Using lattice basis delegation in a fixed dimension, we propose an efficient lattice-based hierarchical identity based encryption (HIBE) scheme in the standard model whose public key size is only (dm2+mn)logq bits and whose message-ciphertext expansion factor is only logq, where d is the maximum hierarchical depth and (n,m,q) are public parameters. In our construction, a novel public key assignment rule is used to averagely assign one random and public matrix to two identity bits, which implies that d random public matrices are enough to build the proposed HIBE scheme in the standard model, compared with the case in which 2d such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is (2dm2+mn+m)logq. To reduce the message-ciphertext expansion factor of the proposed scheme to logq, the encryption algorithm of this scheme is built based on Gentry’s encryption scheme, by which m2 bits of plaintext are encrypted into m2logq bits of ciphertext by a one time encryption operation. Hence, the presented scheme has some advantages with respect to not only the public key size but also the message-ciphertext expansion factor. Based on the hardness of the learning with errors problem, we demonstrate that the scheme is secure under selective identity and chosen plaintext attacks.
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