The document presents a new feebly secure cryptographic construction that improves on previous work. It introduces new techniques for proving lower bounds on circuit complexity through gate elimination methods applied to linear Boolean functions. Specifically: 1) A new feebly secure cryptographic protocol is proposed that uses linear functions and block matrices to make inversion without a trapdoor harder than with a trapdoor, while keeping encryption complexity similar to inversion without a trapdoor. 2) New predicates and algorithms are introduced for applying gate elimination to linear functions represented as matrices, allowing estimation of complexity. 3) Analysis shows the new construction has an order of security approaching 5/4, improving on previous work that achieved 25/22. This represents