Quaternary Reed-Muller Expansions of Mixed Radix Arguments in Cryptographic Circuits

Circuits built using multi-valued fixed polarity Reed-Muller expansions based on Galois field arithmetic, in particular quaternary expansions over GF(4), normally display high efficiency in terms of power consumption, area, etc. However, security application specific gate level mapping shows inefficient results for uniform radix expansions. The idea of the research here is to consolidate binary and quaternary Galois field arithmetic within a single circuit in such a way that the mathematical representations can benefit down to the gate level model. A direct method to compute quaternary fixed polarity Reed-Muller expansions of mixed radix arguments is proposed and implemented in a synthesis tool. The results for the various types of power-balanced signal encoding catered for the security application are compared and analysed.