The Internet and World Wide Web have become important parts of most people's lives. User validation in computer systems is a major concern in computer security for years. Individual users have different Passwords for various systems, but there is a challenge of remembering numerous Passwords for numerous systems from email to web accounts, banking and financial services. The concept of a user id and Password is a cost effective and well-organized method of keeping a secret among user and computer system. Novel method of creating or generating Alpha-Numeric Password for improving the security has been proposed using Context Free Grammar, Markov Chain and Petri Net model. Two factor authentication and three factor authentications also proposed. CFG Password and Markov Password are class of alphanumeric Password which varies from random Passwords as pattern of strings and rule based on character selection respectively. The Objective is to provide Efficient Authentication Procedures for Information Security using Mathematical Models.