Arithmetic Computation Using Self-Assembly of DNA Tiles: Point-Addition on Conic Curves over Finite Field GF(2^n)

Abstract

This paper discusses how to accomplish point-addition, a basic operation in conic curves cryptosystem over finite field GF(2^n), using DNA tile self-assembly. The assembly process is divided into two steps mapping two different sub-models. One of them is a new designed model to generate the input parameters for the second step. The other one is an existing model to compute division over finite field GF(2^n) proposed in our previous work. All possible input cases are considered in the assembly process. The time complexity is T(n)=2n^2+n-1 and space complexity is S(n)=n^4+n^3. It requires 6372 types of computation tiles and 78 types of boundary tiles.