This paper presents the REESSE1 public key cryptosystem including three algorithms for keys

encryption and decryption

discusses the continued fraction attack by presuming that the lever function (.) in the key transform is one constant or does not exists

and proves that (.) is necessary to the private key security of REESSE1 from the contrapositive assertion.The authors argue that the private key security is equivalent to the multivariate arrangement hardness

and the plaintext security is greater than the discrete logarithm hardness when (.) exists in the transform by expounding the indeterminate reasoning

giving counterexamples and reducing parameters

and so show that (.) is sufficient for the private key and the plaintext securities.At last

point out that the complexity of REESSE1 whose private key contains three independent parameters is far higher than those of MH

RSA and ElGamal whose private keys contain only one or two parameters respectively.