Efficient Multiplication Beyond Optimal Normal Bases

In cryptographic applications, the use of normal bases to represent elements of the finite field GFð2Þ is quite advantageous, especially for hardware implementation. In this article, we consider an important field operation, namely, multiplication which is used in many cryptographic functions. We present a class of algorithms for normal basis multiplication in GFð2Þ. Our proposed multiplication algorithm for composite finite fields requires a significantly lower number of bit level operations and, hence, can reduce the space complexity of cryptographic systems.