Efficient identity-based encryption without pairings and key escrow for mobile devices

We propose a new construction of identity-based encryption without key escrow over the tradition cryptosystems. The security of our scheme follows from the decisional Diffie-Hellman assumption and the difficulty of a new problem --- modular inversion hidden number problem with error (MIHNPwE). The latter can be seen as a generalization of the modular inversion hidden number problem. We give an analysis on the hardness of MIHNPwE by lattice techniques. In our construction, we generate each user's partial private key in the form of an MIHNPwE instance. The hardness of MIHNPwE provides our scheme with resistance against key-collusion attacks from any number of traitors.