Efficient Combined Algorithm for Multiplication and Squaring for Fast Exponentiation over Finite Fields $$GF(2^{m})$$

For big data security, high-speed arithmetic units are needed. Finite field arithmetic has received much attention in error-control codes, cryptography, etc. The modular exponentiation over finite fields is an important and essential cryptographic operation. The modular exponentiation can be performed by a sequence of modular squaring and multiplication based on the binary method. In this paper, we propose a combined algorithm to concurrently perform multiplication and squaring over \(GF(2^{m})\) using the bipartite method and common operations. We expect that the architecture based on the proposed algorithm can reduce almost a half of latency compared to the existing architecture. Therefore, we expect that our algorithm can be efficiently used for various applications including big data security which demands high-speed computation.