We present the first generic framework for constructing simulation-secure registered functional encryption (RFE) schemes for various expressive function classes supporting access control and unbounded inputs from the (bilateral) k-Lin assumption. Previously, the only RFEs from standard assumptions [Zhu et al., Eurocrypt’24] support linear and quadratic functions without access control or unbounded inputs. Our framework captures both non-uniform and uniform models of computation, including the following functionalities: For both functionalities, our framework can instantiate g and h by arithmetic branching programs ( \(\textsf{ABP}\) ), deterministic logspace Turing machines ( \(\textsf{L}\) ) or non-determinisitc logspace Turing machines ( \(\textsf{NL}\) ). As a special case, this yields the first registered attribute-based encryption (RABE) scheme supporting uniform models of computation, captured by \(\textsf{L}\) or \(\textsf{NL}\) , without making use of indistinguishability obfuscation. The public parameter sizes of our RFEs supporting \(\textsf{L}\) and \(\textsf{NL}\) grow with the number of states in the Turing machines, but remain compact concerning the other parameters. Notably, secret keys, the master public key and helper secret keys are independent of the input length as well as time and space complexity. Irrespective of compactness, we want to stress the fact that our schemes are the first to support large classes of Turing machines combined with both linear and quadratic computations, based solely on standard assumptions. Conceptually, we transfer the framework of [Lin and Luo, Eurocrypt’20]—combining linear FE with information-theoretic garbling schemes—from the classical to the registration-based setting, thereby solving an open problem mentioned in [Zhu et al., Asiacrypt’23]. At the core of our constructions, we introduce a novel RFE for inner products with user-specific pre-constraining of the functions which enables the randomization of garbling schemes akin to classical inner-product FE.