Privacy-preserving localization in crowdsourcing has drawn much attention recently. Under the classical nonadjacent subtraction-based localization (NSL) model, existing solutions based on homomorphic encryption techniques are of high computational and communication overheads. In this paper, an adjacent subtraction-based localization (ASL) model is first proposed. Then, an efficient privacy-preserving localization (EPPL) algorithm is developed under ASL without using any homomorphic encryption technique. In terms of the correctness, privacy, and efficiency, a comprehensive analysis is presented to investigate EPPL's performance. Furthermore, the statistical equivalence between ASL and NSL is proved through the fact that the difference between their average location estimation results converges toward zero. The lower and upper bounds of the localization error are also derived for ASL under a bounded noise model. Extensive simulations are conducted to illustrate the equivalence between ASL and NSL, and the performance of EPPL regarding the correctness, privacy, and efficiency.