Arithmetic computation using self-assembly of DNA tiles: Integer power over finite field GF(2n)

DNA-based cryptography is a new developing interdisciplinary area which combines cryptography, mathematical modeling, biochemistry and molecular biology. It is still an open question that how to implement the arithmetic operations used in cryptosystem based on DNA computing. This paper proposes a DNA computing model to compute integer power over finite field GF(2ⁿ). The computation tiles performing five different functions assemble into the seed configuration with inputs to figure out the result. It is given that how the computation tiles be coded in bits and how assembly rules work. The assembly time complexity is 2n²+n-1 and the space complexity is n⁴+n³. This model requires 6436 types of computation tiles and 12 types of boundary tiles.