# Bachelor's_Thesis_Code

Code used for my Bachelor's Thesis

# Versions
## Current Version
Compared to V1, this current state `generate_initial_irreducible_polynomials.sage`, `generate_random_irreducible_polynomial.sage`, and `multiply_polynomials_modulo_polynomial.sage` have been removed from the main folder, as they have already been used for implementing their corresponding features in `general_library.cpp`. They will be preserved in the V1 folder.  

This version also contains code relating to Porat-Porat and other random code stumps. This code is going to be completely reimplemented, but is preserved for now to avoid redoing work.  

## V1
#### `general_library.cpp`
- Exports functions for:  
    - Generating a random irreducible polynomial of degree up to 31.  
- Contains code for:  
    - Contains code to multiply polynomials modulo another polynomial.  
    - Doesn't contain code to initially calculate modulo a polynomial. It requires the initial polynomials to all be at most of the same degree as the polynomial that you use for modulo.  
    - A very custom version of calculating Reduced Row Echelon Form assuming all values are in Z2.  

#### `generate_initial_irreducible_polynomials.sage`
- Generates a list of irreducible polynomials, one of each degree. The polynomials are printed in a format that can be copy-pasted directly into `general_library.cpp`.  

#### `generate_random_irreducible_polynomial.sage`
- Contains an general template of how `general_library.cpp` should implement generating a random irreducible polynomial. The output of this program can also be used for debugging, since it uses many (correctly implemented) built-in sagemath functions that have to manually implemented in `general_library.cpp`.  

#### `multiply_polynomials_modulo_polynomial.sage`
- Contains a general template of how `general_library.cpp` should implement multiplying polynomials modulo a polynomial in Z2.  

#### `compare_fingerprint_false_positive_probabilities.sage`
- Contains initial (i.e. very rouch) code, which compares the upper bounds of a false match occuring of the Rabin fingerprint and the fingerprint used in Karp-Rabin.  

#### `test_rabin_fingerprint.sage`
- Contains initial (i.e. very rough) code which debunks my theory that modulo a prime is somewhat equivalent to modulo an irreducible polynomial.