Summary: A linear network code is called \(k\)-secure if it is secure even if an adversary eavesdrops at most \(k\) edges. In this paper, we show an efficient deterministic construction algorithm of a linear transformation \(T\) that transforms an (insecure) linear network code to a \(k\)-secure one for any \(k\), and extend this algorithm to strong \(k\)-security for any \(k\) . Our algorithms run in polynomial time if \(k\) is a constant, and these time complexities are explicitly presented. We also present a concrete size of \(|\mathsf{F}|\) for strong \(k\)-security, where \(\mathsf{F}\) is the underling finite field.