We construct more efficient cryptosystems with provable security against adaptive attacks, based on simple and natural hardness assumptions in the standard model. Concretely, we describe:

– An adaptively-secure variant of the efficient, selectively-secure LWE-based identity-based encryption (IBE) scheme of Agrawal, Boneh, and Boyen (EUROCRYPT 2010).
In comparison to the previously most efficient such scheme by Yamada (CRYPTO 2017) we achieve smaller lattice parameters and shorter public keys of size $mathcal{O}(log lambda)$, where $lambda$ is the security parameter.

– Adaptively-secure variants of two efficient selectively-secure pairing-based IBEs of Boneh and Boyen (EUROCRYPT 2004). One is based on the DBDH assumption, has the same ciphertext size as the corresponding BB04 scheme, and achieves full adaptive security with public parameters of size only $mathcal{O}(log lambda)$. The other is based on a $q$-type assumption and has public key size $mathcal{O}(lambda)$, but a ciphertext is only a single group element and the security reduction is quadratically tighter than the corresponding scheme by Jager and Kurek (ASIACRYPT 2018).

– A very efficient adaptively-secure verifiable random function where proofs, public keys, and secret keys have size $mathcal{O}(log lambda)$.

As a technical contribution we introduce blockwise partitioning, which leverages the assumption that a cryptographic hash function is weak near-collision resistant to prove full adaptive security of cryptosystems.

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