We introduce a novel approach for designing symmetric ciphers to resist fault injection. The approach is fairly generic and applies to round functions of block ciphers, cryptographic permutations and stream ciphers. We showcase our method with a new permutation called FRIT and perform fault analysis on a simulated hardware and actual software implementation. We present performance results for software and hardware implementations with and without the fault detection mechanism. On a Cortex-M4 platform the overhead of the countermeasure in cycles is 83%. The penalty on resources for hardware implementations depends on the hardware and can be as low as 56%.