A variant of a public key cryptosystem based on Goppa Codes

Abstract

This paper suggests a way in which an interesting Public Key Cryptosystem based on Goppa Codes introduced by R. J. McEliece can be modified and used in a classical way to yield several advantages. The primary benefit is that the rate of the code (or data expansion reciporocal) can be increased by approximately 75%. Secondly (for public key and classical versions), by using a polynomial with no linear or repeated factors instead of an irreducible one to generate the Goppa Code, the code parameters remain the same and the decoding apparatus can be used to test candidate generators. Lastly, a wider range of transformations is made possible. No degradation in security is incurred.