Cryptography

Cryptography is the science of securing data. In
the recent past, ‘‘data’’ almost exclusively meant
‘‘electronic data’’. Various mechanisms were invented
to accomplish this goal and to defend
against attacks on security and privacy of electronic
transmissions. The most common technique is to
encrypt data with a key, known only to the sender
and to the receiver of the transmission. Several algorithms
can accomplish this task, most notable is
DES (National Bureau of Standards, 1977). DES is an
example of a symmetric key algorithm, that is,
both parties share the same key and they must
keep it secret. The main problem with symmetric
keys is that they have to be safely distributed to
each pair of users. This if often done with the
help of public key cryptography

The first public key algorithm was proposed by
Diffie and Hellman 1976. Their method calls for
all users to have a pair of keys. One is a public
key that will be published and thus known to all
parties. The other key in the pair would be a private
key, known only to the party that keeps it.
The secrecy of the private key is guaranteed by
the computational complexity of the mathematical
problem that needs to be solved by outsiders
to derive the value of the private key from its public
component. Other public key cryptosystems
such as the RSA algorithm (Rivest et al., 1978)
and elliptic curve cryptosystem (Koblitz, 1987;
Miller, 1986) were introduced later.
Public key cryptography can be used for encryption,
for electronic signatures, etc. One of its main
applications is the derivation and distribution of
symmetric keys to pairs of users. The symmetric
key exchanges with the help of public key cryptography
can be trusted to be secure and valid if all algorithms
were implemented and executed properly.