Paper 2026/1845

Lattice-based NIKE with optimal tightness

Abstract

In this work we present a new variant of the non-interactive key exchange (NIKE) scheme based on the learning with errors (LWE) assumption and prove its security with a security reduction that incurs a security loss that is only linear in the number of users. This improves upon all prior reductions for lattice-based NIKE schemes, which had a security loss that is quadratic in the number of users. Our tight reduction can handle the setting with super-polynomial modulus-to-noise ratio and negligible correctness error as well as the more challenging setting with polynomial modulus-to-noise ratio and inverse polynomial correctness error. We also give a matching lower bound on the tightness for a natural class of lattice-based NIKE schemes (that captures all existing variants of lattice-based NIKE), showing that our security loss is optimal (up to constant factors). This generalizes a lower bound by Hesse, Hofheinz and Kohl (Crypto 2018) and is the first lower bound for the tightness of lattice-based NIKE schemes. Several previous lower bounds for the tightness of NIKE exist, but none of them can be applied to lattice-based schemes.