Low-Complexity Nonlinear Self-Inverse Permutation for Creating Physically Clone-Resistant Identities

New large classes of permutations over based on T-Functions as Self-Inverting Permutation Functions (SIPFs) are presented. The presented classes exhibit negligible or low complexity when implemented in emerging FPGA technologies. The target use of such functions is in creating the so called Secret Unknown Ciphers (SUC) to serve as resilient Clone-Resistant structures in smart non-volatile Field Programmable Gate Arrays (FPGA) devices. SUCs concepts were proposed a decade ago as digital consistent alternatives to the conventional analog inconsistent Physical Unclonable Functions PUFs. The proposed permutation classes are designed and optimized particularly to use non-consumed Mathblock cores in programmable System-on-Chip (SoC) FPGA devices. Hardware and software complexities for realizing such structures are optimized and evaluated for a sample expected target FPGA technology. The attained security levels of the resulting SUCs are evaluated and shown to be scalable and usable even for post-quantum crypto systems.