Cryptography and Computer Security

This repository contains materials for the Cryptography and Computer Security course at the Faculty of Computer Science and Informatics, University of Ljubljana.

Notes from tutorials

• Online tutorials from 2020/21

Notebooks

Currently, the following Jupyter notebooks for Python/Sage are available:

• VigenereCipher.ipynb: Vigenère cipher in Python
• LFSR.ipynb: LFSR in Sage
• Coppersmith.ipynb: Coppersmith's attack on a small exponent
• CommonModulus.ipynb: Common modulus attack
• RSA-ECB.ipynb: RSA in ECB mode
• Jacobi.ipynb: Computing Jacobi symbols
• Factorization.ipynb: Integer factorization
• BabyStepGiantStep.ipynb: Shanks's baby-step/giant-step algorithm
• PohligHellman.ipynb: The Pohlig-Hellman algorithm
• IndexCalculus.ipynb: The Index calculus algorithm
• ReblockingProblem.ipynb: The reblocking problem for RSA
• EllipticCurves.ipynb: Elliptic curves
• GroupSignature.ipynb: The ACJT2000 group signature scheme

algorithms

To use the algorithms in Python, make sure that the root of the repository is visible to Python. Then you may import them with

import algorithms

or

from algorithms import *

Currently, the following functions are available:

• gcd (from euclidean.py)
• inverse (from euclidean.py)
• eea (from euclidean.py)
• crt (from modular.py)
• jacobi (from modular.py)
• solovayStrassen (from primality.py)
• millerRabin (from primality.py)
• pollardP1(from factorization.py)
• pollardRho(from factorization.py)
• totalFactorization (from factorization.py)
• factorizeByBase (from factorization.py)
• babyStepGiantStep (from discreteLogarithm.py)
• pohligHellman (from discreteLogarithm.py)
• logarithmTable (from discreteLogarithm.py)
• indexCalculus (from discreteLogarithm.py)
• points (from ellipticCurves.py)
• pointSum (from ellipticCurves.py)
• pointMultiply (from ellipticCurves.py)

See sources for the documentation.

Note that logarithmTable requires Sage and will therefore not work with plain Python. indexCalculus calls logarithmTable if a table of logarithms is not specified. If it is given, the function can be used with plain Python.