Efficient Scalable Three Operand Multiplier Over GF(2^m) Based on Novel Decomposition Strategy

摘要

It is expected that efficient scalable three operand multiplier (STOM) over GF(2^{m) (polynomial basis) generally can provide quite a number of superior benefits such as low-complexity and flexibility on processing bits and thus is very ideal to many applications like elliptic curve cryptography and pairing cryptography. The actual efficient hardware implementation of STOM, however, is still not covered in the literature. Based on this consideration, in this paper, we propose a novel decomposition strategy based design scheme to obtain efficient STOM on hardware platforms. First of all, a novel decomposition strategy (summarized as Toeplitz Matrix Oriented Karatsuba Algorithm, TMOKA) based STOM is presented with detailed mathematical derivation. Then, the proposed STOM structure is introduced along with a number of optimization techniques. Finally, the complexity analysis and comparison have been given to confirm the efficiency of the proposed STOM, e.g., the proposed structure with scalable digit-size of 64 has at least 50.8% less area-delay product (ADP) than the TOM employing a newly reported finite field multiplier ([8]) on the FPGA platform. The proposed STOM can thus be extended and employed in many cryptographic applications.}