Manju, C; Dr.Pramod, K V(Cochin University of Science and Technology, April 19, 2010)
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Abstract:
Communication is the process of transmitting data across channel.
Whenever data is transmitted across a channel, errors are likely to occur.
Coding theory is a stream of science that deals with finding efficient ways to
encode and decode data, so that any likely errors can be detected and corrected.
There are many methods to achieve coding and decoding. One among them is
Algebraic Geometric Codes that can be constructed from curves.
Cryptography is the science ol‘ security of transmitting messages from
a sender to a receiver. The objective is to encrypt message in such a way that
an eavesdropper would not be able to read it. A eryptosystem is a set of
algorithms for encrypting and decrypting for the purpose of the process of
encryption and decryption. Public key eryptosystem such as RSA and DSS are
traditionally being prel‘en‘ec| for the purpose of secure communication through
the channel. llowever Elliptic Curve eryptosystem have become a viable
altemative since they provide greater security and also because of their usage
of key of smaller length compared to other existing crypto systems. Elliptic
curve cryptography is based on group of points on an elliptic curve over a finite
field.
This thesis deals with Algebraic Geometric codes and their relation to
Cryptography using elliptic curves. Here Goppa codes are used and the curves
used are elliptic curve over a finite field. We are relating Algebraic Geometric
code to Cryptography by developing a cryptographic algorithm, which includes
the process of encryption and decryption of messages. We are making use of
fundamental properties of Elliptic curve cryptography for generating the
algorithm and is used here to relate both.
Description:
Department ofComputer Application, Cochin University of Science and Technology