elliptic curve
Recall that the parabolic equation and circle equation that you learned in high school are both curves and can be expressed by equations, as follows:
Elliptic curves can also be represented by equations:
An elliptic curve is not an ellipse, but its equation is very similar to the equation used to calculate the circumference of an ellipse, hence its name.
The definition of elliptic curve is that an elliptic curve is a smooth projective curve with genus 1 on the field. Just understand it;
Elliptic curves suitable for encryption
Elliptic curves based on real numbers are continuous and not suitable for encryption. We need to discretize it so that the coordinate points are all represented by integers, and all operations performed on it are integer operations.
So we need to define the ellipse on the finite field.
Not all elliptic curves are suitable for encryption.
Elliptic curves and cryptography
Elliptic curves are not simply ellipses, they are a much broader and more complex family. An elliptic curve is a plane curve defined by a simple algebraic equation, and its shape can extend from a perfect circle to a long line segment. Despite its simple and clear definition, elliptic curves hide rich structures and profound mathematical connotations.
The points on the elliptic curve have a magical property: select any two points and draw a straight line passing through the two points. This straight line will intersect the elliptic curve at the third point. This simple property gives elliptic curves their power, making them a key tool in modern cryptography.
Look at a picture to understand, this is one of the elliptic curves;
National secret SM2 algorithm
SM2 is an elliptic curve public key cryptography algorithm released by the State Cryptography Administration on December 17, 2010.
The SM2 algorithm and the RSA algorithm are both public key cryptography algorithms. The SM2 algorithm is a more advanced and secure algorithm and is used to replace the RSA algorithm in our country's commercial cryptography system.
SM2 has better performance and security: high password complexity, fast processing speed, and smaller machine performance consumption