On the Construction of Composite Finite Fields for Hardware Obfuscation

Hardware obfuscation is a technique that modifies the circuit to hide the functionality. Obfuscations through algorithmic modifications add protection in addition to circuit-level techniques, and their effects on the data paths can be analyzed and controlled at the architectural level. Many error-correcting coding and cryptography algorithms are based on finite field arithmetic. For the first time, this paper proposes a hardware obfuscation scheme achieved through varying finite field constructions and primitive element representations. Also the variations are effectively transformed to bit permuters controlled by obfuscation keys to achieve high level of security with very small complexity overheads. To illustrate the effectiveness, the proposed scheme is applied to obfuscate Reed-Solomon decoders, which are broadly used in communication and storage systems. For a (255, 239) RS decoder over finite field $GF(256)$GF(256), the proposed scheme achieves 1239 bits of independent obfuscation key with 4.4 percent area overhead, while yielding no penalty on the throughput and only one extra clock cycle of latency.