To discuss the security of RSA type cryptosystem over conic curves on the ring Z/nZ, two algorithms of short private exponent attack on such cryptosystems were presented. Two simple examples illuminating the algorithms were also given. The results showed that the RSA type cryptosystem over conic curves on the ring Z/nZ can not resist short private exponent attack. In other word, the parameter n can be factored in polynomial time of lnn if the private exponent is too small.
