The palm vein authentication technology is extremely safe, accurate and reliable as it uses the vascular patterns contained within the body to confirm personal identification. The pattern of veins in the palm is complex and unique to each individual. Its non-contact function gives it a healthful advantage over other biometric technologies. This paper presents an algebraic method for personal authentication and identification using internal contactless palm vein images. We use MATLAB image processing toolbox to enhance the palm vein images and employ coset decomposition concept to store and identify the encoded palm vein feature vectors. Experimental evidence shows the validation and influence of the proposed approach.