This paper describes a study of a security method of protecting inside network computers against outside miscreants and unwelcome visitors and a control method when these computers are connected with the Internet. In the present Internet, a method to encipher all data cannot be used, so that it is necessary to utilize PEM (Privacy Enhanced Mail) capable of the encipherment and conversion of secret information. For preventing miscreant access by eavesdropping password, one-time password is effective. The most cost-effective method is a firewall system. This system lies between the outside and inside network. By limiting computers that directly communicate with the Internet, control is centralized and inside network Security is protected. If the security of firewall systems is strictly controlled under correct setting, security within the network can be secured even in open networks such as the Internet. 35 refs., 3 figs.