In this paper, we propose a method to represent a fingerprint image by an ordered, fixed-length bit-string providing improved accuracy performance, faster matching time and compressibility. First, we devise a novel minutia-based local structure modeled by a mixture of 2D elliptical Gaussian functions in the pixel space. Each local structure is mapped to the Euclidean space by normalizing the local structure with the number of minutiae that associates to it. This simple yet crucial crux enables fast dissimilarity computation of two local structures with Euclidean distance without distortion. A complementary texture-based local structure to the minutia-based local structure is also introduced whereby both can be compressed via principal component analysis and fused easily in the Euclidean space. The fused local structure is then converted to a K-bit ordered string via a K-means clustering algorithm. This chain of computation with sole use of Euclidean distance is vital for speedy and discriminative bit-string conversion. The accuracy can be further improved by a finger-specific bit-training algorithm in which two criteria are leveraged to select useful bit positions for matching. Experiments are performed on Fingerprint Verification Competition (FVC) databases for comparison with existing techniques to show the superiority of the proposed method.