Trapdoor Delegation and HIBE from Middle-Product LWE in Standard Model

TL;DR

This paper introduces a novel trapdoor delegation technique enabling the construction of a hierarchical identity-based encryption scheme based on Middle-Product LWE, achieving standard model security.

Contribution

It presents the first hierarchical IBE scheme from MPLWE by developing a new trapdoor delegation method for extended polynomial families.

Findings

Hierarchical IBE scheme from MPLWE in standard model

Novel trapdoor delegation mechanism for polynomial families

Secure in the standard cryptographic model

Abstract

At CRYPTO 2017, Rosca, Sakzad, Stehle 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 Hierachical 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 Hierachy IBE scheme is provably secure in the standard model.