In this paper, we have proved the diminution in error approximation when identity authentication is done with Ideal Password Authentication Scheme (IPAS) for Network Security. Effectiveness of identity authentication parameters for various attacks and security requirements is verified in the paper. Result of analysis proves that IPAS would enhance the transport layer security. Proof of efficiency of result is generated with drastic diminution in error approximation. IPAS would have advanced security parameters with implemented RNA-FINNT which would result in fortification of the transport layer security protocol for enhancement of Network Security.