https://github.com/demining/discrete-logarithm

Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin
https://github.com/demining/discrete-logarithm

bitcoin bitcoin-hacks bitcoin-payment bitcoin-transaction bitcoin-wallet btc btc-fake-sender btc-flashing-software btc-flashing-tool btc-tool btc-wallet btcchina private-key private-key-dump private-key-hacking private-key-tool private-keys

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Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin

• Host: GitHub
• URL: https://github.com/demining/discrete-logarithm
• Owner: demining
• Created: 2025-01-13T13:14:01.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2025-01-13T15:05:31.000Z (over 1 year ago)
• Last Synced: 2025-03-10T05:32:24.259Z (over 1 year ago)
• Topics: bitcoin, bitcoin-hacks, bitcoin-payment, bitcoin-transaction, bitcoin-wallet, btc, btc-fake-sender, btc-flashing-software, btc-flashing-tool, btc-tool, btc-wallet, btcchina, private-key, private-key-dump, private-key-hacking, private-key-tool, private-keys
• Language: Jupyter Notebook
• Homepage: https://cryptodeeptech.ru/discrete-logarithm
• Size: 46.4 MB
• Stars: 5
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

          





In early 2025, the rise in the rate of popular cryptocurrencies had a significant impact on financial transactions. Despite their widespread use and apparent security, these systems remain vulnerable. One of the main problems remains the recovery of lost cryptocurrency wallets and private keys, which can be done using complex mathematical algorithms.


In this article, we will explore methods for solving the discrete logarithm problem and ways to recover lost Bitcoin wallets, focusing on the Ricci Flow algorithm and the Hidden Number Problem for extracting private keys from vulnerable transactions using ECDSA. We will also discuss how modern cryptocurrencies such as Bitcoin and Ethereum rely on complex mathematical foundations that provide security and anonymity, but are susceptible to exploitation due to various vulnerabilities.


---

* Tutorial: https://youtu.be/i9KYih_ffr8

* Tutorial: https://cryptodeeptech.ru/discrete-logarithm

* Tutorial: https://dzen.ru/video/watch/6784be61b09e46422395c236

* Google Colab: https://colab.research.google.com/drive/1Cohb5F2h1CP9CnYdAdMJW9vyl4pwQKuz

---

The Role of Discrete Logarithms in Recovering Lost Cryptocurrency Wallets and Extracting Private Keys .


Discrete logarithm is a mathematical problem that consists of finding an integer x satisfying the equation a=b^x in some finite group. The order of the group of points on this curve is an important parameter determining the cryptographic strength of the secp256k1 elliptic curve system over the field GF(p), where p=2^256−2^32−2^9−2^8−2^7−2^6−2^4−1. For example, if we know a and b, we need to find x, the private key to a Bitcoin wallet. This problem is especially important in cryptography, since it underlies many cryptographic algorithms, such as public key exchange. Modern discrete logarithm algorithms have very high computational power, which allows these algorithms to be used in practice.






Let’s look at the process of recovering a private key using Dockeyhunt Discrete Logarithm software and DarkSignature tool to generate fake transaction data.


First, we will enter the Bitcoin wallet address: 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS for the amount of: 165.10252195 BTC and get its public key. Then, using DarkSignature , we will create fake values ​​for transactions, which will allow us to analyze and manipulate the signature data of the ECDSA algorithm. Finally, we will apply mathematical analysis through the Perelman Work software to solve the discrete logarithm and get the private key to the Bitcoin wallet.


This article is intended not only for cryptography and mathematics experts, but also for anyone who wants to understand how mathematical methods can be used to solve real-world cryptanalysis problems using various cryptocurrencies.














First, we need to run the Dockeyhunt Discrete Logarithm software and "Input date"enter the Bitcoin Address 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS in the field and get the public key of the wallet:


04e87e83f871df1439b7873b4ae449d15306cafc53e03a06fffb534b3bf25b58d8edca74b0faf5cf8c3aed6cad2bd79a7bce92ab53e07440d4590cbf31286d9335




Time-stamped video





Let’s use the DarkSignature tool to get fake R, S, Z values ​​for the ECDSA algorithm transaction. In the field, "Input date"enter the public key of the Bitcoin Address and get the values R, S, Z


04e87e83f871df1439b7873b4ae449d15306cafc53e03a06fffb534b3bf25b58d8edca74b0faf5cf8c3aed6cad2bd79a7bce92ab53e07440d4590cbf31286d9335


Result:


1111,947d6fb75033cc3e342c8538a350e9058134b2a1ae01a7c50fc52b1f56c9169c,5b3ec0d72a2368cdd48c17ff095ab1ab0b9824e010883539cbeb18141de6384b,c7ac826c5a8397c0de993b2d8d597be42d22c77cf006683d7b72a197e1a5cdcf,0000





Time-stamped video





As a tool for mathematical analysis and solving discrete logarithm equations, we will use the Perelman Work software . We will select the option from the Complex Analysis section for a complete relationship between variables through the integration of 


Discrete variation series Variance: [ D = frac{sum_{i=1}^{n} (x_i — bar{x})^2}{N})]


The formula for calculating discrete variation looks like this:








Explanation of the formula components:






D  is the variance (variance) of your data set.




∑∑  is the sum symbol, which means that we will add the values.




i  is an index that runs through all values ​​in the data set from 1 to n.




xi ​is each individual value in your data set.




ˉ x ˉ  is the mean (or arithmetic average) of all the values ​​in the data set.




N  is the total number of values ​​in the data set.



How does this work?






Calculating the Average:  First, you find the average value of your data set.




Difference from mean:  Then for each value  xi​ you calculate how much it differs from the mean ˉ x ˉ .




Square the difference:  You then take the square of that difference (to get rid of negative values ​​and amplify the impact of large deviations).




Summation:  You add up all the squares of the differences.




Dividing by the number of values:  Finally, you divide the resulting sum by the total number of values  ​​N .





Time-stamped video





Using Perelman Work and Dockeyhunt Discrete Logarithm, we arbitrarily change variables to the Joux Lercier vulnerability , this is described in detail at the beginning of the article, this vulnerability in a Bitcoin transaction occurs due to the fact that it is possible to change the value of  R, S , Z  in the signature, while maintaining the validity of the signature, as well as in an arbitrary formula:


X=hex(((S⋅K−Z)⋅modinv(R,N))modN)






S  and  R  are the values ​​from the transaction signature (RawTX).




Z  is the transaction signature hash.




K  is the secret key (nonce).




N  is the order of the elliptic curve group.


modinv( R , N ) is the modular inverse function of  R  modulo  N .



Explanation of the formula






Input parameters :





S  and  R : These values ​​are obtained from the transaction signature. They are needed to recover the private key.




Z : This is the signature hash, which is also used in the process.




K : A secret key (nonce) that should only be known to the wallet owner.







Calculations :



First we  multiply S  by  K.



Then we subtract  Z .


The result is multiplied by the modular inverse  of R  modulo  N . This allows us to “cancel” the influence of  R to obtain a value that can be used to calculate the private key.


Finally, the result is taken modulo  N to ensure that it is within the acceptable range for private key values.







Convert to hexadecimal format :



After all the mathematical operations are performed, the result is converted to hexadecimal format using the function  hex(), which is the standard representation of private keys in Bitcoin.









Ricci Flow Hidden Number Problem


Copy the values R, S, Z​​and paste them into the input field Ricci Flow HNPto build completely new transactions of the ECDSA algorithm .




Time-stamped video













Dockeyhunt Private Key Calculator


Copy the values ​​and paste them into the Dockeyhunt Private Key CalculatorR, S, Z software field




Time-stamped video





Now, according to the vulnerability of Joux Lercier, we copy from the code of ecdsa_impl.h the value of the secret key “K” called in cryptography NONCE – this is a secret, (pseudo) random parameter, which is usually denoted by “K”. Here NONCE, due to a bug in the code , fixed 0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL several HEX bits at the beginning (or at the end) of the record.


!./darksignature -address 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS


....

....

....

/** Difference between field and order, values 'p' and 'n' values defined in

 *  "Standards for Efficient Cryptography" (SEC2) 2.7.1.

 *  $ sage -c 'load("secp256k1_params.sage"); print(hex(P-N))'

 *  0x14551231950b75fc4402da1722fc9baee

 */

static const secp256k1_fe secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(

    0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL

);

....

....

....




https://github.com/bitcoin-core/secp256k1/blob/master/src/ecdsa_impl.h







Time-stamped video





Copy the K value and paste it into the Dockeyhunt Private Key Calculator software field , then click on the button: Calculate Private Key and get the private key to the Bitcoin Wallet 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS


0x6b29781e725708ae4d94e13730a2718ee3383ea5d911e77d4c2a2fd0c99c1232
















To start the algorithm for solving the discrete logarithm, click on the button: Private Key after that, we successfully receive a private key in HEX format


6b29781e725708ae4d94e13730a2718ee3383ea5d911e77d4c2a2fd0c99c1232




Time-stamped video







Next we need to make sure that we have received the required private key value in HEX format.





Time-stamped video







Click on the button Bitcoin Addressand get the required value of the private key in HEX format



6b29781e725708ae4d94e13730a2718ee3383ea5d911e77d4c2a2fd0c99c1232: 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS




Time-stamped video





We also click on the button Balance BTC and get the result of the balance amount:


6b29781e725708ae4d94e13730a2718ee3383ea5d911e77d4c2a2fd0c99c1232: 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS: 165.10252195 BTC

_____________________________________________________________________________________________________





Time-stamped video







Time-stamped video





Private key received!




Bitcoin wallet recovery using mathematically based methods such as the Ricci Flow Hidden Number Problem opens new horizons for understanding cryptographic vulnerabilities and opportunities. We demonstrated how Perelman Work, Dockeyhunt Discrete Logarithm , and DarkSignature software can be used to extract private keys and create fake transactions, highlighting the importance of mathematical analysis in the cryptocurrency space.








The results show that even in a complex system like Bitcoin , there are vulnerabilities that can be exploited to restore access to lost funds. This process requires deep knowledge of cryptography and mathematics, as well as skills in working with specialized software.




Exploitation mechanisms and significant influence in multi-signature systems


The vulnerability of the Joux Lercier algorithm poses a serious threat to systems with multi-signature schemes, since an attacker can generate fake signatures that the system will accept, threatening not only individual transactions, but also the integrity of the entire multi-signature process. An attacker can generate fake signatures that the system will accept, threatening not only individual transactions, but also the entire multi-signature process.




Insufficient verification of user input data can cause serious failures in the Bitcoin system, giving attackers the opportunity to inject malicious code and manipulate the system by creating fake signatures for transactions.





Practical part


According to the theory of vulnerability of the Joux Lercier algorithm , attackers are able to use the identified flaws to attack the Bitcoin network, overloading it with invalid transactions and thereby disrupting its stability. Let’s move on to the practical part of the article and consider an example using a Bitcoin wallet: 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS , where there were lost coins in the amount of: 165.10252195 BTC as of December 2024, this amount is: 15802506.39 USD




165.10252195 > 15802506,39 USD





Tutorials Power AI


Let’s use the list from “Tutorials Power AI” a widely used category of artificial intelligence to introduce business in various fields of cryptanalysis and cryptography in general.






Installation command:



git clone https://github.com/demining/Tutorials-Power-AI.git


cd Tutorials-Power-AI/

python3 tutorials.py





















BitcoinChatGPT is an innovative and cutting-edge AI-powered chatbot that helps users identify vulnerabilities in Bitcoin transactions. This tool allows you to check Bitcoin addresses for various crypto wallet attacks, using machine learning and cryptanalysis techniques to deeply investigate the security algorithms in the Bitcoin ecosystem. In addition, BitcoinChatGPT serves as an important resource for cybersecurity, offering tools to extract private keys from Bitcoin Wallet ledgers.





Exploiting a vulnerability in the implementation of the algorithm (Joux Lercier) to create a Raw transaction using the BitcoinChatGPT machine learning process


Let’s consider the construction of the structure of a vulnerable Raw transaction in which the BitcoinChatGPT module is used












Let’s open the Google Colab version:



https://colab.research.google.com/drive/1Cohb5F2h1CP9CnYdAdMJW9vyl4pwQKuz




State of a vulnerable transaction in Bitcoin:


01000000

....01

........0dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935

............00000000

........8b483045

....0221

...........00

...........947d6fb75033cc3e342c8538a350e9058134b2a1ae01a7c50fc52b1f56c9169c

....0220

........5b3ec0d72a2368cdd48c17ff095ab1ab0b9824e010883539cbeb18141de6384b

.....0141

.....04e87e83f871df1439b7873b4ae449d15306cafc53e03a06fffb534b3bf25b58d8edca74b0faf5cf8c3aed6cad2bd79a7bce92ab53e07440d4590cbf31286d9335

....ffffffff

01

....d204000000000000

........1976

............a914

........f750c55bea03af8a720c46b5d6edea93644cdaf7

....88ac

00000000






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



01000000010dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935000000008b483045022100947d6fb75033cc3e342c8538a350e9058134b2a1ae01a7c50fc52b1f56c9169c02205b3ec0d72a2368cdd48c17ff095ab1ab0b9824e010883539cbeb18141de6384b014104e87e83f871df1439b7873b4ae449d15306cafc53e03a06fffb534b3bf25b58d8edca74b0faf5cf8c3aed6cad2bd79a7bce92ab53e07440d4590cbf31286d9335ffffffff01d2040000000000001976a914f750c55bea03af8a720c46b5d6edea93644cdaf788ac00000000






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



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












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



{

    "addresses": [

        "1QiERrMcv6mtGk4F1TVz4sRp9dFfXTQpK",

        "1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS"

    ],

    "block_height": -1,

    "block_index": -1,

    "confirmations": 0,

    "double_spend": false,

    "fees": 2606688996428,

    "hash": "07160d430b92d957a7b3f0284ec7ff6084629b6385476608a6da5858fcfc2716",

    "inputs": [

        {

            "addresses": [

                "1QiERrMcv6mtGk4F1TVz4sRp9dFfXTQpK"

            ],

            "age": 344419,

            "output_index": 0,

            "output_value": 2606688997662,

            "prev_hash": "35591e5c7f4f1f0e4d81748042f2a4b7dcae3ae01027f361cad7c8746369bc0d",

.......

.......

.......






Let’s pay attention to Bitcoin HASH160: f750c55bea03af8a720c46b5d6edea93644cdaf7









https://github.com/demining/CryptoDeepTools/blob/50de2ffdd7f9f06a34049d1c72559aa16b1bf42c/37DiscreteLogarithm/DecodeRawTX.txt#L31C30-L31C70




Transaction Script


The above script has been decoded


BitcoinChatGPT creates a transaction structure using HASHthe public key, where we see that Bitcoin address: 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS sends 1234 satoshito the same address within its network.










Bitcoin HASH160 was generated using Python Script: wif_to_hash160.py














https://github.com/demining/CryptoDeepTools/blob/main/37DiscreteLogarithm/wif_to_hash160.py






Question – Answer:





























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









https://github.com/demining/CryptoDeepTools/blob/main/37DiscreteLogarithm/KEYFOUND.privkey




BitcoinChatGPT №6 Joux Lercier Vulnerability Algorithm










Vulnerable Raw Transaction


Let’s create a vulnerable Raw transaction from the received data using the  Broadcast Bitcoin Transaction repository




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



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



Catalog:


cd Broadcast-Bitcoin-Transaction




Let’s install three important libraries:





zmq


urllib3


requests





requirements.txt







Let’s run the command:



pip install -r requirements.txt




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




from io import BytesIO

from secp256k1 import *

from sighash import *


pk = PrivateKey.parse("5JdUtcYt3ZBQN8aPZWNffXzNCTPds7aQtJk7zc9iQShNQ9yWe7x")

pk.address()

tx = bytes.fromhex("35591e5c7f4f1f0e4d81748042f2a4b7dcae3ae01027f361cad7c8746369bc0d")

index = 0

send = "1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS"

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()






Let’s run the command:



python main.py




Vulnerable transaction created !





Let’s open the RawTX file in the directory:



01000000010dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935000000008b483045022100947d6fb75033cc3e342c8538a350e9058134b2a1ae01a7c50fc52b1f56c9169c02205b3ec0d72a2368cdd48c17ff095ab1ab0b9824e010883539cbeb18141de6384b014104e87e83f871df1439b7873b4ae449d15306cafc53e03a06fffb534b3bf25b58d8edca74b0faf5cf8c3aed6cad2bd79a7bce92ab53e07440d4590cbf31286d9335ffffffff01d2040000000000001976a914f750c55bea03af8a720c46b5d6edea93644cdaf788ac00000000




The order of actions in the video:










As we know from the prompt responses of the BitcoinChatGPT module , Joux Lercier Vulnerability Algorithm can be used to solve complex cryptographic problems.




Smart Transformers


We will apply Smart Transformers machine learning , integrate the notebook Google Colabwith Pytorch, TensorFlow, JAX and using the obtained data of the vulnerable Raw transaction for Bitcoin Address: 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS we will create an unprotected wallet.dat file from the proposed choice 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 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS






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/smartibase/Smart-Transformers.git


cd Smart-Transformers/












Let’s install all the necessary packages and libraries:



!sudo apt-get update

!sudo apt install libtool

!sudo apt-get install g++

!python setup.py --help

!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()


















Team:



ls -S










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 '01000000010dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935000000008b483045022100947d6fb75033cc3e342c8538a350e9058134b2a1ae01a7c50fc52b1f56c9169c02205b3ec0d72a2368cdd48c17ff095ab1ab0b9824e010883539cbeb18141de6384b014104e87e83f871df1439b7873b4ae449d15306cafc53e03a06fffb534b3bf25b58d8edca74b0faf5cf8c3aed6cad2bd79a7bce92ab53e07440d4590cbf31286d9335ffffffff01d2040000000000001976a914f750c55bea03af8a720c46b5d6edea93644cdaf788ac00000000' > RawTX.txt


!cat RawTX.txt










Now, to get 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 Joux_Lercier_Algorithm method , in earlier studies the same thing was identified by the BitcoinChatGPT module .



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


Joux_Lercier_Algorithm

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












Let’s open the catalog:











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 apply the Joux_Lercier_Algorithm utility.




Let’s run the command:



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


















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



















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:





getaddressinfo 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS













We see that the file: wallet.dat belongs to the Bitcoin Address: 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS





File: wallet.dat is encrypted with a password!














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



dumpprivkey 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS










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




Padding Oracle Attack
















Let’s use the Padding Oracle Attack method on Wallet.dat and decrypt the password for access into a binary password format.




































First we get access to the wallet.dat file for the amount: 165.10 BTC



Clone Repository: Biggest Lost Bitcoin Wallets List


git clone https://github.com/keyhunters/Biggest-Lost-Bitcoin-Wallets-List.git












Total Commander


























https://github.com/keyhunters/Biggest-Lost-Bitcoin-Wallets-List/tree/main/165.10%20BTC










Download and install  Bitcoin Core 0.18.0


















Откроем path: c:\Users\User\AppData\Roaming\Bitcoin\












Let’s move the file: wallet.dat













c:\Users\User\AppData\Roaming\Bitcoin\wallet.dat











Let’s launch the Bitcoin Core wallet










Encryt Wallet…












Let’s open the console




getaddressinfo 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS










Bitcoin Address Information:


Balance: 165.10252195 BTC










Metasploit Framework and use MSFVenom










The Role of Metasploit Framework in the Development of msfvenom




msfvenom is a tool created by combining the two previous tools:  
msfpayloadand   msfencode. It allows users to create payloads for different platforms and encoders, and provides the ability to customize the payload parameters. msfvenom supports various output formats, including executables, scripts, and even code for web applications.


The Metasploit Framework  plays a key role in the development of msfvenom for several reasons:


1. Exploit Integration: msfvenom allows users to create payloads that can be used with exploits from Metasploit. This simplifies the penetration testing process as users can quickly generate payloads that match specific vulnerabilities.


2. Versatility: With support for multiple formats and platforms, msfvenom has become a versatile payload creation tool. This allows security professionals to tailor their attacks to different systems and environments.


3. Updates and Support: The Metasploit Framework is constantly updated to keep msfvenom up to date and effective. New features and improvements in Metasploit directly impact msfvenom’s capabilities, making it more powerful and flexible.


4. Education and Research: Metasploit and msfvenom are important tools for cybersecurity education and research. They allow students and security professionals to study vulnerabilities and exploitation techniques in a secure environment.













Run ExploitDalenePRO.exe




















1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS










c:\BitcoinTools\ExploitDalenePRO\modules\










c:\BitcoinTools\ExploitDalenePRO\modules\exploits\










c:\BitcoinTools\ExploitDalenePRO\modules\exploits\ExploitDarlenePRO\










c:\BitcoinTools\ExploitDalenePRO\modules\exploits\ExploitDarlenePRO\decode_core.rb










decode_core.rb


















c:\BitcoinTools\ExploitDalenePRO\bitcoin\










https://github.com/bitcoin/bitcoin










https://github.com/bitcoin/bitcoin/blob/master/src/crypto/aes.h










c:\BitcoinTools\ExploitDalenePRO\bitcoin\src\










c:\BitcoinTools\ExploitDalenePRO\bitcoin\src\crypto\aes.cpp










c:\BitcoinTools\ExploitDalenePRO\bitcoin\src\crypto\aes.cpp










c:\Users\User\AppData\Roaming\Bitcoin\










Upload Wallet.dat


















result.json








walletpassphrase 1111111101110111010010110110010101100010110010001011111011000111101010010010000110101110100110000001100011001101000100001110101110100101101111000010100000000110100010110011000111111001111000110110001011000010000011001001000100101011001000101100110001101000 60




Run the command and get Private Key




The dumpprivkey command in Bitcoin Core


The dumpprivkey command is a command used in the Bitcoin Core wallet command line interface (CLI) to export the private key associated with a specific Bitcoin address. The syntax for the command is as follows:


“ dumpprivkey “address” “


Where “address” is the Bitcoin address for which you want to receive the private key.


How dumpprivkey command works


When you type the dumpprivkey command, Bitcoin Core looks for the specified address in its wallet and, if found, returns the corresponding private key in WIF format. This allows the user to store the private key in a safe place or import it into another wallet.





dumpprivkey 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS










Private Key Information:


5JdUtcYt3ZBQN8aPZWNffXzNCTPds7aQtJk7zc9iQShNQ9yWe7x












Bitcoin Address Information:


Balance: 165.10252195 BTC










https://www.coinbase.com/converter/btc/usd




165.10252195 > 15802506,39 USD







Let’s install the Bitcoin library



!pip3 install bitcoin












Let’s run  the code  to check the Bitcoin Address match:









__________________________________________________


Private Key WIF: 5JdUtcYt3ZBQN8aPZWNffXzNCTPds7aQtJk7zc9iQShNQ9yWe7x

Bitcoin Address: 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS

total_received 	= 165.10252195 Bitcoin

__________________________________________________


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




Let’s open  bitaddress  and check:


ADDR: 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS

WIF:  5JdUtcYt3ZBQN8aPZWNffXzNCTPds7aQtJk7zc9iQShNQ9yWe7x

HEX:  6b29781e725708ae4d94e13730a2718ee3383ea5d911e77d4c2a2fd0c99c1232










Conclusion and mitigation measures:


In this article, we explored methods for recovering lost cryptocurrency wallets and private keys using mathematical algorithms such as discrete logarithm and Hidden Number Problem . We demonstrated how to use Dockeyhunt Discrete Logarithm, DarkSignature, and Perelman Work software to extract private keys from vulnerable transactions using the ECDSA algorithm. Our research showed that even secure systems such as Bitcoin have vulnerabilities that can be exploited to regain access to lost funds. The recovery process requires deep knowledge of cryptography and mathematics, as well as skills in working with specialized software.


To protect against threats related to the Joux Lercier vulnerability, users should take the following steps:






Software Updates : Regularly updating your cryptocurrency wallets to patched versions is critical to maintaining security.




Improved signature verification mechanisms : Stronger input validation and error handling will help prevent the creation of fake signatures and protect users’ private keys.




Network activity monitoring : Constant analysis of network status and early detection of suspicious transactions allow for prompt response to attempts to exploit vulnerabilities.




Implementing Multi-Factor Authentication : Implementing additional cryptographic security methods will significantly improve security.