https://github.com/fionn/batch-gcd
DJB's batch GCD algorithm for fast factoring sequences of integers
https://github.com/fionn/batch-gcd
batch-gcd cryptanalysis factoring-algorithms integer-factorization number-theory
Last synced: 11 months ago
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DJB's batch GCD algorithm for fast factoring sequences of integers
- Host: GitHub
- URL: https://github.com/fionn/batch-gcd
- Owner: fionn
- Created: 2021-10-05T16:58:02.000Z (over 4 years ago)
- Default Branch: master
- Last Pushed: 2023-06-14T17:01:44.000Z (over 2 years ago)
- Last Synced: 2025-02-28T20:12:29.228Z (11 months ago)
- Topics: batch-gcd, cryptanalysis, factoring-algorithms, integer-factorization, number-theory
- Language: Python
- Homepage: https://pypi.org/project/batch-gcd/
- Size: 10.7 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
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Metadata Files:
- Readme: README.md
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README
# Batch GCD
## Overview
A pure Python implementation of DJB's Batch GCD algorithm.
## Installation
Download and install with `pip`.
Or, download from source and install with `make install` (standard, user) or `make install_dev` (editable, system).
## Usage
This is a library and cannot be invoked directly.
Test with `make test`.
The `batch_gcd` module exposes a `batch_gcd` function which takes integers and returns a list of their GCDs at the corresponding index.
```python
>>> # Example batch_gcd usage
>>> from batch_gcd import batch_gcd
>>> batch_gcd(1909, 2923, 291, 205, 989, 62, 451, 1943, 1079, 2419)
[1909, 1, 1, 41, 23, 1, 41, 1, 83, 41]
```
This calculation involves two intermediate steps: creating a product tree and creating a remainder tree.
These functions are also exposed, as `products` and `remainders`.
`products` take integers and returns a product tree, `remainders` takes an integer and a product tree and returns a list of remainders.
## Resources
* [How to Find Smooth Parts of Integers](https://cr.yp.to/factorization/smoothparts-20040510.pdf)
* [FactHacks: Batch GCD](https://facthacks.cr.yp.to/batchgcd.html)
* [FactHacks: RSA Factorization in the Real World](https://www.hyperelliptic.org/tanja/vortraege/facthacks-29C3.pdf)