towards a massive reduction in the hardware requirements for universal and fault-tolerant quantum computation. The cat-qubits that are stabilized by a two-photon driven dissipative process, exhibit a tunable noise bias where the effective bit-flip errors are exponentially suppressed with the average number of photons. We propose a realization of a set of gates on the cat-qubits that preserve such a noise bias. Combining these base qubit operations, we build, at the level of the repetition cat-qubit, a universal set of fully protected logical gates. This set includes single qubit preparations and measurements, NOT, controlled-NOT and controlled-controlled-NOT (Toffoli) gates. Remarkably, this construction does not come with significant overhead as is the case with more conventional schemes requiring magic states preparation, distillation and injection. Finally, all required operations on the cat-qubits could be performed with simple modifications of existing experimental setups.