GENERALIZED INVERSES IN PUBLIC-KEY CRYPTOSYSTEM DESIGN

The theory of generalised inverses of matrices over finite fields is h ighlighted as a potential tool in cryptographic research, by proposing a public key cryptosystem. Properties of the public key cryptosystem are analysed and compared with those of a previous public key cryptosy stem. The idea is similar to the previous cryptosystem in terms of the usage of an error correction process. However, by using the technique s of generalised matrices, the Hamming weight of the error pattern in the cryptosystem is far larger than the error correction capability of the employed error-correcting code. This is the main reason that the key size is smaller than that of the previous public key cryptosystem with the same level of security. It is also anticipated that the theor y of generalised inverses can be used for a wide variety of cryptograp hic applications.