Abstract
We present an adaptively secure identity-based encryption (IBE) scheme with constant sized parameters and constant security loss in multi-instance multi-ciphertext (MIMC) setting in prime-order groups, in the random oracle model. We then further construct an adaptively secure hierarchical identity-based encryption (HIBE) scheme with shorter sized parameters and constant security loss in the MIMC setting in prime-order groups, in the random oracle model.At the core of our technique, we observe that the pseudorandomness property of the random oracle matches the conditions of Left Subgroup Indistinguishability (LS) and Right Subgroup Indistinguishability (RS) in dual system groups (DSG) well, so that we can transform the queried secret keys and the challenge ciphertexts for once. We construct our IBE scheme from Agrawal and Chase's work (CCS 2017) and construct our HIBE scheme from Boneh et al.'s work (Eurocrypt 2005). As a byproduct of our IBE scheme, we construct a new DSG instantiation from Chen et al.'s work (Eurocrypt 2015) under bi-MDDH assumption.
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