International Association
for Cryptologic Research

Current adaptively secure identity-based encryption (IBE) constructions from lattices are unable to achieve a good balance among the master public key size, secret key size, modulus and reduction loss. All existing IBE schemes are subject to a quadratic restriction of modulus on the trapdoor norm, which harshly increases the modulus. In this work, we remove this restriction and present a new adaptively secure IBE scheme from lattices in the standard model, which improves the state-of-the-art construction proposed by Abla et al. (TCC 2021) and achieves asymptotically better efficiency. More precisely, we achieve the asymptotically minimum number of public vectors among all the previous schemes and a tight security reduction, together with a significantly smaller modulus compared to the scheme by Abla et al. (TCC 2021). Furthermore, our scheme enjoys the smallest Gaussian width of the secret key among all existing schemes. We propose a novel cross-multiplication design for our IBE scheme and several novel tools/techniques including: a) homomorphic computation outputting BGG+-style encoding with two distinct-norm trapdoors; b) sampling algorithm with hybrid Gaussian outputs; c) partial rerandomization. These new tools and techniques are general and could find rich applications in lattice-based cryptography.

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 efficiently exploit 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 and independent 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.