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The authors introduce a new primitive called identity-based encryption with wildcard key derivation (WKD-IBE or `wicked IBE`) that enhances the concept of hierarchical identity-based encryption by allowing more general key delegation patterns. A secret key is derived for a vector of identity strings, where entries can be left blank using a wildcard. This key can then be used to derive keys for any pattern that replaces wildcards with concrete identity strings. For example, one may want to allow the university`s head system administrator to derive secret keys (and hence the ability to decrypt) for all departmental sysadmin email addresses sysadmin@*.univ.edu, where * is a wildcard that can be replaced with any string. The authors provide appropriate security notions and provably secure instantiations with different tradeoffs in terms of ciphertext size and efficiency. The authors also present a generic construction of identity-based broadcast encryption (IBBE) from any WKD-IBE scheme. One of their instantiations yields an IBBE scheme with constant ciphertext size.