Abstract:

The concept of constrained pseudo-random functions (CPRF) was proposed independently by Boneh and Waters, Boyle etc., Kiayias etc. in 2013. In a CPRF a constrained key  ks can be derived from the master key  k. Both  ks and   k can be used to calculate the same pseudo-random function (PRF) value. Based on the CPRF with bit-fixing structure proposed by Boneh and Waters, we propose a construction of hierarchical proxy based on constrained pseudorandom functions. The size of the constrained set cannot be influenced by the layer number of the hierarchical proxy. The proposed scheme is proved to be secure in the standard model under the multilinear decisional Diffie-Hellman assumption. And it can be used to generate the encryption key of broadcast encryption or the session key of the identity-based non-interactive key exchange under the hierarchical proxy in practice.

Key words: constrained pseudo-random functions(CPRF), multilinear maps, hierarchical proxy, standard model