Cryptography Reference
In-Depth Information
(a)
P(x)
(b)
P(x)
D = P(0)
the secret
x
x
Figure 8.3
Shamir's polynomial (4
,n
) threshold secret sharing scheme. (a) Four play-
ers can collaborate in order to retrieve the original third-order polynomial
P
(
x
)
, and
thus the secret information
P
; (b) while three players get infinitely many solutions
and are unable to obtain any information.
(
0
)
secret sharing to be efficient. Second, while keeping the secret unchanged,
new players can be added or old players deleted without the necessity of
modifying the existing access structure. This dynamicity is valuable in many
field situations. Third, when the situation arises, it is easy to completely re-
generate new shares without changing the secret. All that is needed is to
generate a new polynomial or new hyperplanes in projective spaces. Finally,
it is possible to improve on the threshold structure by creating a hierarchical
access structure where more shares are dealt to a certain subset of players.
Secret sharing, in the context of information technology, is still a very ac-
tive research area. A lot of new schemes, developments and applications have
been proposed. Among them are proposals for proactive secret sharing and
verifiable secret sharing. Proactive secret sharing [5] addresses the compro-
mising, loss, or corruption of the shares by periodically renewing the shares
without changing the secret. Verifiable secret sharing [6] offers a way for the
players to check the authenticity of the shares they receive from the dealer, or
the other players from the access structure.
Some applications of secret sharing are
•
The secure access of corporate funding.
In order to secure the money in one
of its accounts, the company can use a
(
)
threshold secret sharing
protocol to share the account access code among all its authorized
employees. In doing so it ensures that at least
k
stackholders need
to collaborate to access the fund and thus lower the risks of having
money being stolen, or syphoned off, by any single person or small
group.
k, n
•
The clipper chip.
This is a National Institute of Standards and Technol-
ogy proposal to provide the governmental agencies the possibility of
