Introduction to ECC Encryption algorithm introduction

Introduction to ECC Encryption algorithm introduction
Objective
As with RSA (Ron Rivest,adi Shamir,len Adleman three-bit genius), ECC (elliptic Curves cryptography, elliptic-curve cryptography) also belongs to the public key algorithm. At present, there is not much public literature on ECC in detail in China (I haven't found it anyway). There are some briefs, but also generalities, after reading still cannot understand the essence of ECC (perhaps my understanding is too poor). Some days ago I found some materials from foreign websites, after reading the ECC seems ignorant. So I want to put my understanding of ECC, and share with you. Of course, ECC profound, my understanding is very superficial, the article must be a lot of mistakes, welcome all the way master criticism, I am all ears, and timely correction. The article will be serialized way, I write a little bit on the post. This article mainly focuses on the theory, code implementation is not involved. This requires you to have a little math skills. It is best that you understand the RSA algorithm and have an understanding of the public key algorithm. "The foundation of Modern Algebra" "Elementary Number Theory" and other books, it is better for you to flip first, which is helpful for you to understand this article. Don't be afraid, I will try to make the language more popular, I hope this article can become a stepping stone to learn ECC.
First, from the parallel line talk about.
Parallel lines, never intersect. No one doubted: but in modern times the conclusion was questioned. Will parallel lines intersect in far and far away places? No one has actually seen it. So "parallel lines, never intersect" is just the assumption (we think of the parallel axiom of junior high school learning, is not proved). Now that you can assume that parallel lines never intersect, you can assume that parallel lines intersect very far away. That is, parallel lines intersect at Infinity Point p∞ (Please close your eyes, imagine that the Infinity point p∞,p∞ is not very unreal, in fact, rather than the mathematical exercise of the abstract ability of people, rather than exercise human imagination). Give a diagram to help understand:
The advantage of having a p∞ point on a line is that all the lines intersect and there is only one intersection. This unifies the parallel and intersection of the lines. The point on the original plane is called the normal point for the difference from the Infinity point.
Here are several properties of the Infinity Point.
▲ The Infinity Point on the straight line L can only have one. (from the definition can be directly derived)
▲ a set of parallel lines on the plane has a common infinity point. (from the definition can be directly derived)
▲ any intersecting two straight lines on the plane l1,l2 have different infinity points. (otherwise L1 and L2 have a public infinity point P, then L1 and L2 have two intersection points a, p, so the assumption is wrong.) ）
▲ All infinity points on the plane form an infinity line. (Imagine this line yourself)
▲ All infinity points on the plane and all the ordinary points constitute the projective plane.
Second, projective plane coordinate system
The projective plane coordinate system is an extension of the normal plane rectangular coordinate system (that is, the Cartesian coordinate system that we have learned at first). We know that the normal plane rectangular coordinate system does not design coordinates for infinity points, and cannot represent infinity points. In order to express the Infinity Point, the projective plane coordinate system is produced, and the projective plane coordinate system can also represent the old common point (mathematics is also "backward compatible").