We propose multi target homomorphic attribute-based encryption (MT-HABE) with dynamic homomorphic evaluation: it can take as input arbitrary additional ciphertexts during homomorphic computation. In the previous MT-HABE of Brakerski et al. (TCC 2016-B), the output of homomorphic computation, which is related to a policy set, cannot be computed with a fresh ciphertext whose attribute does not satisfy any policy in the set. This is because the underlying multi-key fully homomorphic encryption (MKFHE) is single-hop: some keys are related to the output of homomorphic computation, which cannot be combined with ciphertexts encrypted under other keys. To implement dynamic homomorphic evaluations, we construct MT-HABE from a dual variant of multi-hop MKFHE proposed by Peikert and Shiehian (TCC 2016-B).
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