Katz et al. (CANS'17) introduced Subset Predicate Encryption (SPE). This scheme is a generalization of broadcast encryption as it emulates the \emph{subset containment} predicate in the encrypted domain. They proposed two selectively IND-CPA secure SPE constructions in the small universe setting. They also showed some black-box transformations of SPE to well-known primitives like WIBE and ABE to establish the richness of the SPE structure. Chatterjee and Mukherjee (RSA'19) proposed two SPE constructions in the large-universe setting. Their first construction achieved constant-size ciphertexts and secret keys, but it is proven secure in a restricted version of selective security. Although the second construction achieves adaptive security, the ciphertext size depends on the size of the data-attribute set. Furthermore, neither of these two constructions achieves CCA security. In this work, we propose the first large-universe CCA-secure subset predicate encryption with constant-size ciphertext and secret keys. We prove this construction achieves standard selective security under the standard subgroup decision problems. Finally, we transform our extremely efficient SPE into the first CCA-secure WIBE, WKD-IBE, etc., with constant-size ciphertexts and secret keys via black-box transformations.

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