This is the code for my MATH 313 Introduction to Number Theory course finals presentation.
The presentation is delivered by Michael Bedard, Alexander Paolozzi, Daniel Queen, and Ye Shu (ordered by last name). It focuses on the Wiener's attack (also known as the low private exponent attack) on RSA. In the presentation, we mathematically proved how and why the attack works.
Stars and contributions are welcomed!
This repository contains codes implementing Wiener's attack in Python 3.
All dependencies are listed in requirements.txt. To run this program, you need to clone this repo, install the dependencies with pip, and run the main file Wiener.py
# Clone & Enter the repo
git clone https://github.com/yechs/MATH313-Wiener_Attack.git
cd MATH313-Wiener_Attack
# Install the dependencies
pip install -r requirements.txt
# Run it!
python3 Wiener.pyAll codes under the root directory are written by Ye Shu (@yechs) and are open sourced under the MIT license. Anyone can use and redistribute the codes freely as long as they preserve the copyright notices.
However, do note that this repo also contains codes from pablocelayes/rsa-wiener-attack, which are not properly licensed with a free software license.
These codes are used to generate RSA keypairs vulnerable to Wiener's Attack (i.e. with small private exponent), when you do not supply the program with existing ones.
All unlicensed codes are under the libs directory, use them at your own risk.
Boneh, Dan. "Twenty years of attacks on the RSA cryptosystem." Notices of the AMS 46.2 (1999): 203-213. https://www.ams.org/notices/199902/boneh.pdf
Calderbank, Alexander. “The RSA Cryptosystem: History, Algorithm, Primes”. Web. 2007. Accessed 27 April 2021. https://www.math.uchicago.edu/~may/VIGRE/VIGRE2007/REUPapers/FINALAPP/Calderbank.pdf
Celayes, Pablo. “rsa-wiener-attack”. Web. 2017. Accessed 24 April 2021. https://github.com/pablocelayes/rsa-wiener-attack
Schneier, Bruce. "Chapter 19.3: RSA". Applied cryptography: protocols, algorithms, and source code in C. john wiley & sons, 2007
Wiener, M.J. "Cryptanalysis of short RSA secret exponents," in IEEE Transactions on Information Theory, vol. 36, no. 3, pp. 553-558, May 1990, doi: 10.1109/18.54902.