An Improved Molecular Computing Model of Modular-Multiplication over Finite Field GF(2n)

With the rapid development of DNA computing, there are some questions worth study that how to implement the arithmetic operations used in cryptosystem based on DNA computing models. This paper proposes an improved DNA computing model to calculate modular-multiplication over finite field GF(2n). Comparing to related works, both assembly time complexity and space complexity are more optimal. The computation tiles performing 4 different functions assemble into the seed configuration with inputs to figure out the result. It is given that how the computation tiles be bitwise coded and how assembly rules work. The assembly time complexity is Θ(n) and the space complexity is Θ(n2). This model requires 148 types of computation tiles and 8 types of boundary tiles.