The repository for study cryptographical protocols on the number theory
This project contains functionality that allows you to solve small and simple problems related to number theory, the Galois field, it is for students and can help students in solving simple problems.
- For serious tasks, this is not suitable.
- There is no GUI, all displays are in the console.
- There is a step-by-step display, they can be enabled by sending the True variable during initialization.
- Main contains an initialization example and a function call.
- GCD Euclidian
- Euler functions
- a software product for solving comparisons of the first degree, indicating all intermediate steps of calculation (the current value of the coefficients in the extended Euclidean algorithm), the software product must also implement the possibility that the comparison has no solutions or has more than one solution. In the first case, inform the user with an explanation, in the second, construct all possible solutions.
- Chinese remainder theorem
- a software product for solving a quadratic comparison indicating intermediate results. The program should show cases where solutions exist, find the number of solutions, or indicate that finding is difficult. (include check Legandre and Jacobi)
- interactive calculator in the Galois field with a user-specified generating polynomial (addition, multiplication, division, gcd, exponentiation and multiplication table). (This poly view: x [1] x^2 [1 0 0] x^2+x+1 [1 1 1] etc.)
- a software product that allows you to carry out the Number Farm test for primality. Conduct from one to one hundred tests for each number. Generate a list of composite numbers up to one billion for which the first pass of the test gives a simple answer, note for each of these numbers what answer the test will give in the case of conducting from 2 to 100 tests. Generate a final table of the form
number 1 test 2 3 4 5 6 … 100
561 - - - - - - + We get xlsx file: look screenshot - software product for constructing sha-256 for the entered text.
- file signing and verification protocol for the DSS protocol. It is possible to use built-in language libraries.
- encryption and decryption of DES in CFB mode; library methods can be used to implement DES.
- Finding Elliptic Curve Points to Verify a Signature (TODO: need check work)
cryptodome