https://github.com/david-r-cox/pydlp

Python implementation of the index calculus method for solving discrete logarithm problems
https://github.com/david-r-cox/pydlp

Last synced: about 2 months ago
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Python implementation of the index calculus method for solving discrete logarithm problems

• Host: GitHub
• URL: https://github.com/david-r-cox/pydlp
• Owner: david-r-cox
• Created: 2016-11-08T19:38:49.000Z (about 8 years ago)
• Default Branch: master
• Last Pushed: 2020-03-17T15:56:55.000Z (almost 5 years ago)
• Last Synced: 2023-10-20T00:39:08.219Z (about 1 year ago)
• Language: Python
• Size: 5.86 KB
• Stars: 19
• Watchers: 4
• Forks: 4
• Open Issues: 3
• Metadata Files:
  • Readme: README.md

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README

        
# pyDLP

Python implementation of the index calculus method for solving discrete logarithms.

## About

[Index calculus](https://en.wikipedia.org/wiki/Index_calculus_algorithm) is a probabilistic method for solving [discrete logarithm](https://en.wikipedia.org/wiki/Discrete_logarithm) problems. As of this writing, there do not appear to be many implementations of index calculus. Hopefully this can serve as a useful reference.

## Setup

This script requires that [SageMath](https://www.sagemath.org/) be installed to solve the system of linear equations. The `primefac` module is also required and can be installed with `pip install -r ./requirements.txt`

## Usage

```

$ python2.7 ./pyDLP.py

p: 18443, g: 37, h: 211, B: 5

searching for congruences.

congruences: 6

bases: 3

converting to matrix format.

solving linear system with sage:

sage done.

checking congruences: Passed!

checking dlog exponents:

37^5733 = 2 (mod 18443)

37^15750 = 3 (mod 18443)

37^6277 = 5 (mod 18443)

Passed!

searching for k such that h*g^-k is B-smooth.

found k = 13999

Solving the main dlog problem:

37^8500 = 211 (mod 18443) holds!

DLP solution: 8500

```