Parallel Montgomery multiplication and squaring over GF(2m) based on cellular automata

Exponentiation in the Galois Field GF(2(m)) is a primary operation for public key cryptography, such as the Diffie-Hellman key exchange, ElGamal. The current paper presents a new architecture that can simultaneously process modular multiplication and squaring using the Montgomery algorithm over GF(2(m)) in m clock cycles based on a cellular automata. The proposed architecture makes use of common-multiplicand multiplication in LSB-first modular exponentiation over GF(2(m)). In addition, modular exponentiation, division, and inversion architecture can also be implemented, and since cellular automata architecture is simple, regular, modular, and cascadable, it can be utilized efficiently for the implementation of VLSI.