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In this paper, we propose a method of inertial sensor-based gait authentication by inter-period phase registration of an owner's gallery. In spite of the importance for gait authentication of constructing a gallery of phase-registered gait patterns, previous implementations just relied on simple methods of period detection based on heuristic knowledge such as local peaks/valleys or local auto-correlation of the gait signals. Consequently, we propose to improve a gait gallery by incorporating a phase registration technique which globally optimizes inter-period phase consistency in an energy minimization framework. However, the previous phase registration technique suffers from a phase distortion problem due to ambiguities in the combination of a periodic signal function and a phase evolution function. We present a linear phase evolution prior to constructing an undistorted gait signal for better matching performance. Experiments using real gait signals from 32 subjects show that the proposed methods outperform the latest methods in the field.