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Efficient and privacy-preserving constructions for search functionality on encrypted data are important issues for data outsourcing, and data retrieval, etc. Fully secure anonymous Hierarchical ID-Based Encryption (HIBE) schemes is useful primitives that can be applicable to searchable encryptions, such as ID-based searchable encryption, temporary searchable encryption, and anonymous forward secure HIBE . The authors propose a fully secure anonymous HIBE scheme with constant size ciphertexts. Shamir introduced the notion of Identity-Based Encryption (IBE) which is a public-key cryptosystem being able to use any string, such as e-mail, as a public key, and Boneh and Franklin proposed the first IBE scheme using pairing .
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