Programmable Montgomery Modular Multiplier for Trinomial Reduction Polynomials in GF(2m)

With cryptosystems pervading most information security systems, cryptoprocessors that are adaptable to changing security requirements are needed. Montgomery modular multiplication in GF(2^m) is commonly used in elliptic curve cryptography to implement encryption and decryption engines. This paper introduces a programmable Montgomery multiplier for a class of finite fields that have a trinomial reduction polynomial. A novel architecture is proposed that can be programmed to operate in any extended binary field, GF(2^m), of order m such that m les M where M is the maximum field order supported by the multiplier. The proposed architecture is further extended to the design of Montgomery squarer. The area-delay trade offs that accompany the programmability of architectures are discussed.