Cryptanalysis of Simple Matrix Scheme for Encryption

Recently, Tao et al. presented a new simple and efficient multivariate pubic key encryption scheme based on matrix multiplication, which is called Simple Matrix Scheme or ABC. Using linearization equation attack, we propose a polynomial time algorithm, which directly recovers an equivalent private key from the public key of ABC. Furthermore, our attack can also be applied to the variants of ABC since these variants have the same algebraic structure as the original ABC scheme. Therefore, the ABC cryptosystem and its variants are insecure.