Install SageMath in Google Colab

 CRYPTO DEEP TECH

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In this article, we will do a fresh install SageMathin Google Colab. We previously published an article: “ Install SageMath for cryptanalysis on Fedora 64bit(10GB) Cloud Virtual Server ”, but in order to continue cryptanalysis of the Bitcoin blockchain, many of our readers prefer to use Debian and, Ubuntuin contrast to Fedora. As far as we know, Google Colab it has been updated to "Ubuntu 20.04.5 LTS".

We can check this by running the command:

!cat /etc/lsb-release

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Therefore "Ubuntu 20.04.5 LTS", the version allows us to install only SageMath version 9.0, Release Date: 2020-01-01

Using the standard install command:

!sudo apt-get install -y sagemath-common

Unfortunately this version does not work properly.

For a complete cryptanalysis, we will install in Google Colab a completely new version SageMath version 9.3

File: Install_SageMath_in_Google_Colab.ipynb we published in GitHub

Let’s go to the official website: https://colab.research.google.com

Select the option “Upload notepad”

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Upload the file: Install_SageMath_in_Google_Colab.ipynb

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Now, through the utility, wget download tar-file: sage-9.3-Ubuntu_20.04-x86_64.tar.bz2

!wget https://cryptodeeptech.ru/sage-9.3-Ubuntu_20.04-x86_64.tar.bz2
!tar -xf sage-9.3-Ubuntu_20.04-x86_64.tar.bz2

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Let’s go through the directory:

cd SageMath/

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Open the panel and go to the folder: SageMath

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Check if Python-script: relocate-once.py is there

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Run Python-script: relocate-once.py with the command:

!python3 relocate-once.py

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All is ready!

Now let’s run SageMath the command:

!./sage -sh

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Let’s run the version check command:

sage -v

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All right!

We’ve got a new version: SageMath version 9.3, Release Date: 2021-05-09

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Implementing the Twist Attack algorithm , download   Python-script:discrete.py

wget https://raw.githubusercontent.com/demining/CryptoDeepTools/bbd83042e7405508cd2e646ad1b0819da0f9c58d/18TwistAttack/discrete.py

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To solve the discrete logarithm  (Pollard's rho algorithm for logarithms) run  Python-script:discrete.py

Now, to get the private key, we just need to run the command:

python3 discrete.py

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Sage Math 9.3  solve the discrete logarithm problem (Pollard's rho algorithm for logarithms)

Now everything is working properly!

We received the private key to the Bitcoin Wallet in decimal format, then for cryptanalysis we need to follow the instructions of the article dedicated to  Twist Attack

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Source

Telegram: https://t.me/cryptodeeptech

Video: https://youtu.be/DBu0UnVe0ig

Source: https://cryptodeeptech.ru/install-sagemath-in-google-colab

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 Cryptanalysis