Adaptively Secure Hierarchical Attribute-Based Encryption from Witness Encryption

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Hierarchical attribute-based encryption (HABE), also called delegatable ABE, augments ABE with a public delegation algorithm that lets any user holding a secret key for a predicate $f$ locally derive a key for a more restrictive predicate $f \land g$. Since keys are no longer produced only by the master authority, an attacker may adaptively corrupt keys generated by honest users, which makes security far more delicate than for plain ABE. For general predicates, HABE was previously known in the s