A random number generator (RNG), a cryptographic technology that plays an important role in security and sensor networks, can be designed using a linear feedback shift register (LFSR). This cryptographic transformation is currently done through CMOS. It has been developed by reducing the size of the gate and increasing the degree of integration, but it has reached the limit of integration due to the quantum tunneling phenomenon. Quantum-dot cellular automata (QCA), one of the quantum circuit design technologies to replace this, has superior performance compared to CMOS in most performance areas, such as space, speed, and power. Most of the LFSRs in QCA are designed as shift registers (SR), and most of the SR circuits proposed based on the existing QCA have a planar structure, so the cell area is large and the signal is unstable when a plane intersection is implemented. Therefore, in this paper, we propose a multilayered 2-to-1 QCA multiplexer and a D-latch, and we make blocks based on D-latch and connect these blocks to make SR. In addition, the LFSR structure is designed by adding an XOR operation to it, and we additionally propose an LFSR capable of dual-edge triggering. The proposed structures were completed with a very meticulous design technique to minimize area and latency using cell interaction, and they achieve high performance compared to many existing circuits. For the proposed structures, the cost and energy dissipation are calculated through simulation using QCADesigner and QCADesigner-E, and their efficiency is verified.

Many studies have addressed the physical limitations of complementary metal-oxide semi-conductor (CMOS) technology and the need for next-generation technologies, and quantum-dot cellular automata (QCA) are emerging as a replacement for nanotechnology. Meanwhile, the divider is the most-used circuit in arithmetic operations with squares and multipliers, and the development of effective dividers is crucial for improving the efficiency of inversion and exponentiation, which is known as the most complex operation. In most public-key cryptography systems, the corresponding operations are used by applying algebraic structures such as fields or groups. In this paper, an improved design of a non-restoring array divider (N-RAD) is proposed based on the promising technology of QCA. Our QCA design is focused on the optimization of dividers using controlled add/subtract (CAS) cells composed of an XOR and full adder. We propose a new CAS cell using a full adder that is designed to be very stable and compact so that power dissipation is minimized. The proposed design is considerably improved in many ways compared with the best existing N-RADs and is verified through simulations using QCADesigner and QCAPro. The proposed full adder reduces the energy loss rate by at least 25% compared to the existing structures, and the divider has about 23%~4.5% lower latency compared to the latest coplanar and multilayer structures.