Brain signals have long been studied within various fields like medical, physiotherapy, and neurology for many years. One of the main reasons for this interest is to better understand brain diseases like Parkinson's, Schizophrenia, Alzheimer's, epilepsy, spinal cord injuries, and stroke among others. More recently, they have been used in brain-computer interface systems for rehabilitation, entertainment, and assistance applications. Even with the growing interest in clinical applications, the scientific community has only recently investigated the possibility of using brain signals as a potential biometric feature that can be used in people authentication and recognition systems. In this research, the authors have studied the use of brain signals acquired using electroencephalogram (EEG) during both eyes open and eyes closed states for identification based on a large dataset of 109 subjects. The use of a novel mind relaxation metric to determine the optimum epochs to select for the classification and verification has generated very high classification results, in the range of 97-99% based on a single channel. The approach has also been validated against another dataset to verify its consistency and repeatability. The results demonstrate that it is possible to move towards a single-channel biometric identification system with a very high level of reliability and accuracy.