Description: The false acceptance rate (FAR) is a critical concept in the realm of authentication systems, referring to the probability that a security system incorrectly accepts an unauthorized user. This metric is essential for assessing the effectiveness of authentication mechanisms, as a high false acceptance rate can compromise the security of a system, allowing access to individuals without permission. FAR is typically expressed as a percentage and is calculated by dividing the number of unauthorized access attempts accepted by the total number of unauthorized access attempts. In the context of authentication systems, where various verification methods (such as passwords, tokens, biometrics, etc.) are used, the false acceptance rate becomes a crucial parameter to ensure that the system is not only accessible to legitimate users but also robust enough to deny intruders. Managing FAR is a delicate balance; a system that is too strict may result in a high false rejection rate, where authorized users are incorrectly denied, while one that is too lenient may allow unwanted access. Therefore, the false acceptance rate is a key indicator in evaluating the security and usability of authentication systems.