关键词: 非确定性多项式（NP）完全, 多项式规约, Hamilton路, 3SAT, RSA密码

Abstract: It gets a fast algorithm on the Hamilton path. It transforms the 3SAT to the Hamilton path by a polynomial transform. Though there has been some methods to transform 3SAT to Hamilton path, that is only for NPC proof. It is polynomial but not the most efficient. In order to get the most efficient transform from 3SAT to Hamilton path, so as to calculate 3SAT efficiently by calculating the Hamilton path in a possibly good way, this paper uses two vertices to denote a variable in 3SAT, uses a good graph structure which contains 13 vertices to denote a clause in 3SAT, then realizes the above goal. It needs the least number of vertices and edges. It transforms the problem of large number of qualitative factors to 3SAT. So at last, it can decode the RSA by calculating the Hamilton path.

Key words: Non-deterministic Polynomial（NP） complete, polynomial transform, Hamilton path, 3SAT, RSA code