Look-up table-based Montgomery algorithm in GF(2k) for public-key cryptosystem

The cur-rent paper presents a fast implementation of finite field multiplication, squaring, and exponentiation operations using two look-up tables, thereby reducing the number of operations, saving time through precomputation, and avoiding the complicated computations required in the Montgomery method. Furthermore, look-up table-based algorithms have the advantage of speed and are particularly suitable for cryptographic applications, where k is large, and memory-constrained environments, such as smart cards and embedded cryptosystems.