A new approach in iris recognition based on Circular Fuzzy Iris Segmentation (CFIS) and Gabor Analytic Iris Texture Binary Encoder (GAITBE) is proposed and tested here. CFIS procedure is designed to guarantee that similar iris segments will be obtained for similar eye images, despite the fact that the degree of occlusion may vary from one image to another. Its result is a circular iris ring (concentric with the pupil) which approximates the actual iris. GAITBE proves better encoding of statistical independence between the iris codes extracted from different irides using Hilbert Transform. Irides from University of Bath Iris Database are binary encoded on two different lengths (768 / 192 bytes) and tested in both single-enrollment and multi-enrollment identification scenarios. All cases illustrate the capacity of the newly proposed methodology to narrow down the distribution of inter-class matching scores, and consequently, to guarantee a steeper descent of the False Accept Rate.