The mathematical basis of public key cryptography

Group:

The set G and the Operation ° are collectively called groups (g,°), provided the operation satisfies the following conditions:

1. Closure law: Any A, b belongs to G, and A°b belongs to G

2. Binding law: Any a,b,c belongs to G, there is a° (b°c) = (a°b) °c

3. Unit element Law: the existence of a unique element e belongs to G, yes any a belongs to G, all have a°e=e°a=a

4. Reversible law: Any A belongs to G, existence A-1 belongs to G, make a°a-1=a-1°a=e

Abelian group:

If all of a, A and b belong to G, all have a°b=b°a, then the group G is the abelian group, and the abelian group is the commutative group.

Ring :

A set of two operations: addition + and multiplication, if the following properties are met, called ring R:

1.R is an alpha group under addition +, and the addition unit is 0 (called 0 yuan).

Domain:

If a non-0 element in a ring forms a group under a multiplication operation, the ring is called a domain

Finite fields:

The finite field with the simplest structure is the finite field of the order (the number of elements) as prime, however, the domain is the most widely used in cryptography.

Number of Mason primes:

A prime number shaped like a 2p-1

The mathematical basis of public key cryptography