We implement and test the recently proposed Inhibitor gate for Recurrent Neural Networks (RNNs) that is both efficient and accurate under Homomorphic Encryption. Gated RNNs such as LSTM and GRU have applications in numerous real-world use cases for sequential data, such as time-series analysis and natural language processing, due to their ability to capture long-term dependencies. Conventionally, the update based on current inputs and the previous state history is each multiplied with the dynamic gate values and combined to compute the next state. However, as it is a multiplication between two variables that depend on the input, it can be com-putationally expensive, especially under homomorphic en-cryption, where it involves a multiplication between two cipher text variables. Therefore, the novel gating mechanism replaces the multiplication and sigmoid function of the conventional RNN with addition and ReLU activation. Numerical experiments on three synthetic benchmark tests demonstrate that our algorithm outperforms a conventional gated RNN showing at least an order of magnitude faster execution already at 4-bit quantization. At a fixed computational budget , we get 7-bit precision with the novel gate that executes faster than the 4-bit conventional gate. The gating mechanism employed in this paper may enable privacy-preserving AI applications based on gated RNNs operating under homomorphic encryption by avoiding the multiplication of encrypted variables.