<s>
In	O
cryptography	O
,	O
homomorphic	B-Algorithm
secret	I-Algorithm
sharing	I-Algorithm
is	O
a	O
type	O
of	O
secret	O
sharing	O
algorithm	O
in	O
which	O
the	O
secret	O
is	O
encrypted	O
via	O
homomorphic	O
encryption	O
.	O
</s>
<s>
Homomorphic	B-Algorithm
secret	I-Algorithm
sharing	I-Algorithm
is	O
used	O
to	O
transmit	O
a	O
secret	O
to	O
several	O
recipients	O
as	O
follows	O
:	O
</s>
<s>
Suppose	O
a	O
community	O
wants	O
to	O
perform	O
an	O
election	O
,	O
using	O
a	O
decentralized	O
voting	O
protocol	B-Protocol
,	O
but	O
they	O
want	O
to	O
ensure	O
that	O
the	O
vote-counters	O
wo	O
n't	O
lie	O
about	O
the	O
results	O
.	O
</s>
<s>
Using	O
a	O
type	O
of	O
homomorphic	B-Algorithm
secret	I-Algorithm
sharing	I-Algorithm
known	O
as	O
Shamir	B-Architecture
's	I-Architecture
secret	I-Architecture
sharing	I-Architecture
,	O
each	O
member	O
of	O
the	O
community	O
can	O
add	O
their	O
vote	O
to	O
a	O
form	O
that	O
is	O
split	O
into	O
pieces	O
,	O
each	O
piece	O
is	O
then	O
submitted	O
to	O
a	O
different	O
vote-counter	O
.	O
</s>
<s>
This	O
protocol	B-Protocol
works	O
as	O
long	O
as	O
not	O
all	O
of	O
the	O
k	O
authorities	O
are	O
corrupt	O
—	O
if	O
they	O
were	O
,	O
then	O
they	O
could	O
collaborate	O
to	O
reconstruct	O
P(x )	O
for	O
each	O
voter	O
and	O
also	O
subsequently	O
alter	O
the	O
votes	O
.	O
</s>
<s>
The	O
protocol	B-Protocol
requires	O
authorities	O
to	O
be	O
completed	O
,	O
therefore	O
in	O
case	O
there	O
are	O
authorities	O
,	O
authorities	O
can	O
be	O
corrupted	O
,	O
which	O
gives	O
the	O
protocol	B-Protocol
a	O
certain	O
degree	O
of	O
robustness	O
.	O
</s>
<s>
The	O
protocol	B-Protocol
manages	O
the	O
IDs	O
of	O
the	O
voters	O
(	O
the	O
IDs	O
were	O
submitted	O
with	O
the	O
ballots	O
)	O
and	O
therefore	O
can	O
verify	O
that	O
only	O
legitimate	O
voters	O
have	O
voted	O
.	O
</s>
<s>
The	O
protocol	B-Protocol
implicitly	O
prevents	O
corruption	O
of	O
ballots	O
.	O
</s>
