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With a significant advance in ciphertext searchability, Public-key Encryption with Keyword Search (PEKS) is the first keyword searchable encryption scheme based on the probabilistic encryption, such that it is more secure than almost all previous schemes. However, there is an open problem in PEKS that its search complexity is linear with the sum of ciphertexts, such that it is inefficient for a mass of ciphertexts. Fortunately, the authors find an elegant method that by adaptively taking the keyword trapdoor of each query as an index, the search complexity of the queried keywords can be decreased in a huge degree.
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