We present the first adaptively-secure HIBE, that does not rely on bilinear pairings or random oracle heuristics. Notably, we prove adaptive security of the Döttling-Garg HIBE scheme based on any selectively secure IBE system in the standard model. Combining this with known results, this gives the first adaptively-secure HIBE system from a wide variety of standard assumptions such as CDH/Factoring/LWE/LPN. We also extend our adaptively-secure HIBE system to satisfy full-anonymity, giving the first adaptively-secure anonymous-HIBE under CDH/LWE assumption. All our HIBE systems support unbounded length identities as well as unbounded number of recursive delegation operations.