Adaptively Secure Distributed PRFs from $$\textsf {LWE}$$

In distributed pseudorandom functions (DPRFs), a PRF secret key SK is shared among N servers so that each server can locally compute partial evaluation of the on some input X. A combiner collects t evaluations then reconstruct F(SK, X) under initial key. So far, all non-interactive constructions in standard model are based lattice assumptions. One caveat they only known to be secure static corruption setting, where adversary chooses corrupt at very beginning game, before any query. this work, we construct first fully adaptively DPRF model. Our construction proved $$\textsf {LWE}$$ assumption against adversaries may decide which want corrupt. We also extend our order achieve robustness malicious adversaries.