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Range query on encrypted data has been widely studied to achieve fast query processing while keeping data and queries secret. Prior work hides even the ordering information of the data, but sacrifices accuracy (e.g., false positives) and efficiency (e.g., exponential complexity in the domain size) as a trade-off. Moreover, hiding the order alone is not sufficient to prevent the recent database reconstruction attacks on range query abusing access pattern and volume leakage. Several countermeasures prevent such information leakage but incur practically unacceptable storage or computational overhead due to fake records embedded in the database and database re-encryption procedures. In this paper, we first propose a range query scheme <inline-formula> <tex-math notation="LaTeX">$\mathsf{RevealRE}$ </tex-math></inline-formula>, which is highly efficient, but reveals ordering information. We then extend <inline-formula> <tex-math notation="LaTeX">$\mathsf{RevealRE}$ </tex-math></inline-formula> to construct <inline-formula> <tex-math notation="LaTeX">$\mathsf{HideRE}$ </tex-math></inline-formula>, a range query scheme that does not leak data ordering information while accurate (i.e., no false positives/negatives) and efficient (i.e., logarithmic search time). <inline-formula> <tex-math notation="LaTeX">$\mathsf{HideRE}$ </tex-math></inline-formula> can mitigate the database reconstruction attacks by introducing <italic>deceptive</italic> queries, which are indistinguishable from regular queries while obfuscating the queried ranges. We experimentally confirm efficiency of our construction under various data distribution models, demonstrating the practicality. Resilience to database reconstruction attacks of our order-hiding range query scheme is formally proved.