<s>
The	O
most	O
basic	O
types	O
are	O
the	O
so-called	O
threshold	O
schemes	O
,	O
where	O
only	O
the	O
cardinality	B-Application
of	O
the	O
set	O
of	O
shares	O
matters	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
given	O
a	O
secret	O
S	O
,	O
and	O
n	O
shares	O
,	O
any	O
set	O
of	O
t	O
shares	O
is	O
a	O
set	O
with	O
the	O
smallest	O
cardinality	B-Application
from	O
which	O
the	O
secret	O
can	O
be	O
recovered	O
,	O
in	O
the	O
sense	O
that	O
any	O
set	O
of	O
t-1	O
shares	O
is	O
not	O
enough	O
to	O
give	O
S	O
.	O
This	O
is	O
known	O
as	O
a	O
threshold	B-General_Concept
access	I-General_Concept
structure	I-General_Concept
.	O
</s>
<s>
The	O
first	O
ones	O
are	O
Shamir	B-Architecture
's	I-Architecture
threshold	I-Architecture
secret	I-Architecture
sharing	I-Architecture
scheme	I-Architecture
,	O
which	O
is	O
based	O
on	O
polynomial	O
interpolation	O
in	O
order	O
to	O
find	O
S	O
from	O
a	O
given	O
set	O
of	O
shares	O
,	O
and	O
George	O
Blakley	O
's	O
geometric	O
secret	O
sharing	O
scheme	O
,	O
which	O
uses	O
geometric	O
methods	O
to	O
recover	O
the	O
secret	O
S	O
.	O
Threshold	O
secret	O
sharing	O
schemes	O
based	O
on	O
the	O
CRT	O
are	O
due	O
to	O
Mignotte	O
and	O
Asmuth-Bloom	O
,	O
they	O
use	O
special	O
sequences	O
of	O
integers	O
along	O
with	O
the	O
CRT	O
.	O
</s>
<s>
In	O
this	O
manner	O
,	O
thanks	O
to	O
the	O
CRT	O
,	O
we	O
can	O
uniquely	O
determine	O
S	O
from	O
any	O
set	O
of	O
k	O
or	O
more	O
shares	O
,	O
but	O
not	O
from	O
less	O
than	O
k	O
.	O
This	O
provides	O
the	O
so-called	O
threshold	B-General_Concept
access	I-General_Concept
structure	I-General_Concept
.	O
</s>
