© 2020, Springer Nature Switzerland AG. At CRYPTO 2017, Roşca, Sakzad, Stehlé and Steinfeld introduced the Middle–Product LWE (MPLWE) assumption which is as secure as Polynomial-LWE for a large class of polynomials, making the corresponding cryptographic schemes more flexible in choosing the underlying polynomial ring in design while still keeping the equivalent efficiency. Recently at TCC 2019, Lombardi, Vaikuntanathan and Vuong introduced a variant of MPLWE assumption and constructed the first IBE scheme based on MPLWE. Their core technique is to construct lattice trapdoors compatible with MPLWE in the same paradigm of Gentry, Peikert and Vaikuntanathan at STOC 2008. However, their method cannot directly offer a Hierarchical IBE construction. In this paper, we make a step further by proposing a novel trapdoor delegation mechanism for an extended family of polynomials from which we construct, for the first time, a Hierachical IBE scheme from MPLWE. Our Hierarchy IBE scheme is provably secure in the standard model.
Le, H., Duong, H., Susilo, W. & Pieprzyk, J. (2020). Trapdoor Delegation and HIBE from Middle-Product LWE in Standard Model. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 12146 LNCS 130-149.