Algebraic Geometric Codes and their relation to Cryptography using Elliptic Curves

 dc.contributor.author Manju, C dc.contributor.author Dr.Pramod, K V dc.date.accessioned 2014-04-28T08:47:34Z dc.date.available 2014-04-28T08:47:34Z dc.date.issued 2010-04-19 dc.identifier.uri http://dyuthi.cusat.ac.in/purl/3702 dc.description Department ofComputer Application, Cochin University of Science and Technology en_US dc.description.abstract Communication is the process of transmitting data across channel. en_US 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. dc.description.sponsorship Cochin University ofScience and Technology en_US dc.language.iso en en_US dc.publisher Cochin University of Science and Technology en_US dc.subject Algebraic Geometric Codes en_US dc.subject Public Key cryptography en_US dc.subject Secret sharing, en_US dc.subject Cryptographic algorithm, en_US dc.subject Implementation. en_US dc.title Algebraic Geometric Codes and their relation to Cryptography using Elliptic Curves en_US dc.type Thesis en_US
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