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The main objective of the research is to propose the hybrid methods for secure authentication methods using two-dimensional nxn passwords. When an intrusion attack strikes the system then its services have to be truncated and system become unavailable temporarily. To make the system available to the end user in the vulnerable state, the specialized access control should be in place. Therefore, specialized and secure authentication methods are required. Authenticating through these methods, users can become active again to the system and considered as safe. The long and complex nxn passwords are used and considered to be very useful in certain alarming situations such as the system being under threat. Proposed hybrid methods works on the two portions of the password that is server generated part and user created part and ensure the secure authentication to the system resources that is under threat. Proposed methods are classified on the basis of symmetrical displacement of server generated part and user created part of the password. The strength and limitations of all the proposed methods have also been analyzed.