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Abstract:
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Cryptosystem using linear codes was developed in 1978 by Mc-Eliece.
Later in 1985 Niederreiter and others developed a modified version of cryptosystem using concepts of
linear codes. But these systems were not used frequently because of its larger key size. In this study we
were designing a cryptosystem using the concepts of algebraic geometric codes with smaller key size.
Error detection and correction can be done efficiently by simple decoding methods using the
cryptosystem developed. Approach: Algebraic geometric codes are codes, generated using curves.
The cryptosystem use basic concepts of elliptic curves cryptography and generator matrix. Decrypted
information takes the form of a repetition code. Due to this complexity of decoding procedure is
reduced. Error detection and correction can be carried out efficiently by solving a simple system of
linear equations, there by imposing the concepts of security along with error detection and correction.
Results: Implementation of the algorithm is done on MATLAB and comparative analysis is also done
on various parameters of the system. Attacks are common to all cryptosystems. But by securely
choosing curve, field and representation of elements in field, we can overcome the attacks and a stable
system can be generated. Conclusion: The algorithm defined here protects the information from an
intruder and also from the error in communication channel by efficient error correction methods. |