A tile assembly model to calculate point-multiplication on conic curves over finite field GF(2n)
Yongnan Li · 2020
Point-multiplication is the fundamental operation to construct discrete logarithm, the intractability of which ensures the security of mathematical curves cryptography. This paper proposes a tile assembly model to calculate point-multiplication on conic curves over finite field GF(2n). The whole model consists of two types of sub-models accomplishing different functions. Both of two sub-models contain three parts and they share the second and the third parts which are designed based on a tile assembly model of division. The main differences between two sub-models are in the first part that computes point-doubling and generates different parameters for the other parts. The assembly time complexity of this model is Θ(n3), and the space complexity is Θ(n6).