In this paper, we propose a new technique that uses fault injection to reverse-engineer a private block cipher implemented with an unknown S-box. The private algorithm we wish to retrieve differs from a known algorithm in the choice of the S-Box, which we find using a novel, fault-injecting technique. The main idea is to consider the components of the S-Box as the solutions of a linear boolean system, whose equations stem from the faults injected, using existing fault models. We focus on two well-known block ciphers, DES and AES, and prove it to be feasible to retrieve the the S-Box for both cases. We present the fault models used, the equations extracted from the faults injected, and analyse the final results. Given the detailed analysis, the technique can be applied with ease to most ciphers employing an S-box.