Anonymous Identity-Based Hash Proof System from Lattices in the Standard Model

An Identity-Based Hash Proof System (IB-HPS) is a fundamental and important primitive, which is widely adapted to construct a number of cryptographic schemes and protocols, especially for leakage-resilient ones. Therefore it is significant to instantiate IB-HPSs from various assumptions. However, all existing IB-HPSs based on lattices are set only in the random oracle model. Thus, proposing an IB-HPS from lattices in the standard model is an essential and interesting work. In this paper, we introduce a much more compact definition for an anonymous IB-HPS, defining computational indistinguishability of valid/invalid ciphertexts and anonymity of identity simultaneously. Then, through utilizing the technique for delegating a short lattice basis due to Agrawal et al. in CRYPTO 2010 and the property of the smoothing parameter over random lattices, we present a new construction of IB-HPS in the standard model. Furthermore, we show that our new construction is selectively secure and anonymous based on the standard learning with errors (LWE) assumption in the standard model.