Cryptanalysis of the WD public-key cryptosystem

The theory of generalized inverses of matrices over finite fields has been used in cryptographic applications in recent years. Wu and Dawson (1998) proposed a public-key cryptosystem based on generalized inverses of matrices. In 2001, Sun proposed a scheme for cryptanalysing Wu and Dawson´s public-key cryptosystem. However, his method is time intensive because message recovery requires the pre-computation of many plaintext and ciphertext pairs (m_i, c_i). This paper shows how anyone knowing only the public key and a ciphertext can easily retrieve the corresponding message by solving the linear equation system. Thus, it proves that the proposed cryptanalysis method is very efficient for breaking Wu and Dawson´s public-key cryptosystem.