Paper 2025/1466

Revisiting Adaptively Secure IBE from Lattices with Smaller Modulus: A Conceptually Simple Framework with Low Overhead

Abstract

Most adaptively secure identity-based encryption (IBE) constructions from lattices in the standard model follow the framework proposed by Agrawal et al. (EUROCRYPT 2010). However, this framework has an inherent restriction: the modulus is quadratic in the trapdoor norm. This leads to an unnecessarily large modulus, reducing the efficiency of the IBE scheme. In this paper, we propose a novel framework for adaptively secure lattice-based IBE in the standard model, that removes this quadratic restriction of modulus while keeping the dimensions of the master public key, secret keys, and ciphertexts unchanged. More specifically, our key observation is that the original framework has a \textit{natural} cross-multiplication structure of trapdoor. Building on this observation, we design two novel algorithms with non-spherical Gaussian outputs that fully utilize this structure and thus remove the restriction. Furthermore, we apply our framework to various IBE schemes with different partitioning functions in both integer and ring settings, demonstrating its significant improvements and broad applicability. Besides, compared to a concurrent work by Ji et al. (PKC 2025), our framework is significantly simpler in design, and enjoys a smaller modulus, a more compact master public key and shorter ciphertexts.