We present two hierarchical identity-based encryption (HIBE) schemes, denoted as $\\ahibe$ and $\\hibe$,
from Type-3 pairings with constant sized ciphertexts. Scheme $\\ahibe$ is anonymous and $\\hibe$ is non-anonymous.
The constructions are obtained by extending the IBE scheme recently proposed by Jutla and Roy (Asiacrypt 2013).
Security is based on the standard decision Symmetric eXternal Diffie-Hellman (SXDH) assumption. In terms of provable
security properties, all previous
constructions of constant-size ciphertext HIBE schemes had one or more of the following drawbacks: secure in the weaker model of
selective-identity attacks; exponential security degradation in the depth of the HIBE; and use of non-standard assumptions.
The security arguments for $\\ahibe$ and $\\hibe$ avoid all of these drawbacks. Along with theoretically satisfying security,
the parameter sizes and efficiencies of the different algorithms of the two schemes compare very well with all previously known
constructions. Based on currently known techniques, $\\ahibe$ and $\\hibe$ fill an
important gap in the state-of-the-art on efficient (anonymous) HIBE constructions.