  Cryptography is the science of using mathematics to encrypt and decrypt data.
Cryptography enables you to store sensitive information or transmit it across
insecure networks so that it cannot be read by anyone except the intended
recipient. While cryptography is the science of securing data, cryptanalysis is
the science of analyzing and breaking secure communication. Classical
cryptanalysis involves an interesting combination of analytical reasoning,
application of mathematical tools and pattern finding. The objectives of the
proposed work are to propose a new cryptographic method based on the special
matrix called the Hilbert matrix for authentication and confidentiality and to
propose a model for confidentiality and authentication using a combination of
symmetric and public cryptosystems. Further, it is extended to shared key
cryptosystems with the concept of digital enveloping using a session key. In
the present work an algorithm for shared key encryption is developed using
Hilbert matrix cryptosystem. In this the block chaining modes of operation have
been used to tackle the issues of confusion and diffusion.
