# Number-Theory

**Repository Path**: resfzdfdz/Number-Theory

## Basic Information

- **Project Name**: Number-Theory
- **Description**: Basic implementation of elementary number theory functions
- **Primary Language**: Python
- **License**: Apache-2.0
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2020-04-25
- **Last Updated**: 2020-12-19

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# Number Theory Functions  
ENTF.py  
    --> gcd(a, b):                  Greatest Common Divisor  
    --> moddiv(x, y, m):            modular division x/y mod m  
    --> modsqroot(a, p):            modular square root of a   
    --> Fermat_test(p, T):          Fermat Prime Test  
    --> Miller_Labin(p, T):         Miller Labin Prime Test  
    --> geneprime(a, b):            Generate a prime in range(a, b)  
    --> primetable():               Get primes less than 1000  
    --> ptn(n):                     Get the first nth primes  
    --> ptm(m):                     Get primes less than m  
    --> CRT(a, m):                  Chinese Remainder Theory  
    --> pollard_rho(n):             Pollard Rho algorithm, prime divisor factorize  
    --> get_standard_factorize(s):  Standard Factorize  
    --> phi(n):                     Get Euler Totient  
    --> get_all_proper_factors(unique_factorize): Get all factors   
    --> primitive_root(m):          Get primitive root of modulo m  
    --> Fermat(n):                  Fermat numbers (2 ** (2 ** n)) + 1  
    --> Jacobi(a, m):               Jacobi symbol  
    --> Legendre(x, p):             Legendre symbol  
    --> PF_* : GF(2^n)              Field Arithmetic  

SM2.py  
    --> moddiv(a, b, p):            modular division b/a mod p  
    --> ECSM/PA/PD:                 Affine Coornidate Elliptic Curve Arithmetic  
    --> ECSM_P/PA_P/PD_P:           Projective Coordinate Elliptic Curve Arithmetic  
    --> ECSM_J/PA_J/PD_J:           Jacobian Coordinate Elliptic Curve Arithmetic  
    --> Fp2_* :                     Field Fp2 = Fp(sqrt(2)) Arithmetic and Elliptic Curve Arithmetic  
    --> X25519(swap, x_2, x_3):     X25519 git from https://github.com/nnathan/eccsnacks.git  
    --> Montgomery_Ladder(G, k, mode): Only X-coordinate Montgomery Ladder.  
                                       mode = 0: return P = kG = (px, py)  
                                       mode = 1: return P = kG = (Lx/Lz, Hx/Hz)  
    --> get_ref():                  Get parameters of SM2  
    --> test_* :                    Test Functions