Emerging reconfigurable nanotechnologies allow the implementation of self-dual functions with a fewer number of transistors as compared to traditional CMOS technologies. To achieve better area results for Reconfigurable Field-Effect Transistors (RFET)-based circuits, a large portion of a logic representation must be mapped to self-dual logic gates. This, in turn, depends upon how self-duality is preserved in the logic representation during logic optimization and technology mapping. In the present work, we develop Boolean size-optimization methods– a rewriting and a resubstitution algorithms using Xor-Majority Graphs(XMGs) as a logic representation aiming at better preserving self-duality during logic optimization. XMGs are more compact for both unate and binate logic functions as compared to conventional logic representations such as And-Inverter Graphs(AIGs) or Majority-Inverter Graphs (MIGs). We evaluate the proposed algorithm over crafted benchmarks (with various levels of self-duality), and cryptographic benchmarks. For cryptographic benchmarks with a high self-duality ratio, the XMG-based logic optimisation flow can achieve an area reduction of up to17% when compared to AIG-based optimization flows implemented in the academic logic synthesis tool ABC.