{"id":24192700,"url":"https://github.com/demining/discrete-logarithm","last_synced_at":"2026-05-15T05:03:09.162Z","repository":{"id":272294248,"uuid":"916102927","full_name":"demining/Discrete-Logarithm","owner":"demining","description":"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin","archived":false,"fork":false,"pushed_at":"2025-01-13T15:05:31.000Z","size":48612,"stargazers_count":5,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-03-10T05:32:24.259Z","etag":null,"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"],"latest_commit_sha":null,"homepage":"https://cryptodeeptech.ru/discrete-logarithm","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/demining.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2025-01-13T13:14:01.000Z","updated_at":"2025-02-02T13:12:41.000Z","dependencies_parsed_at":"2025-01-13T14:54:30.365Z","dependency_job_id":null,"html_url":"https://github.com/demining/Discrete-Logarithm","commit_stats":null,"previous_names":["demining/discrete-logarithm"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/demining/Discrete-Logarithm","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FDiscrete-Logarithm","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FDiscrete-Logarithm/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FDiscrete-Logarithm/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FDiscrete-Logarithm/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/demining","download_url":"https://codeload.github.com/demining/Discrete-Logarithm/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FDiscrete-Logarithm/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":33054454,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-05-13T13:14:54.681Z","status":"online","status_checked_at":"2026-05-15T02:00:06.351Z","response_time":103,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["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"],"created_at":"2025-01-13T16:19:55.941Z","updated_at":"2026-05-15T05:03:09.119Z","avatar_url":"https://github.com/demining.png","language":"Jupyter Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/GOLD1031B-1024x576.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5107\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eIn 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.\u003c/p\u003e\n\n\n\n\u003cp\u003eIn 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.\u003c/p\u003e\n\n\n---\n\n* Tutorial: https://youtu.be/i9KYih_ffr8\n* Tutorial: https://cryptodeeptech.ru/discrete-logarithm\n* Tutorial: https://dzen.ru/video/watch/6784be61b09e46422395c236\n* Google Colab: https://colab.research.google.com/drive/1Cohb5F2h1CP9CnYdAdMJW9vyl4pwQKuz\n\n---\n\n\n\n\u003cp\u003e\u003cstrong\u003eThe Role of Discrete Logarithms in Recovering Lost Cryptocurrency Wallets and Extracting Private Keys\u003c/strong\u003e\u0026nbsp;.\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Discrete_logarithm\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eDiscrete logarithm\u003c/a\u003e\u003c/strong\u003e is a mathematical problem that consists of finding an integer \u003cstrong\u003e\u003cem\u003e\u003ccode\u003ex\u003c/code\u003e\u003c/em\u003e\u003c/strong\u003e satisfying the equation \u003cstrong\u003e\u003ccode\u003e\u003cem\u003ea=b^x\u003c/em\u003e\u003c/code\u003e\u003c/strong\u003e in some finite group. The order of the group of points on this curve is an important parameter determining the cryptographic strength of the \u003cstrong\u003e\u003ccode\u003e\u003cem\u003esecp256k1\u003c/em\u003e\u003c/code\u003e\u003c/strong\u003e elliptic curve system over the field \u003cstrong\u003e\u003cem\u003e\u003ccode\u003eGF(p)\u003c/code\u003e\u003c/em\u003e\u003c/strong\u003e, where \u003cstrong\u003e\u003ccode\u003e\u003cem\u003ep=2^256−2^32−2^9−2^8−2^7−2^6−2^4−1\u003c/em\u003e\u003c/code\u003e\u003c/strong\u003e. For example, if we know \u003cstrong\u003e\u003cem\u003e\u003ccode\u003ea\u003c/code\u003e\u003c/em\u003e\u003c/strong\u003e and \u003cstrong\u003e\u003cem\u003e\u003ccode\u003eb\u003c/code\u003e\u003c/em\u003e\u003c/strong\u003e, we need to find \u003cstrong\u003e\u003cem\u003e\u003ccode\u003ex\u003c/code\u003e\u003c/em\u003e\u003c/strong\u003e, 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.\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eLet’s look at the process of recovering a private key using\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://dockeyhunt.com/dockeyhunt-discrete-logarithm/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eDockeyhunt Discrete Logarithm\u003c/a\u003e\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;software and DarkSignature\u003c/strong\u003e\u0026nbsp;tool\u0026nbsp;to generate fake transaction data.\u003c/p\u003e\n\n\n\n\u003cp\u003eFirst, we will enter the Bitcoin wallet address:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://btc1.trezor.io/address/1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;for the amount of:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://btc1.trezor.io/address/1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e165.10252195 BTC\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;and get its public key. Then, using\u0026nbsp;\u003cstrong\u003eDarkSignature\u003c/strong\u003e\u0026nbsp;, 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\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://perelmanwork.com/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePerelman Work\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;software to solve the discrete logarithm and get the private key to the Bitcoin wallet.\u003c/p\u003e\n\n\n\n\u003cp\u003eThis 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.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-full is-resized\"\u003e\u003ca href=\"https://www.youtube.com/watch?v=i9KYih_ffr8\"\u003e\u003cimg decoding=\"async\" width=\"749\" height=\"432\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-1.png\" alt=\"Discrete Logarithms\" class=\"wp-image-3137\" style=\"width:840px;height:auto\" srcset=\"https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-1.png 749w, https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-1-300x173.png 300w\" sizes=\"(max-width: 749px) 100vw, 749px\"\u003e\u003c/a\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eFirst, we need to run the\u0026nbsp;\u003ca href=\"https://dockeyhunt.com/dockeyhunt-discrete-logarithm\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eDockeyhunt Discrete Logarithm\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;software and\u0026nbsp;\u003ccode\u003e\u003cstrong\u003e\"Input date\"\u003c/strong\u003e\u003c/code\u003eenter the Bitcoin Address\u0026nbsp;\u003ca href=\"https://btc1.trezor.io/address/1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;in the field and get the public key of the wallet:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-11910058ecc209480e8f96491843ac6e\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e04e87e83f871df1439b7873b4ae449d15306cafc53e03a06fffb534b3bf25b58d8edca74b0faf5cf8c3aed6cad2bd79a7bce92ab53e07440d4590cbf31286d9335\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-1-1024x573.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-258\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/ErjCph1mI9Y?t=63\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eLet’s use the DarkSignature\u003c/strong\u003e\u0026nbsp;tool to get fake\u0026nbsp;\u003cstrong\u003eR, S, Z\u003c/strong\u003e\u0026nbsp;values\u0026nbsp;​​for the ECDSA algorithm transaction. In the field,\u0026nbsp;\u003ccode\u003e\"Input date\"\u003c/code\u003eenter the public key of the Bitcoin Address and get the values \u003cstrong\u003eR, S, Z\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp class=\"has-text-color has-link-color wp-elements-4d58c3aa418a19369b0ffbae46da84ac\" style=\"color:#4092c2\"\u003e\u003cstrong\u003e\u003ccode\u003e04e87e83f871df1439b7873b4ae449d15306cafc53e03a06fffb534b3bf25b58d8edca74b0faf5cf8c3aed6cad2bd79a7bce92ab53e07440d4590cbf31286d9335\u003c/code\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eResult:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-f8ff710280f83a94fbf585529b9da688\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e1111,947d6fb75033cc3e342c8538a350e9058134b2a1ae01a7c50fc52b1f56c9169c,5b3ec0d72a2368cdd48c17ff095ab1ab0b9824e010883539cbeb18141de6384b,c7ac826c5a8397c0de993b2d8d597be42d22c77cf006683d7b72a197e1a5cdcf,0000\u003c/strong\u003e\n\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-2-1024x573.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-259\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/ErjCph1mI9Y?t=76\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://perelmanwork.com/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eAs a tool for mathematical analysis and solving discrete logarithm equations, we will use the Perelman Work\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;software\u0026nbsp;. We will select the option from the\u0026nbsp;\u003cstrong\u003eComplex Analysis\u003c/strong\u003e\u0026nbsp;section for a complete relationship between variables through the integration of\u0026nbsp;\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ccode\u003eDiscrete variation series Variance: [ D = frac{sum_{i=1}^{n} (x_i — bar{x})^2}{N})]\u003c/code\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eThe formula for calculating discrete variation looks like this:\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-1(1).png\" alt=\"Discrete variation series Variance formula: [ D = frac{sum_{i=1}^{n} (x_i - bar{x})^2}{N} ) ]\" class=\"wp-image-1376\" style=\"width:458px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003ch3 class=\"wp-block-heading\"\u003eExplanation of the formula components:\u003c/h3\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eD\u003c/strong\u003e\u0026nbsp;\u0026nbsp;is the variance (variance) of your data set.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003e∑∑\u003c/strong\u003e\u0026nbsp;\u0026nbsp;is the sum symbol, which means that we will add the values.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003e\u003cem\u003ei\u003c/em\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;is an index that runs through all values ​​in the data set from 1 to n.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003e\u003cem\u003exi\u003c/em\u003e\u0026nbsp;​is\u003c/strong\u003e\u0026nbsp;each individual value in your data set.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eˉ\u0026nbsp;\u003cem\u003ex\u003c/em\u003e\u0026nbsp;ˉ\u003c/strong\u003e\u0026nbsp;\u0026nbsp;is the mean (or arithmetic average) of all the values ​​in the data set.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003e\u003cem\u003eN\u003c/em\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;is the total number of values ​​in the data set.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003eHow does this work?\u003c/h3\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eCalculating the Average:\u003c/strong\u003e\u0026nbsp;\u0026nbsp;First, you find the average value of your data set.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eDifference from mean:\u003c/strong\u003e\u0026nbsp;\u0026nbsp;Then for each value\u0026nbsp;\u0026nbsp;\u003cem\u003exi\u003c/em\u003e​ you calculate how much it differs from the mean ˉ\u0026nbsp;\u003cem\u003ex\u003c/em\u003e\u0026nbsp;ˉ .\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eSquare the difference:\u003c/strong\u003e\u0026nbsp;\u0026nbsp;You then take the square of that difference (to get rid of negative values ​​and amplify the impact of large deviations).\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eSummation:\u003c/strong\u003e\u0026nbsp;\u0026nbsp;You add up all the squares of the differences.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eDividing by the number of values:\u003c/strong\u003e\u0026nbsp;\u0026nbsp;Finally, you divide the resulting sum by the total number of values\u0026nbsp;\u0026nbsp;\u003cem\u003e​​N\u003c/em\u003e\u0026nbsp;.\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-4-1024x576.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-261\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/ErjCph1mI9Y?t=146\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cem\u003eUsing\u0026nbsp;\u003ca href=\"https://perelmanwork.com/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ePerelman Work\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;and\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://dockeyhunt.com/dockeyhunt-discrete-logarithm\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eDockeyhunt Discrete Logarithm,\u003c/strong\u003e\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;we arbitrarily change variables to the\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://cryptodeeptech.ru/discrete-logarithm\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eJoux Lercier\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;vulnerability , this is described in detail at the beginning of\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/discrete-logarithm\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ethe article,\u003c/a\u003e\u0026nbsp;this vulnerability in a Bitcoin transaction occurs due to the fact that it is possible to change the value of\u0026nbsp;\u0026nbsp;\u003cstrong\u003eR,\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eS\u003c/strong\u003e\u0026nbsp;,\u0026nbsp;\u003cstrong\u003eZ\u003c/strong\u003e\u0026nbsp;\u0026nbsp;in the signature, while maintaining the validity of the signature, as well as in an arbitrary formula:\u003c/em\u003e\u003c/p\u003e\n\n\n\n\u003cp class=\"has-text-align-center has-large-font-size\"\u003e\u003ccode\u003e\u003cem\u003eX\u003c/em\u003e=hex(((\u003cem\u003eS\u003c/em\u003e⋅\u003cem\u003eK\u003c/em\u003e−\u003cem\u003eZ\u003c/em\u003e)⋅modinv(\u003cem\u003eR\u003c/em\u003e,\u003cem\u003eN\u003c/em\u003e))mod\u003cem\u003eN\u003c/em\u003e)\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cem\u003eS\u003c/em\u003e\u0026nbsp;\u0026nbsp;and\u0026nbsp;\u0026nbsp;\u003cem\u003eR\u003c/em\u003e\u0026nbsp;\u0026nbsp;are the values ​​from the transaction signature (RawTX).\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003eZ\u003c/em\u003e\u0026nbsp;\u0026nbsp;is the transaction signature hash.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003eK\u003c/em\u003e\u0026nbsp;\u0026nbsp;is the secret key (nonce).\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003eN\u003c/em\u003e\u0026nbsp;\u0026nbsp;is the order of the elliptic curve group.\u003c/li\u003e\n\n\n\n\u003cli\u003emodinv(\u0026nbsp;\u003cem\u003eR\u003c/em\u003e\u0026nbsp;,\u0026nbsp;\u003cem\u003eN\u003c/em\u003e\u0026nbsp;) is the modular inverse function of\u0026nbsp;\u0026nbsp;\u003cem\u003eR\u003c/em\u003e\u0026nbsp;\u0026nbsp;modulo\u0026nbsp;\u0026nbsp;\u003cem\u003eN\u003c/em\u003e\u0026nbsp;.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003eExplanation of the formula\u003c/h3\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eInput parameters\u003c/strong\u003e\u0026nbsp;:\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003e\u003cem\u003eS\u003c/em\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;and\u0026nbsp;\u003cstrong\u003e\u003cem\u003e\u0026nbsp;R\u003c/em\u003e\u003c/strong\u003e\u0026nbsp;: These values ​​are obtained from the transaction signature. They are needed to recover the private key.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003e\u003cem\u003eZ\u003c/em\u003e\u003c/strong\u003e\u0026nbsp;: This is the signature hash, which is also used in the process.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003e\u003cem\u003eK\u003c/em\u003e\u003c/strong\u003e\u0026nbsp;: A secret key (nonce) that should only be known to the wallet owner.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eCalculations\u003c/strong\u003e\u0026nbsp;:\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eFirst we\u0026nbsp;\u0026nbsp;multiply\u0026nbsp;\u003cem\u003eS\u003c/em\u003e\u0026nbsp;\u0026nbsp;by\u0026nbsp;\u0026nbsp;\u003cem\u003eK.\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003eThen we subtract\u0026nbsp;\u0026nbsp;\u003cem\u003eZ\u003c/em\u003e\u0026nbsp;.\u003c/li\u003e\n\n\n\n\u003cli\u003eThe result is multiplied by the modular inverse\u0026nbsp; of\u0026nbsp;\u003cem\u003eR\u003c/em\u003e\u0026nbsp;\u0026nbsp;modulo\u0026nbsp;\u0026nbsp;\u003cem\u003eN\u003c/em\u003e\u0026nbsp;. This allows us to “cancel” the influence of\u0026nbsp;\u0026nbsp;\u003cem\u003eR\u003c/em\u003e\u0026nbsp;to obtain a value that can be used to calculate the private key.\u003c/li\u003e\n\n\n\n\u003cli\u003eFinally, the result is taken modulo\u0026nbsp;\u0026nbsp;\u003cem\u003eN\u003c/em\u003e\u0026nbsp;to ensure that it is within the acceptable range for private key values.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eConvert to hexadecimal format\u003c/strong\u003e\u0026nbsp;:\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eAfter all the mathematical operations are performed, the result is converted to hexadecimal format using the function\u0026nbsp;\u0026nbsp;\u003ccode\u003ehex()\u003c/code\u003e, which is the standard representation of private keys in Bitcoin.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://perelmanwork.com/discrete-logarithm-ricci-flow-hnp\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eRicci Flow Hidden Number Problem\u003c/a\u003e\u003c/h2\u003e\n\n\n\n\u003cp\u003eCopy the values\u0026nbsp;\u003cstrong\u003e\u003ccode\u003eR, S, Z\u003c/code\u003e\u003c/strong\u003e​​and paste them into the input field\u0026nbsp;\u003ccode\u003e\u003cstrong\u003eRicci Flow HNP\u003c/strong\u003e\u003c/code\u003eto build completely new transactions of the\u0026nbsp;\u003cstrong\u003eECDSA\u003c/strong\u003e\u0026nbsp;algorithm .\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-3-1024x570.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-260\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/ErjCph1mI9Y?t=173\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-5-1024x575.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-264\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003cstrong\u003e\u003ca href=\"https://dockeyhunt.com/dockeyhunt-private-key-calculator/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eDockeyhunt Private Key Calculator\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\n\u003cp\u003eCopy the values ​​and paste them into the\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://dockeyhunt.com/dockeyhunt-private-key-calculator/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eDockeyhunt Private Key Calculator\u003c/a\u003e\u003c/strong\u003e\u003cstrong\u003e\u003ccode\u003eR, S, Z\u003c/code\u003e\u003c/strong\u003e\u0026nbsp;software field\u003cstrong\u003e\u003ca href=\"https://dockeyhunt.com/dockeyhunt-private-key-calculator/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-6-1024x575.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-265\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/ErjCph1mI9Y?t=258\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eNow, according to\u0026nbsp;\u003cem\u003ethe vulnerability\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://cryptodeeptech.ru/discrete-logarithm\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eof Joux Lercier,\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;we copy from the code of\u0026nbsp;\u003ca href=\"https://github.com/bitcoin-core/secp256k1/blob/master/src/ecdsa_impl.h\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eecdsa_impl.h\u003c/strong\u003e\u003c/a\u003e\u003c/em\u003e\u0026nbsp;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\u0026nbsp;\u003ca href=\"https://github.com/bitcoin-core/secp256k1/blob/master/src/ecdsa_impl.h\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ea bug in the code\u003c/a\u003e\u0026nbsp;, fixed\u0026nbsp;\u003ccode\u003e\u003cstrong\u003e0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL\u003c/strong\u003e\u003c/code\u003e several\u0026nbsp;\u003ca href=\"https://github.com/bitcoin-core/secp256k1/blob/master/src/ecdsa_impl.h\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eHEX\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;bits at the beginning (or at the end) of the record.\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e!./darksignature -address 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-5ccd751f271d981ae42081aab22e4aa7\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e....\n....\n....\n/** Difference between field and order, values 'p' and 'n' values defined in\n *  \"Standards for Efficient Cryptography\" (SEC2) 2.7.1.\n *  $ sage -c 'load(\"secp256k1_params.sage\"); print(hex(P-N))'\n *  0x14551231950b75fc4402da1722fc9baee\n */\nstatic const secp256k1_fe secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(\n    0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL\n);\n....\n....\n....\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-7-1024x576.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-267\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/bitcoin-core/secp256k1/blob/master/src/ecdsa_impl.h\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://github.com/bitcoin-core/secp256k1/blob/master/src/ecdsa_impl.h\u003c/a\u003e\u003c/strong\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-8-1024x577.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-269\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/ErjCph1mI9Y?t=289\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eCopy the\u0026nbsp;\u003cstrong\u003eK value and paste it into the\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e\u003ca href=\"https://dockeyhunt.com/dockeyhunt-private-key-calculator/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eDockeyhunt Private Key Calculator\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;software field\u0026nbsp;, then click on the button:\u0026nbsp;\u003cstrong\u003eCalculate Private Key\u003c/strong\u003e\u0026nbsp;and get the private key to the Bitcoin Wallet\u0026nbsp;\u003ca href=\"https://btc1.trezor.io/address/1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-9d20aa28621489371c437c08a19c5c64\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e0x6b29781e725708ae4d94e13730a2718ee3383ea5d911e77d4c2a2fd0c99c1232\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-9-1024x576.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-270\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003eTo start\u0026nbsp;\u003cem\u003ethe algorithm for solving the discrete logarithm,\u003c/em\u003e\u0026nbsp;click on the button:\u0026nbsp;\u003cstrong\u003e\u003ccode\u003ePrivate Key\u003c/code\u003e\u003c/strong\u003e after that, we successfully receive a private key in\u0026nbsp;\u003cstrong\u003eHEX format\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-white-background-color has-text-color has-background has-link-color wp-elements-97b2b53b553edcfec4d450bfce140429\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e6b29781e725708ae4d94e13730a2718ee3383ea5d911e77d4c2a2fd0c99c1232\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-10-1024x576.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-273\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/ErjCph1mI9Y?t=309\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eNext we need to make sure that we have received the required private key value in\u0026nbsp;\u003cstrong\u003eHEX format.\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-11-1024x576.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-274\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/ErjCph1mI9Y?t=378\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eClick on the button\u0026nbsp;\u003cstrong\u003e\u003ccode\u003eBitcoin Address\u003c/code\u003e\u003c/strong\u003eand get the required value of the private key in\u0026nbsp;\u003cstrong\u003eHEX format\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-ec86aca25b8ce356c0b6386161abe555\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e6b29781e725708ae4d94e13730a2718ee3383ea5d911e77d4c2a2fd0c99c1232: 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-12-1024x576.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-275\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/ErjCph1mI9Y?t=324\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eWe also click on the button\u0026nbsp;\u003cstrong\u003e\u003ccode\u003eBalance BTC\u003c/code\u003e\u003c/strong\u003e and get the result of the balance amount:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-fa8633ecad20845d2c0ce232af1fb30d\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e6b29781e725708ae4d94e13730a2718ee3383ea5d911e77d4c2a2fd0c99c1232: 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS: 165.10252195 BTC\n_____________________________________________________________________________________________________\n\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-13-1024x576.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-276\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/ErjCph1mI9Y?t=330\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-14-1024x576.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-277\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/ErjCph1mI9Y?t=366\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-d814c7804ab404e79fd861e72594ebbd\" style=\"color:#108258\"\u003e\u003cstrong\u003ePrivate key received!\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eBitcoin wallet recovery using mathematically based methods such as\u0026nbsp;\u003cstrong\u003ethe Ricci Flow Hidden Number Problem opens new horizons for understanding cryptographic vulnerabilities and opportunities. We demonstrated how\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003ePerelman Work, Dockeyhunt Discrete Logarithm\u003c/strong\u003e\u0026nbsp;, and\u0026nbsp;\u003cstrong\u003eDarkSignature\u003c/strong\u003e\u0026nbsp;software can be used\u0026nbsp;to extract private keys and create fake transactions, highlighting the importance of mathematical analysis in the cryptocurrency space.\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-full is-resized\"\u003e\u003ca href=\"https://www.youtube.com/watch?v=ErjCph1mI9Y\"\u003e\u003cimg decoding=\"async\" width=\"746\" height=\"426\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-4.png\" alt=\"Discrete Logarithms\" class=\"wp-image-3142\" style=\"width:840px;height:auto\" srcset=\"https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-4.png 746w, https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-4-300x171.png 300w\" sizes=\"(max-width: 746px) 100vw, 746px\"\u003e\u003c/a\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\n\n\n\n\u003cp\u003eThe results show that even in a complex system like\u0026nbsp;\u003cstrong\u003eBitcoin\u003c/strong\u003e\u0026nbsp;, 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.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003eExploitation mechanisms and significant influence in multi-signature systems\u003c/h3\u003e\n\n\n\n\u003cp\u003eThe vulnerability of the\u0026nbsp;\u003cstrong\u003eJoux Lercier\u003c/strong\u003e\u0026nbsp;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.\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003eInsufficient 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.\u003c/em\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/37DiscreteLogarithm/Joux_Lercier_Vulnerability_Algorithm_and_Tools_for_Extracting_Private_Key.ipynb\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePractical part\u003c/a\u003e\u003c/h2\u003e\n\n\n\n\u003cp\u003eAccording to the theory\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/discrete-logarithm\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eof vulnerability of the Joux Lercier algorithm\u003c/a\u003e\u0026nbsp;, 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:\u0026nbsp;\u003ca href=\"https://btc1.trezor.io/address/1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\"\u003e\u003cstrong\u003e1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;, where there were lost coins in the amount of:\u0026nbsp;\u003cstrong\u003e165.10252195 BTC\u003c/strong\u003e\u0026nbsp;as of December 2024, this amount is:\u0026nbsp;\u003cstrong\u003e15802506.39 USD\u003c/strong\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-1024x382.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5018\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cstrong\u003e165.10252195 \u0026gt; 15802506,39 USD\u003c/strong\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://github.com/demining/Tutorials-Power-AI\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTutorials Power AI\u003c/a\u003e\u003c/h3\u003e\n\n\n\n\u003cp\u003eLet’s use the list from\u0026nbsp;\u003ca href=\"https://github.com/demining/Tutorials-Power-AI\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e“Tutorials Power AI”\u003c/a\u003e\u0026nbsp;a widely used category of artificial intelligence to introduce business in various fields of cryptanalysis and cryptography in general.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eInstallation command:\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-f0946a14b11461b3e0cc0f3f342dabfd\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003egit clone https://github.com/demining/Tutorials-Power-AI.git\n\ncd Tutorials-Power-AI/\n\npython3 tutorials.py\u003c/strong\u003e\n\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/process.gif\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-large\"\u003e\u003cimg loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"276\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-1024x276.png\" alt=\"Discrete Logarithms\" class=\"wp-image-3118\" srcset=\"https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-1024x276.png 1024w, https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-300x81.png 300w, https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-768x207.png 768w, https://cryptodeeptech.ru/wp-content/uploads/2025/01/image.png 1431w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://bitcoinchatgpt.org/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBitcoinChatGPT\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;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.\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://cryptodeeptech.ru/discrete-logarithm\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eExploiting a vulnerability in the implementation of the algorithm (Joux Lercier) to create a Raw transaction using the BitcoinChatGPT machine learning process\u003c/a\u003e\u003c/h2\u003e\n\n\n\n\u003cp\u003eLet’s consider the construction of the structure of a vulnerable\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/37DiscreteLogarithm/RawTX.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eRaw\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;transaction in which the\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://bitcoinchatgpt.org/joux-lercier-vulnerability-algorithm/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBitcoinChatGPT module is used\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-full is-resized\"\u003e\u003ca href=\"https://www.youtube.com/watch?v=vI-S3ua0QEA\"\u003e\u003cimg loading=\"lazy\" decoding=\"async\" width=\"749\" height=\"428\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-2.png\" alt=\"Discrete Logarithms\" class=\"wp-image-3140\" style=\"width:840px;height:auto\" srcset=\"https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-2.png 749w, https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-2-300x171.png 300w\" sizes=\"auto, (max-width: 749px) 100vw, 749px\"\u003e\u003c/a\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s open the Google Colab version:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://colab.research.google.com/drive/1Cohb5F2h1CP9CnYdAdMJW9vyl4pwQKuz\"\u003ehttps://colab.research.google.com/drive/1Cohb5F2h1CP9CnYdAdMJW9vyl4pwQKuz\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-97b9ce2b1ac732b5d52989b21ac03ea9\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003eState of a vulnerable transaction in Bitcoin:\n\n01000000\n....01\n........0dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935\n............00000000\n........8b483045\n....0221\n...........00\n...........947d6fb75033cc3e342c8538a350e9058134b2a1ae01a7c50fc52b1f56c9169c\n....0220\n........5b3ec0d72a2368cdd48c17ff095ab1ab0b9824e010883539cbeb18141de6384b\n.....0141\n.....04e87e83f871df1439b7873b4ae449d15306cafc53e03a06fffb534b3bf25b58d8edca74b0faf5cf8c3aed6cad2bd79a7bce92ab53e07440d4590cbf31286d9335\n....ffffffff\n01\n....d204000000000000\n........1976\n............a914\n........f750c55bea03af8a720c46b5d6edea93644cdaf7\n....88ac\n00000000\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s combine all the output values ​​into one common line:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-be1abb8e5e2cddd0fbe3cb346114a243\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e01000000010dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935000000008b483045022100947d6fb75033cc3e342c8538a350e9058134b2a1ae01a7c50fc52b1f56c9169c02205b3ec0d72a2368cdd48c17ff095ab1ab0b9824e010883539cbeb18141de6384b014104e87e83f871df1439b7873b4ae449d15306cafc53e03a06fffb534b3bf25b58d8edca74b0faf5cf8c3aed6cad2bd79a7bce92ab53e07440d4590cbf31286d9335ffffffff01d2040000000000001976a914f750c55bea03af8a720c46b5d6edea93644cdaf788ac00000000\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s open the BlockCypher option\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e\u003ca href=\"https://live.blockcypher.com/btc/decodetx\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e“Decode A Transaction”\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://live.blockcypher.com/btc/decodetx\"\u003ehttps://live.blockcypher.com/btc/decodetx\u003c/a\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-1-1024x547.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5035\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eAfter decoding the vulnerable Bitcoin Raw transaction we get the result:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-0b0865fcc14a90efc73a27954ac6714b\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e{\n    \"addresses\": [\n        \"1QiERrMcv6mtGk4F1TVz4sRp9dFfXTQpK\",\n        \"1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\"\n    ],\n    \"block_height\": -1,\n    \"block_index\": -1,\n    \"confirmations\": 0,\n    \"double_spend\": false,\n    \"fees\": 2606688996428,\n    \"hash\": \"07160d430b92d957a7b3f0284ec7ff6084629b6385476608a6da5858fcfc2716\",\n    \"inputs\": [\n        {\n            \"addresses\": [\n                \"1QiERrMcv6mtGk4F1TVz4sRp9dFfXTQpK\"\n            ],\n            \"age\": 344419,\n            \"output_index\": 0,\n            \"output_value\": 2606688997662,\n            \"prev_hash\": \"35591e5c7f4f1f0e4d81748042f2a4b7dcae3ae01027f361cad7c8746369bc0d\",\u003c/strong\u003e\n\u003cstrong\u003e.......\n.......\n.......\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eLet’s pay attention to Bitcoin HASH160:\u0026nbsp;\u003cstrong\u003ef750c55bea03af8a720c46b5d6edea93644cdaf7\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-3.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5668\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/50de2ffdd7f9f06a34049d1c72559aa16b1bf42c/37DiscreteLogarithm/DecodeRawTX.txt#L31C30-L31C70\"\u003ehttps://github.com/demining/CryptoDeepTools/blob/50de2ffdd7f9f06a34049d1c72559aa16b1bf42c/37DiscreteLogarithm/DecodeRawTX.txt#L31C30-L31C70\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://coinbin.ru/#verify\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTransaction Script\u003c/a\u003e\u003c/h2\u003e\n\n\n\n\u003ch5 class=\"wp-block-heading\"\u003eThe above script has been decoded\u003c/h5\u003e\n\n\n\n\u003cp\u003eBitcoinChatGPT creates a transaction structure using\u0026nbsp;\u003ccode\u003e\u003cstrong\u003eHASH\u003c/strong\u003e\u003c/code\u003ethe public key, where we see that Bitcoin address:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://btc1.trezor.io/address/1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;sends\u0026nbsp;\u003cstrong\u003e\u003ccode\u003e1234 satoshi\u003c/code\u003e\u003c/strong\u003eto the same address within its network.\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-2-1024x424.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5037\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eBitcoin HASH160 was generated using Python Script:\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/37DiscreteLogarithm/wif_to_hash160.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ewif_to_hash160.py\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-3(1).png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5039\" style=\"width:840px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-4-1024x735.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5041\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/37DiscreteLogarithm/wif_to_hash160.py\"\u003ehttps://github.com/demining/CryptoDeepTools/blob/main/37DiscreteLogarithm/wif_to_hash160.py\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eQuestion – Answer:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-5-1024x439.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5043\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-6-1024x421.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5045\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-7-1024x451.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5046\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eFinally, the\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/BitcoinChatGPT/Jacobian-Curve-Vulnerability-Algorithm/blob/main/BitcoinChatGPT_%E2%84%964_Joux_Lercier_Vulnerability_Algorithm.ipynb\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBitcoinChatGPT\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;module outputs the response to the file:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/37DiscreteLogarithm/KEYFOUND.privkey\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eKEYFOUND.privkey\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;storing the private key in two most used formats\u0026nbsp;\u003cstrong\u003eHEX \u0026amp; WIF\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-8-1024x680.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5047\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/37DiscreteLogarithm/KEYFOUND.privkey\"\u003ehttps://github.com/demining/CryptoDeepTools/blob/main/37DiscreteLogarithm/KEYFOUND.privkey\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://youtu.be/eqQw4vY4RmI\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBitcoinChatGPT №6 Joux Lercier Vulnerability Algorithm\u003c/a\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-full is-resized\"\u003e\u003ca href=\"https://www.youtube.com/watch?v=yRGZ41jvGKw\"\u003e\u003cimg loading=\"lazy\" decoding=\"async\" width=\"748\" height=\"428\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-5.png\" alt=\"Discrete Logarithms\" class=\"wp-image-3144\" style=\"width:840px;height:auto\" srcset=\"https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-5.png 748w, https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-5-300x172.png 300w\" sizes=\"auto, (max-width: 748px) 100vw, 748px\"\u003e\u003c/a\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://www.youtube.com/watch?v=yRGZ41jvGKw\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eVulnerable\u0026nbsp;Raw\u0026nbsp;Transaction\u003c/a\u003e\u003c/h2\u003e\n\n\n\n\u003cp\u003eLet’s create a vulnerable Raw transaction from the received data using the\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/smartibase/Broadcast-Bitcoin-Transaction\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBroadcast Bitcoin Transaction repository\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eDownload and install the source code, open the terminal and run the command:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-ed1ed2d6bd8eb54429f361c28733fbae\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003egit clone https://github.com/smartibase/Broadcast-Bitcoin-Transaction.git\n\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cp\u003eCatalog:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-37c252389923970f49833153c041c31d\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ecd Broadcast-Bitcoin-Transaction\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eLet’s install three important libraries:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003ca href=\"https://pypi.org/project/zmq/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ezmq\u003c/strong\u003e\u003c/a\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ca href=\"https://pypi.org/project/urllib3/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eurllib3\u003c/strong\u003e\u003c/a\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ca href=\"https://pypi.org/project/requests/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003erequests\u003c/strong\u003e\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-8-1024x495.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-4733\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ca href=\"https://github.com/smartibase/Broadcast-Bitcoin-Transaction/blob/main/requirements.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003erequirements.txt\u003c/strong\u003e\u003c/a\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eLet’s run the command:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-c3638457a19a8e59dfd773c6eeb0aa38\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003epip install -r requirements.txt\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eLet’s open the main file in\u0026nbsp;\u003ca href=\"https://keyhunters.ru/the-benefits-of-the-popular-notepad-program/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eNotepad\u0026nbsp;\u003c/a\u003e\u003ca href=\"https://keyhunters.ru/the-benefits-of-the-popular-notepad-program/\"\u003e++\u003c/a\u003e\u0026nbsp;and make a small change to the Python Script code:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/smartibase/Broadcast-Bitcoin-Transaction/blob/main/main.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003emain.py\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-a82bc4470ec38fe7bfdbc705de88fba2\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003efrom io import BytesIO\nfrom secp256k1 import *\nfrom sighash import *\n\npk = PrivateKey.parse(\"5JdUtcYt3ZBQN8aPZWNffXzNCTPds7aQtJk7zc9iQShNQ9yWe7x\")\npk.address()\ntx = bytes.fromhex(\"35591e5c7f4f1f0e4d81748042f2a4b7dcae3ae01027f361cad7c8746369bc0d\")\nindex = 0\nsend = \"1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\"\ntx_in = TxIn(tx, index, b'', 0xffffffff)\ntx_in._script_pubkey = Tx.get_address_data(pk.address())['script_pubkey']\ntx_in._value = 2345\ntx_ins = [ tx_in ]\ntx_outs = [\n    TxOut(1234, Tx.get_address_data(send)['script_pubkey'].serialize())\n]\ntx = Tx(1, tx_ins, tx_outs, 0, testnet=True)\nsignature(tx, 0, pk)\ntx.serialize().hex()\nprint(tx.serialize().hex())\nf = open(\"RawTX.txt\", 'w')\nf.write(\"\" + tx.serialize().hex() + \"\" + \"\\n\")\nf.close()\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eLet’s run the command:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-ba63856e6306b76b5e1e36b8e2c44d96\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003epython main.py\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://www.youtube.com/watch?v=8B2LKMBsVSE\"\u003eVulnerable transaction created\u0026nbsp;\u003c/a\u003e\u003ca href=\"https://www.youtube.com/watch?v=8B2LKMBsVSE\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e!\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eLet’s open the RawTX file in the directory:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-be1abb8e5e2cddd0fbe3cb346114a243\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e01000000010dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935000000008b483045022100947d6fb75033cc3e342c8538a350e9058134b2a1ae01a7c50fc52b1f56c9169c02205b3ec0d72a2368cdd48c17ff095ab1ab0b9824e010883539cbeb18141de6384b014104e87e83f871df1439b7873b4ae449d15306cafc53e03a06fffb534b3bf25b58d8edca74b0faf5cf8c3aed6cad2bd79a7bce92ab53e07440d4590cbf31286d9335ffffffff01d2040000000000001976a914f750c55bea03af8a720c46b5d6edea93644cdaf788ac00000000\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eThe order of actions in the video:\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-full is-resized\"\u003e\u003ca href=\"https://www.youtube.com/watch?v=8B2LKMBsVSE\"\u003e\u003cimg loading=\"lazy\" decoding=\"async\" width=\"748\" height=\"429\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-6.png\" alt=\"Discrete Logarithms\" class=\"wp-image-3145\" style=\"width:840px;height:auto\" srcset=\"https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-6.png 748w, https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-6-300x172.png 300w\" sizes=\"auto, (max-width: 748px) 100vw, 748px\"\u003e\u003c/a\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cem\u003eAs we know from\u0026nbsp;\u003ca href=\"https://keyhunters.ru/what-is-prompt-answers-and-how-is-it-related-to-machine-learning-and-artificial-intelligence/\"\u003ethe prompt responses of the\u0026nbsp;\u003c/a\u003e\u003ca href=\"https://colab.research.google.com/drive/1Cohb5F2h1CP9CnYdAdMJW9vyl4pwQKuz\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eBitcoinChatGPT\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;module ,\u0026nbsp;Joux Lercier Vulnerability Algorithm can be used to solve complex cryptographic problems.\u003c/em\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://github.com/smartibase/Smart-Transformers\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSmart Transformers\u003c/a\u003e\u003c/h2\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://github.com/smartibase/Smart-Transformers\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eWe will apply Smart Transformers\u003c/a\u003e\u0026nbsp;machine learning\u0026nbsp;, integrate the notebook\u0026nbsp;\u003ccode\u003eGoogle Colab\u003c/code\u003ewith\u0026nbsp;\u003ca href=\"https://keyhunters.ru/pytorch-tensorflow-and-jax-powerful-tools-for-deep-learning/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ePytorch, TensorFlow, JAX\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;and using the obtained data of the vulnerable\u0026nbsp;\u003cstrong\u003eRaw\u003c/strong\u003e\u0026nbsp;transaction for Bitcoin Address:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://btc1.trezor.io/address/1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;we will create an unprotected\u0026nbsp;\u003cstrong\u003ewallet.dat\u003c/strong\u003e\u0026nbsp;file from the proposed choice of all existing algorithms from\u0026nbsp;\u003ca href=\"https://github.com/smartibase/Smart-Transformers\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eSMART_IDENTIFY\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;. Then we will perform\u0026nbsp;\u003ca href=\"https://exploitdarlenepro.com/1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ea Padding Oracle Attack\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;on the newly created file:\u0026nbsp;\u003cstrong\u003ewallet.dat\u003c/strong\u003e\u0026nbsp;to decrypt the password into the original binary format in order to obtain and extract the private key from the\u0026nbsp;\u003cstrong\u003eBitcoin Core\u003c/strong\u003e\u0026nbsp;software console using the standard \u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eCommand:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp class=\"has-text-color has-link-color wp-elements-b8050f18ede30d9cecebd65c5f278406\" style=\"color:#4092c2\"\u003e\u003cstrong\u003e\u003ccode\u003edumpprivkey 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/code\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://colab.research.google.com/#create=true\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eLet’s open a new Google Colab\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;notebook\u0026nbsp;using the link:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://colab.research.google.com/#create=true\"\u003ehttps://colab.research.google.com/#create=true\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eClone the\u0026nbsp;\u003ca href=\"https://github.com/smartibase/Smart-Transformers\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eSmart Transformers repository\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-0e81a03486a8cf1e5650ee50b407378c\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!git clone https://github.com/smartibase/Smart-Transformers.git\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-632951219b9ef5ef12a9094e1ce22644\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ecd Smart-Transformers/\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-9-1024x487.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5048\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eLet’s install all the necessary packages and libraries:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-2c8f3e908370f30a871ab98849567239\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!sudo apt-get update\n!sudo apt install libtool\n!sudo apt-get install g++\u003c/strong\u003e\n\u003cstrong\u003e!python setup.py --help\u003c/strong\u003e\n\u003cstrong\u003e!sudo apt-get install libgmp3-dev libmpfr-dev\n!chmod +x Generic_Algorithms\n!./Generic_Algorithms\n!pip3 install transformers\nfrom transformers import AutoModelForCausalLM, AutoTokenizer\nmodel_name = \"microsoft/DialoGPT-medium\"\ntokenizer = AutoTokenizer.from_pretrained(model_name)\nmodel = AutoModelForCausalLM.from_pretrained(model_name)\nmodel = model.cpu()\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-10-1024x434.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5049\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-11-1024x437.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5050\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eTeam:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-bca520022a768d38883e56a4e9824597\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003els -S\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-12.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5051\" style=\"width:840px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eLet’s add our vulnerable\u0026nbsp;\u003cstrong\u003eRaw\u003c/strong\u003e\u0026nbsp;transaction to a text document:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/37DiscreteLogarithm/RawTX.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eRawTX.txt\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;for this we will use the utility\u003ccode\u003eecho\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eLet’s run the command:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-b051553e70b66302168f456d33990ed8\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!echo '01000000010dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935000000008b483045022100947d6fb75033cc3e342c8538a350e9058134b2a1ae01a7c50fc52b1f56c9169c02205b3ec0d72a2368cdd48c17ff095ab1ab0b9824e010883539cbeb18141de6384b014104e87e83f871df1439b7873b4ae449d15306cafc53e03a06fffb534b3bf25b58d8edca74b0faf5cf8c3aed6cad2bd79a7bce92ab53e07440d4590cbf31286d9335ffffffff01d2040000000000001976a914f750c55bea03af8a720c46b5d6edea93644cdaf788ac00000000' \u0026gt; RawTX.txt\u003c/strong\u003e\n\n\u003cstrong\u003e!cat RawTX.txt\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-13-1024x118.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5052\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eNow, to get the exact algorithm and method for cryptanalysis we need to identify the vulnerable\u0026nbsp;\u003cstrong\u003eRawTX\u003c/strong\u003e\u0026nbsp;using the\u0026nbsp;\u003cstrong\u003eSMART_IDENTIFY\u003c/strong\u003e\u0026nbsp;utility .\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eLet’s run the command:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-240fdaa09efd66594dcdbea0ea7b3c10\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!./SMART_IDENTIFY\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eAs a result, we get the\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://bitcoinchatgpt.org/joux-lercier-vulnerability-algorithm\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eJoux_Lercier_Algorithm\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;method , in earlier studies the same thing was identified by the\u0026nbsp;\u003ca href=\"https://www.youtube.com/watch?v=eqQw4vY4RmI\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eBitcoinChatGPT\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;module .\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-551191813893119b84938648157869a7\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e#################################################\n\nJoux_Lercier_Algorithm\n\n#################################################\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-14-1024x364.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5053\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s open the catalog:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-15-1.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5056\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eLet’s start the process of creating the\u0026nbsp;\u003cstrong\u003ewallet.dat\u003c/strong\u003e\u0026nbsp;file. For this, we use the identified data of the vulnerable\u0026nbsp;\u003cstrong\u003eRaw\u003c/strong\u003e\u0026nbsp;transaction in the file:\u0026nbsp;\u003cstrong\u003eRawTX.txt.\u003c/strong\u003e\u0026nbsp;For the process, we apply the\u0026nbsp;\u003cstrong\u003eJoux_Lercier_Algorithm utility.\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s run the command:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-68a1c4de3c995b27fe32b00e707b55a3\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!./Joux_Lercier_Algorithm -o RawTX.txt -s wallet.dat\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-16-1024x436.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5058\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-18-1024x427.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5060\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eLet’s open the directory in the left panel\u0026nbsp;\u003ccode\u003eGoogle Colab\u003c/code\u003eand see the file:\u0026nbsp;\u003cstrong\u003e\u003ccode\u003ewallet.dat\u003c/code\u003e\u003c/strong\u003eSuccessfully created!\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-19-1024x531-1.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5062\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-large\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-20-1024x658-1.png\" alt=\"Discrete Logarithms\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center has-text-color has-link-color wp-elements-83a6de34308b009290e5f761759ab745\" style=\"color:#4092c2\"\u003eDownload and Install Bitcoin Core 0.18.0\u0026nbsp;\u003ca href=\"https://bitcoincore.org/bin/bitcoin-core-0.18.0\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://bitcoincore.org/bin/bitcoin-core-0.18.0\u003c/a\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-full is-resized\"\u003e\u003ca href=\"https://www.youtube.com/watch?v=LTzMQPstvpM\"\u003e\u003cimg loading=\"lazy\" decoding=\"async\" width=\"751\" height=\"426\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-7.png\" alt=\"Discrete Logarithms\" class=\"wp-image-3146\" style=\"width:840px;height:auto\" srcset=\"https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-7.png 751w, https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-7-300x170.png 300w\" sizes=\"auto, (max-width: 751px) 100vw, 751px\"\u003e\u003c/a\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eLet’s open the console and run the command:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-1878b7529b18cb6f1b202acff2f4bb06\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\n\u003cstrong\u003egetaddressinfo 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/strong\u003e\n\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-21-1024x671.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5065\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eWe see that the file:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/bitcoin-core-wallet-and-the-importance-of-the-wallet-dat-file/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ewallet.dat\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;belongs to the Bitcoin Address:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://btc1.trezor.io/address/1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center has-text-color has-background has-link-color wp-elements-b160b45eaa849940cbc72bf6c52496dc\" style=\"color:#943939;background-color:#f78da817\"\u003eFile: wallet.dat is encrypted with a password!\u003c/h2\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-24.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-4839\" style=\"width:839px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eLet’s run the command to check the private key:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-39f801194894bafde5a968537a8c7a57\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003edumpprivkey 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-22-1024x675.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5066\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003eWe see a warning:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/understanding-and-resolving-the-error-please-enter-the-wallet-passphrase-with-walletpassphrase-first-code-13-in-bitcoin-core/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eError: Please enter the wallet passphrase with walletpassphrase first. (code -13)\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch1 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://exploitdarlenepro.com/1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePadding Oracle Attack\u003c/a\u003e\u003c/h1\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-28.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5793\" style=\"width:840px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-29.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5795\" style=\"width:840px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://exploitdarlenepro.com/1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eLet’s use the Padding Oracle Attack\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;method on Wallet.dat\u0026nbsp;and decrypt the password for access into a binary password format.\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-full is-resized\"\u003e\u003ca href=\"https://www.youtube.com/watch?v=gDBDP9bseE0\"\u003e\u003cimg loading=\"lazy\" decoding=\"async\" width=\"746\" height=\"429\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-8.png\" alt=\"Discrete Logarithms\" class=\"wp-image-3147\" style=\"width:838px;height:auto\" srcset=\"https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-8.png 746w, https://cryptodeeptech.ru/wp-content/uploads/2025/01/image-8-300x173.png 300w\" sizes=\"auto, (max-width: 746px) 100vw, 746px\"\u003e\u003c/a\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-23-1024x460.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5067\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-24-1024x455.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5068\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-25-1024x452.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5069\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003eFirst we get access to the\u0026nbsp;\u003ca href=\"https://github.com/smartibase/Biggest-Lost-Bitcoin-Wallets-List/raw/main/165.10%20BTC/wallet.dat\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ewallet.dat\u003c/a\u003e\u0026nbsp;file for the amount:\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/smartibase/Biggest-Lost-Bitcoin-Wallets-List/tree/main/165.10%20BTC\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e165.10 BTC\u003c/a\u003e\u003c/strong\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/smartibase/Biggest-Lost-Bitcoin-Wallets-List/tree/main/165.10%20BTC\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003eClone Repository:\u0026nbsp;\u003ca href=\"https://github.com/smartibase/Biggest-Lost-Bitcoin-Wallets-List.git\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBiggest Lost Bitcoin Wallets List\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-25f100f67d0aea637778e7f45a3ad0c0\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003egit clone https://github.com/keyhunters/Biggest-Lost-Bitcoin-Wallets-List.git\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-26-1024x574.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5070\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/total-commander/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTotal Commander\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-1(2).png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-982\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-27.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5071\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-28(1).png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5072\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://github.com/keyhunters/Biggest-Lost-Bitcoin-Wallets-List/tree/main/165.10%20BTC\"\u003ehttps://github.com/keyhunters/Biggest-Lost-Bitcoin-Wallets-List/tree/main/165.10%20BTC\u003c/a\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-5-1536x674.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-left\"\u003e\u003cstrong\u003eDownload and install\u0026nbsp;\u0026nbsp;\u003ca href=\"https://bitcoincore.org/bin/bitcoin-core-0.18.0\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBitcoin Core 0.18.0\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-7-1024x551.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-994\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-9.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-997\" style=\"width:839px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003eОткроем path:\u0026nbsp;\u003ca href=\"https://keyhunters.ru/bitcoin-core-wallet-dat/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ec:\\Users\\User\\AppData\\Roaming\\Bitcoin\\\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-11.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1003\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003eLet’s move the file:\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/smartibase/Biggest-Lost-Bitcoin-Wallets-List/raw/main/165.10%20BTC/wallet.dat\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ewallet.dat\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-6-1536x584.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003ca href=\"file:///C:/Users/User/AppData/Roaming/Bitcoin/wallet.dat\"\u003e\u003cstrong\u003ec:\\Users\\User\\AppData\\Roaming\\Bitcoin\\wallet.d\u003c/strong\u003e\u003c/a\u003e\u003ca href=\"https://keyhunters.ru/bitcoin-core-wallet-dat/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eat\u003c/strong\u003e\u003c/a\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-4(1).png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1090\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/bitcoin-core-wallet/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eLet’s launch the Bitcoin Core\u003c/a\u003e\u0026nbsp;wallet\u003ca href=\"https://keyhunters.ru/bitcoin-core-wallet/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-13.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1008\" style=\"width:840px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch1 class=\"wp-block-heading has-text-align-left\"\u003e\u003ca href=\"https://exploitdarlenepro.com/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eEncryt Wallet…\u003c/strong\u003e\u003c/a\u003e\u003c/h1\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-14.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1010\" style=\"width:837px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch1 class=\"wp-block-heading\"\u003e\u003cstrong\u003eLet’s open the console\u003c/strong\u003e\u003c/h1\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e\u003cstrong\u003egetaddressinfo 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-8-1536x1011.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003e\u003ca href=\"https://dockeyhunt.com/Cryptocurrency-Prices\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBitcoin Address Information:\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003eBalance: 165.10252195 BTC\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-22-1024x550.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/rapid7/metasploit-framework\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eMetasploit Framework and use MSFVenom\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-17.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1021\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/metasploit-framework-msfvenom/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eThe Role of Metasploit Framework in the Development of msfvenom\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003ca href=\"https://keyhunters.ru/metasploit-framework-msfvenom/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003emsfvenom\u003c/a\u003e\u0026nbsp;is a tool created by combining the two previous tools:\u0026nbsp;\u0026nbsp;\u003cbr\u003e\u003ccode\u003emsfpayload\u003c/code\u003eand\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003ccode\u003emsfencode\u003c/code\u003e. 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.\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://keyhunters.ru/metasploit-framework-msfvenom/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eThe Metasploit Framework\u003c/a\u003e\u0026nbsp;\u0026nbsp;plays a key role in the development of msfvenom for several reasons:\u003c/p\u003e\n\n\n\n\u003cp\u003e1. 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.\u003c/p\u003e\n\n\n\n\u003cp\u003e2. 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.\u003c/p\u003e\n\n\n\n\u003cp\u003e3. 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.\u003c/p\u003e\n\n\n\n\u003cp\u003e4. 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.\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-18-1024x908.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1022\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003cstrong\u003e\u003ca href=\"https://t.me/exploitdarlenepro\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eRun ExploitDalenePRO.exe\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-19.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1025\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-20-1024x699.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1028\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-4f6e6d7ec599a4ab5fc655aa081838bf\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-10.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-639af7c85b80e040598106a689591570\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ec:\\BitcoinTools\\ExploitDalenePRO\\modules\\\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-28(2).png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1040\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-4554f2d477fc2a29c8e7da1425fe5021\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ec:\\BitcoinTools\\ExploitDalenePRO\\modules\\exploits\\\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-29(1).png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1041\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-48553e5b26ad87491e9fc488cd080a99\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ec:\\BitcoinTools\\ExploitDalenePRO\\modules\\exploits\\ExploitDarlenePRO\\\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-30.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1042\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-67521ba430d0c5137ea7c2552e879ae9\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ec:\\BitcoinTools\\ExploitDalenePRO\\modules\\exploits\\ExploitDarlenePRO\\decode_core.rb\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-31.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1043\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003e\u003ca href=\"https://t.me/exploitdarlenepro\" target=\"_blank\" rel=\"noreferrer noopener\"\u003edecode_core.rb\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-13(1).png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-14(1).png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-bed44c1f9f610b2e8c69e258fdc4b2b1\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ec:\\BitcoinTools\\ExploitDalenePRO\\bitcoin\\\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-24(1).png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1034\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/bitcoin/bitcoin\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://github.com/bitcoin/bitcoin\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-26-1024x471.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1037\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/bitcoin/bitcoin/blob/master/src/crypto/aes.h\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://github.com/bitcoin/bitcoin/blob/master/src/crypto/aes.h\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-27(1).png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1038\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e\u003cstrong\u003ec:\\BitcoinTools\\ExploitDalenePRO\\bitcoin\\src\\\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-23.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1032\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-d23feeedf412a61510ef40143d773991\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ec:\\BitcoinTools\\ExploitDalenePRO\\bitcoin\\src\\crypto\\aes.cpp\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-22.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1030\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-d23feeedf412a61510ef40143d773991\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ec:\\BitcoinTools\\ExploitDalenePRO\\bitcoin\\src\\crypto\\aes.cpp\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-16.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-bf271f467b93ca96913ee2b488c3446b\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ec:\\Users\\User\\AppData\\Roaming\\Bitcoin\\\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-4(1).png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-1090\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/smartibase/Biggest-Lost-Bitcoin-Wallets-List/raw/main/165.10%20BTC/wallet.dat\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eUpload Wallet.dat\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-18.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/msfvenom_006.gif\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/smartibase/Biggest-Lost-Bitcoin-Wallets-List/blob/main/165.10%20BTC/result.json\"\u003eresult.json\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-19-1536x163.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-1e32b02bba1e534e8f2871556249c62b\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ewalletpassphrase 1111111101110111010010110110010101100010110010001011111011000111101010010010000110101110100110000001100011001101000100001110101110100101101111000010100000000110100010110011000111111001111000110110001011000010000011001001000100101011001000101100110001101000 60\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003eRun the command and get\u0026nbsp;\u003ca href=\"https://keyhunters.ru/bitcoin-core-dumpprivkey/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePrivate Key\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eThe dumpprivkey command in Bitcoin Core\u003c/p\u003e\n\n\n\n\u003cp\u003eThe\u0026nbsp;\u003ccode\u003e\u003cstrong\u003edumpprivkey\u003c/strong\u003e\u003c/code\u003e\u0026nbsp;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:\u003c/p\u003e\n\n\n\n\u003cp\u003e“\u003ccode\u003e\u0026nbsp;\u003cstrong\u003edumpprivkey “address”\u003c/strong\u003e\u0026nbsp;“\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eWhere “address” is the Bitcoin address for which you want to receive the\u0026nbsp;\u003ca href=\"https://keyhunters.ru/bitcoin-core-dumpprivkey/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eprivate key\u003c/a\u003e.\u003c/p\u003e\n\n\n\n\u003cp\u003eHow dumpprivkey command works\u003c/p\u003e\n\n\n\n\u003cp\u003eWhen you type the\u0026nbsp;\u003ccode\u003e\u003cstrong\u003edumpprivkey\u003c/strong\u003e\u003c/code\u003e\u0026nbsp;command, Bitcoin Core looks for the specified address in its wallet and, if found, returns the corresponding\u0026nbsp;\u003ca href=\"https://keyhunters.ru/bitcoin-core-dumpprivkey/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eprivate key\u003c/a\u003e\u0026nbsp;in WIF format. This allows the user to store the private key in a safe place or import it into another wallet.\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-39f801194894bafde5a968537a8c7a57\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003edumpprivkey 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-20.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003e\u003ca href=\"https://dockeyhunt.com/Bitcoin-Address\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePrivate Key Information:\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-d54d94916fc72e22809c03b8c8a1518b\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e5JdUtcYt3ZBQN8aPZWNffXzNCTPds7aQtJk7zc9iQShNQ9yWe7x\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-21-1536x823.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003e\u003ca href=\"https://dockeyhunt.com/Cryptocurrency-Prices\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBitcoin Address Information:\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-color has-link-color wp-elements-f267b2e604240017d98ca74e3bde8ca0\" style=\"color:#4092c2\"\u003e\u003cstrong\u003eBalance: 165.10252195 BTC\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-22-1536x824.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003e\u003cstrong\u003e\u003ca href=\"https://www.coinbase.com/converter/btc/usd\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://www.coinbase.com/converter/btc/usd\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cstrong\u003e165.10252195 \u0026gt; 15802506,39 USD\u003c/strong\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003e\u003ca href=\"https://keyhunters.ru/exploring-bitcoin-tools-in-python-a-comprehensive-guide-to-the-bitcoin-package-on-pypi/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003c/a\u003e\u003c/em\u003e\u003ca href=\"https://keyhunters.ru/exploring-bitcoin-tools-in-python-a-comprehensive-guide-to-the-bitcoin-package-on-pypi/\"\u003e\u003cstrong\u003eLet’s install the Bitcoin\u0026nbsp;\u003c/strong\u003e\u003c/a\u003e\u003ca href=\"https://keyhunters.ru/exploring-bitcoin-tools-in-python-a-comprehensive-guide-to-the-bitcoin-package-on-pypi/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003elibrary\u003c/strong\u003e\u003c/a\u003e\u003ca href=\"https://keyhunters.ru/exploring-bitcoin-tools-in-python-a-comprehensive-guide-to-the-bitcoin-package-on-pypi/\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-9a0f1a67ae8617004ae12ce64ce4a4b7\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!pip3 install bitcoin\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-25-1024x271.png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5734\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eLet’s run\u0026nbsp;\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/37DiscreteLogarithm/priv_addr.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ethe code\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;\u0026nbsp;to check the Bitcoin Address match:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-30(1).png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5078\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-a346db937579cfa0c287f6309f8b8a07\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e__________________________________________________\n\nPrivate Key WIF: 5JdUtcYt3ZBQN8aPZWNffXzNCTPds7aQtJk7zc9iQShNQ9yWe7x\nBitcoin Address: 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\ntotal_received \t= 165.10252195 Bitcoin\n__________________________________________________\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eThat’s right! The private key corresponds to the Bitcoin Wallet.\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eLet’s open\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://cryptodeeptech.ru/bitaddress.html\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ebitaddress\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;and check:\u003c/h2\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-1a5ad58687258b2668d429e375eadd82\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003eADDR: 1PYgfSouGGDkrMfLs6AYmwDqMLiVrCLfeS\nWIF:  5JdUtcYt3ZBQN8aPZWNffXzNCTPds7aQtJk7zc9iQShNQ9yWe7x\nHEX:  6b29781e725708ae4d94e13730a2718ee3383ea5d911e77d4c2a2fd0c99c1232\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Discrete Logarithms - «CRYPTO DEEP TECH»_files/image-31(1).png\" alt=\"Discrete Logarithm mathematical methods and tools for recovering cryptocurrency wallets Bitcoin\" class=\"wp-image-5079\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eConclusion and mitigation measures:\u003c/h2\u003e\n\n\n\n\u003cp\u003eIn this article, we explored methods for recovering lost cryptocurrency wallets and private keys using mathematical algorithms such as discrete logarithm and Hidden\u0026nbsp;\u003cstrong\u003eNumber Problem . We demonstrated how to use\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eDockeyhunt Discrete Logarithm, DarkSignature,\u003c/strong\u003e\u0026nbsp;and\u0026nbsp;\u003cstrong\u003ePerelman Work\u003c/strong\u003e\u0026nbsp;software\u0026nbsp;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.\u003c/p\u003e\n\n\n\n\u003cp\u003eTo protect against threats related to the Joux Lercier vulnerability, users should take the following steps:\u003c/p\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eSoftware Updates\u003c/strong\u003e\u0026nbsp;: Regularly updating your cryptocurrency wallets to patched versions is critical to maintaining security.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eImproved signature verification mechanisms\u003c/strong\u003e\u0026nbsp;: Stronger input validation and error handling will help prevent the creation of fake signatures and protect users’ private keys.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eNetwork activity monitoring\u003c/strong\u003e\u0026nbsp;: Constant analysis of network status and early detection of suspicious transactions allow for prompt response to attempts to exploit vulnerabilities.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eImplementing Multi-Factor Authentication\u003c/strong\u003e\u0026nbsp;: Implementing additional cryptographic security methods will significantly improve security.\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quot","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdemining%2Fdiscrete-logarithm","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdemining%2Fdiscrete-logarithm","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdemining%2Fdiscrete-logarithm/lists"}