<p>Conventional biometric authentication systems require accessing stored biometric templates, exposing sensitive data to risks such as hacking and data breaches. Here we present an all-wave computational fingerprint identification framework that replaces digital postprocessing and template matching with single-step physical computation. We introduce a loop-diffractive neural network in which ultrasonic waves propagate through a single learned metasurface, enabling hardware-level computation via diffraction. By exploiting three-parameter modulation—phase, amplitude and switch state—the metasurface expands the design space of the loop-diffractive neural network. During authentication, acoustic energy is routed to a predefined detector region only when the input fingerprint corresponds to a registered user; otherwise, the energy concentrates in an alternative region and comparing the intensities determines the match outcome. This approach removes the need to store biometric templates and provides efficient, inherently parallel, wave-based processing for advanced biometric security.</p>