Compact hierarchical IBE from lattices in the standard model

Abstract

At Crypto’10, Agrawal et al. proposed a lattice-based selectively secure Hierarchical Identity-based Encryption (HIBE) scheme (ABB10b) with small ciphertext on the condition that λ (the length of identity at each level) is small in the standard model. In this paper, we present another lattice-based selectively secure HIBE scheme with depth d, using a gadget matrix G′∈Zqn×n⌈logbq⌉ with enough large b= 2 d to replace the matrix B∈Zqn×m in the HIBE scheme proposed by Agrawal et al. at Eurocrypt’10. In our HIBE scheme, not only the size of ciphertext at level ℓ is (Formula Presented) larger than the size in ABB10b and at least O(ℓ) smaller than the sizes in the previous HIBE schemes except ABB10b, but also the size of the master public key is at least O(d) times smaller than the previous schemes.