TOTAL EMBEDDED SURFACE ATTACK ON MPKCS FROM DIOPHANTINE EQUATIONS

In 2011, Gao and Heindl presented a new multivariate public key cryptosystems from Diophantine equations. However, by observing the decryption process, Ding et al. found recently that some special embedded surfaces could be used to decrypt the message efficiently. They showed that the three systems proposed by Gao and Heindl could be broken at the complexity of 252,261 and 252 respectively. But, the attack by Ding et al. can not implemented on a usual PC. It was mainly theoretical and worked only for finite fields of characteristic 2. In this paper, We present a practical attack on this family of multivariate public key cryptosystems. Our attack is implemented on a PC and it works for all finite fields. By doing computer experiments, we find many new lower-degree embedded surfaces which help us to break the cryptosystem.