ElGamal cryptography is one of the most important Public Key Cryptography(PKC)since Diffie-hellman exchangs was proposed,however these PKCs which are based on the hard problems that dis-crete logarithm problem and integer factorization problem are weak with advances in quantum computers.So some alternatives should be pro-posed.Majid Khan et al.proposed two ElGamal-like public-key encryp-tion schemes based on large abelian subgroup of general linear group over a residue ring,however the two schcmes were not long before it was proved unsafe by us.Then,Saba Inam and Rashid(2016)proposed an improved cryptosystem which can resist my attack on "NEURAL COMPUTING & APPLICATIONS".By analyzing the security of the public key cryptography,we propose an improved method of algebraic kcy-rccovcry attack in the polynomial computational complexity dcspitc-ing the designers claim the cryptosystem is optimal security.Besides,we provide corresponding practical attack example to illustrate the at-tack method in our cryptanalysis,which breaks instances claiming 80 bits of security less than one minute on a single desktop computer.