In this article, we will look at how you can make money using mathematics using Bitcoin wallet recovery methods. Specifically, we will focus on using the Ricci Flow algorithm and the Hidden Number Problem to extract private keys from vulnerable transactions created using the ECDSA digital signature algorithm.

Modern cryptocurrencies like Bitcoin are based on complex mathematical principles that ensure the security and anonymity of transactions. However, due to various vulnerabilities associated with the implementation of these algorithms, there is a possibility of their exploitation. We will take a detailed look at the process of recovering a private key using Dockeyhunt Lattice Attack software and the DarkSignature tool for generating fake transaction data.

First, we will enter the Bitcoin wallet address and obtain its public key. Then, using DarkSignature , we will create fake values ​​for the transactions, which will allow us to analyze and manipulate the signature data. Finally, we will apply mathematical analysis via Perelman Work software to solve differential equations and obtain the private key.

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 problems in the world of cryptocurrencies.

First, we need to run the Dockeyhunt Lattice Attack software and "Input date"enter the Bitcoin Address 1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw in the field and get the public key of the wallet:

049b4069d8237fae8f2417c71c5512ec1b0547b5597474480cc28ea1bbfeecaab8b90fdec161ad6ef4378f274a60b900452431533596bf3bd23e01202ebf679461

Let’s use the DarkSignature tool to get fake data R, S, Z values ​​for the ECDSA algorithm transaction. In the field, "Input date"enter the public key of the Bitcoin Address 049b4069d8237fae8f2417c71c5512ec1b0547b5597474480cc28ea1bbfeecaab8b90fdec161ad6ef4378f274a60b900452431533596bf3bd23e01202ebf679461and get the data R, S, Z values ​​in the amount of 32 Bitcoin transactions .

In the root directory: c:\PerelmanWork\Dockeyhunt Lattice Attack\we get the file: Signatures.txt

As a tool for mathematical analysis and solving differential equations, we will use the Perelman Work software . We will select the option from the Functions and Graphs section for a complete relationship between variables through the integration of First-order differential equations: [ frac{dy}{dx} = g(y)h(x) quad Rightarrow quad frac{1}{g(y)} dy = h(x) dx ]

Ricci Flow Hidden Number Problem

We copy the values ​​from the file: Signatures.txt according to the list and paste them into the input field Ricci Flow HNPto build completely new transactions of the ECDSA algorithm .

Using Perelman Work and Dockeyhunt Lattice Attack, we arbitrarily change variables to the Signature Malleability vulnerability (this is described in detail at the beginning of the article) this vulnerability in a Bitcoin transaction arises due to the fact that it is possible to change the value of  S  in the signature, while maintaining the validity of the signature, and also in an arbitrary formula all this is possible due to the fact that for the same signature it is possible to obtain several equivalent values  ​​(r,s′) :

As a final result of the transformation of variables in the signature value R, S′, Z we see two digits the value S ′ is built as a field structure (P) :

P = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f

This number defines the field in which the secp256k1 curve operates to perform mathematical operations on points on the elliptic curve.

Let’s consider obtaining a private key using the Dockeyhunt Lattice Attack software as an example

To start the lattice reduction algorithm, click on the button:Private Key

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

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

17e96966f15a56993e13f8c19ce34a99111ad768a051d9febc24b6d48cae1951: 1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw

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

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17e96966f15a56993e13f8c19ce34a99111ad768a051d9febc24b6d48cae1951: 1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw: 21.2529214 BTC
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Private key received!

In conclusion , recovering a Bitcoin wallet 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 Lattice Attack , 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.

We hope that this article has been useful for you and has inspired you to further study mathematics in the context of cryptocurrencies. Use the acquired knowledge wisely and observe ethical standards in your practice.