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The rapid development of location-based service (LBS) drives one special kind of LBS, in which the service provider verifies user location before providing services. In distributed location proof generating schemes, preventing users from colluding with each other to create fake location proofs and protecting user's location privacy at the same time, are the main technical challenges to bring this kind of LBS into practical. Existing solutions tackle these challenges with low collusion-detecting efficiency and defected collusion-detecting method. We proposed two novel location proof generating schemes, which inversely utilized a secure secret-sharing scheme and a pseudonym scheme to settle these shortcomings. Our proposed solution resists and detects user collusion attacks in a more efficient and correct way. Meanwhile, we achieve a higher level of location privacy than that of previous work. The correctness and efficiency of our proposed solution is testified by intensive security analysis, performance analysis, as well as experiments and simulation results.