## Short Concepts

The cryptography is a particular Math. That are the groups of sets. For example, the Numbers Z form a group with respect to the Adittion and the Multiplication. All numbers x,y,z € Z complex the associative property with respect to the multiplication and the addition. Also the commutative with respect to the operations + (Adittion) and x (Multiplication). Zero is a neutral element of the Adittion and 1 of de Multiplicattion because x+0= x and x*1 = x.
The idea is that the list: 1) Has to be cyclical. 2) That by operating with addition and multiplication we obtain another value from the list. 3) That there is an inverse of addition and multiplication, and 4) Finally that there are no repeated elements within the list. These lists are perfect for cryptography. This is achieved with lists obtained by doing the modulo operation, with a prime number. For this purpose, the prime number that is used is huge, obtaining lists of very large numbers, so as not to have collisions (that two elements of the source haven't the same image) and given an image, not being able to obtain the preimage or element of the source. Later I will explain this, relying on Venn diagrams. For this reason, the web has to calculate in JavaScript the Adittion and the product of these subsets Q = {0,1,2,3,4}, and prove these properties of group of sets. Also the symmetric of the Adittion and the Multiplication.
Also in his proposal, to create the square array of the numbers of these subsets Q. I repeat that it has to happen that the square array of one x€Q, has to donate another number y€Q. Exercice more dificult. I will practice too.

The objective is to understand the elliptic corbes: fundamental Mathematics for the Blockchain and to begin to understand one of the 3 fundamental principles:
1) Cryptography. The other two sources are
2) the network of computers, the consensus and its protocols such as PoW, PoS, P2P, etc. The third or special method is the
3) JOCS THEORY to calculate the incentives that must be high for the BlockChain to work.