Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process BitcoinChatGPT

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

In this article we will look at an example of a method Gauss-Jacobithat uses modern technologies, such as a pre-trained model Bitcoin ChatGPT, which allows us to more effectively solve complex problems in the field of digital technologies. It is important to note that alternative algorithms such as Gauss-Jacobiplay a key role and open new horizons for the development of computational mathematics.

The method Gauss-Jacobiis an iterative numerical method for solving systems of linear equations. It is widely used in various fields such as cryptography, cryptanalysis, engineering and computational mathematics. The Bitcoin network uses cryptographic algorithms such as hash functions SHA-256, signature algorithms ECDSA, and elliptic curves secp256k1to create public and private keys, which are points on an elliptic curve. The private key is the secret numeric value that is used to generate the public key, and the public key is the point on the curve obtained by computing with the private key. Thus, elliptic curves secp256k1form the basis of cryptographic mechanisms that provide secure transactions and protection against various attacks. Modern technologies that develop pre-trained models Bitcoin ChatGPTfind effective ways to solve complex cryptographic problems underlying the algorithms used in Bitcoin.



What are the advantages of the Gauss-Jacobi algorithm :

  • High speed and efficiency , which makes it ideal for searching for attack keys.
  • Interactivity uses only one search step, which allows it to reduce the number of calculations.
  • Availability and ease of implementation , which has simple codes and can easily be implemented in various programs.
  • Available to a wide range of users , who can use it to search for attacks on cryptographic strength for various cryptocurrencies.
  • The flexibility can be applied to a variety of types of cryptographic systems.

How the Gauss-Jacobi algorithm works :

Gauss-Jacobithe algorithm is based on a recursive function f(x)that, for any element xin S(the blockchain data network), returns a string code representing x. If xis an attacking key, then f(x) = 0.

Gauss-Jacobithe algorithm is based on a recursive function f(x)that, for any element xin S(the blockchain data set), returns a string code representing x. If xis an attacking key, then f(x) = 0.

The algorithm works in the following stages:

  1. Computes Gthe -matrix, which is the matrix of all mixed pairs of elements S, where the i-th element corresponds to the i-th elements of S, and the j-th element to the j-th element S.
  2. Computes the X-matrix, which is a matrix of mixed hash function pairs.
  3. Recursively determines the value of f(x) for each element of S.
  4. If f(x) = 0, this means that xis the attacking key, and the algorithm terminates.
  5. And else, the algorithm continuesrecursively calculates f(x)for various elements Sand adds these elements to Хthe -matrix.
  6. If His a matrix of ones, then the algorithm terminates and we have found the attacking key.

The method’s algorithm Gauss-Jacobican be used to solve systems of equations with a large number of unknowns. This means that this method can be used to solve systems of equations derived from secp256k1 elliptic curves used in cryptography that may have a large number of unknowns, and methods like Gauss-Jacobi can potentially speed up the solution of some discrete logarithm and factorization problems, by which public key cryptography is based on.


Potential application of the Gauss-Jacobi method in cryptanalysis of the Bitcoin blockchain

Let’s consider building the structure of a vulnerable Raw transaction that uses the BitcoinChatGPT module


Let’s open the Google Colab version:

https://colab.research.google.com/drive/1MJ4G5azqqpSlamEdPcjOCBkKn6oQofwL#scrollTo=HBzK0Ff7utn0&line=1&uniqifier=1


Let’s combine all the output values ​​into one common line:


Let’s open the option from BlockCypher “Decode A Transaction” :

https://live.blockcypher.com/btc/decodetx

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

After decoding the vulnerable Raw Bitcoin transaction, we get the result:


Let’s pay attention to Bitcoin HASH160: ac9ea341afb74843f80205e8c8da0abc822fa5

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

https://github.com/demining/CryptoDeepTools/blob/470292cd9bf60232e2ea4011ab9929106c63477f/30GaussJacobiMethod/DecodeRawTX.txt#L31


BitcoinChatGPT creates a transaction structure using HASHa public key, where we see that Bitcoin address: 1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k sends 1234 satoshito the same address within its network.

https://live.blockcypher.com/widget/btc/1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k/received

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Bitcoin HASH160 was obtained using Python Script: wif_to_hash160.py

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process
Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

https://github.com/demining/CryptoDeepTools/blob/main/30GaussJacobiMethod/wif_to_hash160.py


Question answer:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Ultimately, the BitcoinChatGPT module outputs a response to the file: KEYFOUND.privkey , saving the private key in the two most used formats HEX & WIF

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

https://github.com/demining/CryptoDeepTools/blob/main/30GaussJacobiMethod/KEYFOUND.privkey


BitcoinChatGPT №1 Gauss Jacobi Method Algorithm


Practical part

To move on to the practical part, let’s create a vulnerable Raw transaction from the received data using the Broadcast Bitcoin Transaction repository

Download and install the source code, open a terminal and run the command:

Catalog:

Let’s install three important libraries:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process
requirements.txt

Let’s run the command:


Let’s open the main file in Notepad ++ and make small changes to the Python Script code: main.py



Let’s run the command:

A vulnerable transaction has been created!

Let’s open the RawTX file in the directory:


The order of actions in the video:


As we know from the prompt responses of the BitcoinChatGPT module , the Gauss-Jacobi method algorithm can be used to solve four variants of complex cryptographic problems.

Let’s consider the option №3 The Gauss-Jacobi algorithm can compromise the security of the software file wallet.dat, which is an additional unprotected mechanism where the algorithm creates the wallet.dat file and extracts the private key to the Bitcoin Wallet from the file’s code using the command “dumpprivkey” “address” from the internal software console.

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Option #3


Smart Transformers

Let’s apply machine learning Smart Transformers , integrate the notebook Google Colabwith Pytorch, TensorFlow, JAX and using the received data from a vulnerable Raw transaction for Bitcoin Addresses: 1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k we will create an unprotected file wallet.dat from the proposed selection of all existing algorithms from SMART_IDENTIFY . Then we will perform a Padding Oracle Attack on the newly created file: wallet.dat to decrypt the password into the original binary format in order to obtain and extract the private key from the Bitcoin Core software console using the standard command:dumpprivkey 1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k


Let’s open a new Google Colab notebook using the link:

https://colab.research.google.com/#create=true

Clone the Smart Transformers repository

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s install all the necessary packages and libraries:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process
Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Command:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s add our vulnerable Raw transaction to a text document: RawTX.txt, for this we will use the utilityecho

Let’s run the command:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Now, in order to obtain the exact algorithm and method for cryptanalysis, we need to identify the vulnerable RawTX using the SMART_IDENTIFY utility .

Let’s run the command:

As a result, we get the Gauss_Jacobi_Algorithm method, in early studies the BitcoinChatGPT module identified the same thing .


Let’s open the directory:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s start the process of creating the wallet.dat file , for this we use the identified data of the vulnerable Raw transaction in the file: RawTX.txt for the process we use the Gauss_Jacobi_Algorithm utility

Let’s run the command:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process
Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process
Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s open the directory in the left panel Google Colaband see the file: wallet.datSuccessfully created!

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Download and Install Bitcoin Core 0.18.0 https://bitcoincore.org/bin/bitcoin-core-0.18.0


Let’s open the console and run the command:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

We see that the file: wallet.dat belongs to Bitcoin Address: 1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k


File: wallet.dat is encrypted with a password!


Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s run the command to check the private key:


Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

We see a warning: Error: Please enter the wallet passphrase with walletpassphrase first. (code -13)


Padding Oracle Attack

We previously published the article Padding Oracle Attack on Wallet.dat. We will use this method and decrypt the password to access the binary format.

Let’s install Ruby

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

To run the programs we need, we will install the object-oriented programming language  Ruby

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s check the installation version

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process
Ruby version 3.0.2p107 (2021-07-07 revision 0db68f0233) [x86_64-linux-gnu]

Let’s install all the libraries we need  to interact with the Bitcoin protocol/network :

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s install the Metasploit Framework and use MSFVenom

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s install  the Metasploit Framework  from  GitHub  and use the  MSFVenom tool  to create the payload.

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Options:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Establish  Bitcoin Core integration/staging tree  in Google Colab:

We clone the Bitcoin Core repository by running the command:


Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s go through the directory to the file:  aes.cpp  to integrate the exploit to launch  Padding Oracle Attack on Wallet.dat

Let’s go to the crypto directory

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Open the file:  aes.cpp  using the cat utility

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

To carry out the attack, move the file: wallet.dat to the directory:  bitcoin/src/crypto/

Let’s use the utility   and move  wallet.datmv

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s check the contents of the directory:  bitcoin/src/crypto/

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s go back to Metasploit Framework

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s open the folders according to the directory: /modules/exploits/

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

ExploitDarlenePRO

Download  "ExploitDarlenePRO" from the catalogue: /modules/exploits/

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Unzip the contents  ExploitDarlenePRO.zip using the utility unzip

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s go through the catalogue: /ExploitDarlenePRO/

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

To run the exploit, let’s go back to Metasploit Framework

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

We need to identify our  LHOST (Local Host) attacking  IP-address virtual machine. Let’s run the commands:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s use the tool to create a payload MSFVenom

For operation, select Bitcoin Wallet:  1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k 


Launch command:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Result:


We need to save the resulting binary format to a file:  walletpassphrase.txt we will use  a Python script .

Team:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s open the file: walletpassphrase.txt

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Result:


The password for access to the private key has been found!


Let’s use the command   via the console dumpprivkey "address"Bitcoin Core



Result:

Private Key Received!



I establish a Bitcoin library 

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Let’s run  the code  to check the compliance of Bitcoin Addresses:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

That’s right! The private key corresponds to the Bitcoin Wallet.


Let’s open  bitaddress  and check:

Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

References:

  1. “Numerical Recipes in C: The Art of Scientific Computing” – Andrew W. Reynolds, Warren P. Symes, Walter G. Weiss and Simon F. Taylor. This book provides various algorithms for solving nonlinear systems, including the Gauss-Jacobi method, and provides examples of its implementation.
  2. “Iterative Methods for Linear and Nonlinear Equations” – Kenneth Craig Cooper, Thomas M. Meyer. This book details various iteration methods for solving linear and nonlinear systems, including the Gauss-Jacobi method, and-presented.
  3. “Nonlinear Programming: Concepts, Algorithms, and Applications” – Daniel Apstein and Jerry B. Stephenson. This work presents various approaches to solving nonlinear programs involving iteration methods such as Gauss-Jacobi.
  4. “Handbook of Numerical Analysis” – Jonathan M. Goldstein and Benjamin B. Warshaw, editors. This is definitely an encyclopedic source containing various articles on numerical methods, including the Gauss-Jacobi method.
  5. “The Pioneering Work of Carl Friedrich Gauss: Unveiling the Gauss-Jacobi Method” – The original article by Carl Friedrich Gauss “Beitrag zur Theorie der algebraischen Gleichungen” (1845), in which he first described the Gauss-Jacobi method.
  6. “Iterative Solution of Large Linear Systems” (1971) – David M. Young’s book contains a detailed description and analysis of the Gauss-Jacobi method.
  7. “Iterative Methods for Solving Linear Systems” – The chapter in Richard Bourdain and Douglas Fairs’ book Numerical Analysis (2010) gives a good introduction to the method.
  8. “On the Convergence of the Jacobi Method for Diagonally Dominant Matrices” (1986) by Milos Fehrmann analyzes the convergence of the Gauss-Jacobi method.
  9. “Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods” (1994) by Richard Barrett et al. – a useful guide to iterative methods, including Gauss-Jacobi.
  10. “A Survey of Parallel Nonlinear System Solvers” (1991) by John Ortega and Robert Foigel examines parallel implementations of the Gauss-Jacobi method.
  11. Exploring the Gauss-Jacobi Method in Numerical Methods Textbooks – Many textbooks on numerical methods, such as Ward Cheney and David Kincaid’s Numerical Mathematics and Computing, contain sections on the Gauss-Jacobi method.

This material was created for the  CRYPTO DEEP TECH portal  to ensure financial security of data and elliptic curve cryptography  secp256k1  against weak  ECDSA signatures  in the  BITCOIN cryptocurrency . The creators of the software are not responsible for the use of materials.


Source

Telegram: https://t.me/cryptodeeptech

Video material: https://www.youtube.com/@cryptodeeptech

Video tutorial: https://dzen.ru/video/watch/66119078be267c07401d9e4c

Source: https://cryptodeeptech.ru/gauss-jacobi-method


Decrypting Passwords to Access Lost Bitcoin Wallets Using Gauss-Jacobi Method and Machine Learning Process

Crypto Deep Tech