Noise-based logic gates by operations on the reference system

We propose a new, low-complexity solution to realize multi-input-bit gates acting on exponentially large superpositions in noise-based logic processors. Two examples are shown, the NOT gate and the CNOT gate. The operations can be executed and repeated with polynomial time and hardware complexity. The lack of solution of this problem had been one of the major issues prohibiting the efficient realization of Shor algorithm by Instantaneous Noise-Based, which runs on a classical Turing computer with a true random number generator. With the method described in this paper, we are one step closer to this goal.