Quantum-dot cellular automata (QCA) technology is considered to be the future of nanoelectronic device fabrication technology. The fabrication density of the transistors in a particular area in the current nanoelectronic industry has saturated. Adroit alternate to current CMOS based VLSI technology is being researched upon. QCA technology is considered to be the noblest post-CMOS era fabrication technology. In this paper, novel energy-efficient QCA designs for 1/2 and 1/3 convolution encoders have been presented. Both the presented designs were proven to be efficient than previously designed circuits. The efficiency of the design is calculated for critical design parameters like cell count, cell area, latency (clock phases), complexity and energy dissipation. The proposed 1/2 convolution encoder uses 21 QCA cells consuming an area of 0.012µm2. The complexity of this design was calculated to be 2. The energy dissipation analysis revealed that the presented circuit dissipated 14.03meV of energy. The proposed 1/3 convolution encoder uses 32 QCA cells consuming an area of 0.025µm2. The energy dissipation analysis revealed that the presented circuit dissipated 16.88meV of energy. Both the proposed designs used only a few more extra cells than the previously designed circuits but induced stronger polarizations and were more fault-tolerant. It was found that the circuits proposed are 25% more energy efficient than previously designed circuits. The latency of the proposed designs was of 2 clock phases, thus making it suitable for high-speed operation. Significant improvement of the designs was done to optimize the circuit for secure nano-communication devices.