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.