O
</s>
<s>
See	O
decisional	O
Diffie-Hellman	B-Protocol
assumption	O
for	O
a	O
discussion	O
of	O
groups	O
where	O
the	O
assumption	O
is	O
believed	O
to	O
hold	O
.	O
</s>
<s>
CEILIDH	B-Protocol
encryption	O
is	O
unconditionally	O
malleable	O
,	O
and	O
therefore	O
is	O
not	O
secure	O
under	O
chosen	O
ciphertext	O
attack	O
.	O
</s>
