Cryptography Reference
In-Depth Information
verifiable like a hand-written signature. Also, special care needs to be
taken to prevent forgery. Digital signatures can be used for authentica-
tion and non-repudiation.
• Digital Certificate: If a candidate wants to convince an interviewer about
some awards that he/she has achieved, he/she can do so by presenting a
certificate from a “trusted” third party (often, the award-issuing author-
ity). The Digital Certificate [47] borrows the same idea in the digital
domain. For example, a digital certificate can bind the identity of an en-
tity to its public key. The entities may use a trusted third party (TTP)
to certify the public key of each entity. The TTP has a private signing
algorithm S
T
and a verification algorithm V
T
assumed to be known by
all entities. The TTP verifies the identity of each entity, and signs a
message consisting of an identifier and the entity's authentic public key.
• Secret Sharing: Suppose there is a locker and three managers are in
charge of it. It is required that that no single manager should be able
to open the locker, but any two out of the three managers together can.
This is an example of secret sharing [160]. In military and Government
systems, such mechanisms are often required. A simple method of se-
cret sharing among n persons so that any k (< n) together can access
the secret would be to choose a (k−1)-degree polynomial P
k−1
(x), and
distribute to each of the n persons one distinct point (x,P
k−1
(x)) on the
plot of P
k−1
(x) versus x. Since the polynomial is completely character-
ized by any set of k distinct points, the scheme works. Getting less than
k distinct points does not allow to compute the polynomial and hence
the secret cannot be obtained.
• Multicast Security: Suppose a pay-TV movie is to be broadcast only to
a privileged set S of authentic subscribers. Such one-to-many secure
communication in a network of users is the main theme of multicast
security [79]. The set S is, in general, not known before the scheme is
initialized.
• Multiparty Computation: Suppose a group of people want to know who
is the richest among them, but no one wants to reveal to the others
how much wealth he/she possesses. In a general multiparty computa-
tion [39] scenario, n participants p
1
,p
2
,...,p
n
each have private data
d
1
,d
2
,...,d
n
respectively, and they want to compute a global function
f(d
1
,d
2
,...,d
n
) without revealing the individual d
r
's to each other.
• Zero-Knowledge Proof: A person may want to convince somebody else
that he or she possesses certain knowledge, without having to reveal even
a single bit of information about that knowledge. Such a requirement
can be fulfilled by what is called a zero-knowledge proof [56, 57]. Zero-
knowledge proofs provide a powerful tool for the design of cryptographic
protocols [55, Chapter 4].
