This is a finite field emulator that functions as an arithmetic calculator for polynomials in the field F_p^m

Tech Stack

Python: The program has been written entirely in Python. The GUI has been created using the library Tkinter

How to Run

• Download the main.exe

• Run the downloaded file on your machine (Windows)

• The application is ready to use

GUI

1

Working

• The program takes as input a prime number p, an integer m, and an irreducible polynomial of degree m in the field F_p
• Next, the program presents to the user a dropdown list of all polynomials in the field F_p^m i.e. polynomials of degree less than m in field F_p
• The user can choose from the field elements and operators and enter an expression for the calculator to parse.
• The calculator displays the resulting polynomial on the screen.

Error Detection

• The parser detects an invalid expression, for example, unbalanced parenthesis, zero division, etc.

Update (Display Multiplication Table)

• The display button generates a multiplication table showcasing the products of various field elements with every other field element