Finite field algebra library

Project attribution: Project done in collaboration with Teodor Lungu.
Source: (Part of) The project’s source code is available here
Short description: Python library with fast arithmetic, polynomial and finite field operations.
Technologies: Python.
What I did: I implemented many of the operations, like: long division, find primitive, fast addition, multiplication, Euclid’s algorithm etc.

Python library that offers arithmetic functions:

• Integer arithmetic
  • Addition, Subtraction, Multiplication, Division
  • Fast Multiplication with Karatsuba’s technique
  • Greatest Common Divisor with Euclid’s Algorithm
• Modular arithmetic
  • Modular Addition, Subtraction, Multiplication, Inversion
• Polynomial arithmetic
  • Polynomial Addition, Subtraction, Multiplication
  • Polynomial Long Division
  • Euclid’s algorithm for polynomials
  • Checking and finding irreducible polynomials
• Arithmetic in finite fields
  • Generate final fields
  • Generating Addition and Multiplication tables
  • Final field Addition, Subtraction, Multiplication, Inverse, Division
  • Finding a Primitive