1. A method of authenticating a user of a terminal using an icon password, the method comprising: requesting an authentication to a server through an electronic communication network, wherein the terminal is connected to the server through the electronic communication network, and an icon database and an authentication database are connected to the server, the icon database configured to store a plurality of icons, each icon assigned a same unique value, and the authentication database storing authentication information containing passwords associated with users; retrieving a plurality of unique values, wherein each unique value corresponds to a different icon of the plurality of icons; assigning a second value to each unique value of the plurality of unique values, through a non-duplicate random number generation; transmitting icon information containing each assigned second value for each unique value of the plurality of unique values and each corresponding icon for each unique value of the plurality of unique values to the terminal through the electronic communication network; implementing a password input screen based on the transmitted icon information, wherein each assigned second value indicates where each icon corresponding to each unique value is to be displayed on the password input screen; displaying only each icon transmitted in the icon information on the password input screen in a location indicated by each icon's assigned second value; transmitting authentication information containing each assigned second value associated with each icon selected by a user on the password input screen to the server through the electronic communication network; converting each assigned second value contained in the transmitted authentication information to its corresponding unique value; querying the authentication database using authentication information converted from each assigned second value; and accepting the authentication request in response to the authentication information being valid, wherein the server randomly extracts the same unique value and one icon among the plurality of icons assigned to the same unique value from the icon database for an icon retrieving process.