Bachelors_Thesis_Code/README.md

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.