{"id":19915482,"url":"https://github.com/demining/twist-attack-2","last_synced_at":"2025-06-24T21:03:38.540Z","repository":{"id":144620989,"uuid":"608600649","full_name":"demining/Twist-Attack-2","owner":"demining","description":"In this article, we will implement a Twist Attack with an example and show how, using certain points on the secp256k1 elliptic curve, we can get partial private key values ​​and restore a Bitcoin Wallet within 5-15 minutes using “Sagemath pollard rho function: (discrete_log_rho)” and “ Chinese Remainder Theorem” .","archived":false,"fork":false,"pushed_at":"2023-09-09T14:15:22.000Z","size":4494,"stargazers_count":11,"open_issues_count":0,"forks_count":3,"subscribers_count":2,"default_branch":"main","last_synced_at":"2025-03-01T09:24:11.307Z","etag":null,"topics":["attack","attacker","bitcoin","bitcoin-wallet","blockchain","blockchain-technology","cryptocurrency","exploit","exploiting","exploiting-vulnerabilities","hack","hacking","vulnerabilities","vulnerability","vulnerability-scanners"],"latest_commit_sha":null,"homepage":"https://cryptodeeptech.ru/twist-attack-2","language":"HTML","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":"2023-03-02T11:02:23.000Z","updated_at":"2024-08-12T20:30:04.000Z","dependencies_parsed_at":null,"dependency_job_id":"1cf5262e-18d9-4303-9b7d-753865d7b518","html_url":"https://github.com/demining/Twist-Attack-2","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/demining/Twist-Attack-2","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FTwist-Attack-2","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FTwist-Attack-2/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FTwist-Attack-2/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FTwist-Attack-2/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/demining","download_url":"https://codeload.github.com/demining/Twist-Attack-2/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FTwist-Attack-2/sbom","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":261756524,"owners_count":23205146,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","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":["attack","attacker","bitcoin","bitcoin-wallet","blockchain","blockchain-technology","cryptocurrency","exploit","exploiting","exploiting-vulnerabilities","hack","hacking","vulnerabilities","vulnerability","vulnerability-scanners"],"created_at":"2024-11-12T21:40:17.382Z","updated_at":"2025-06-24T21:03:38.489Z","avatar_url":"https://github.com/demining.png","language":"HTML","funding_links":[],"categories":[],"sub_categories":[],"readme":"\n# Twist Attack Example №2\n\n---\n\n\n---\n\n\n\n\n\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/034-1024x576.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2357\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n---\n\n\n* Tutorial: https://youtu.be/pOviZOYItv4\n* Tutorial: https://cryptodeeptech.ru/twist-attack-2\n\n---\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eIn this article, we will implement a Twist Attack using example #2, according to\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/twist-attack\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ethe first theoretical part of the article,\u003c/a\u003e\u0026nbsp;we made sure that with the help of certain points on the secp256k1 elliptic curve, we can get partial values ​​​​of the private key and within 5-15 minutes restore a Bitcoin Wallet using the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm_for_logarithms\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e“Sagemath pollard rho function : (discrete_log_rho)”\u003c/a\u003e\u0026nbsp;and\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Chinese_remainder_theorem\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e“Chinese Remainder Theorem”\u003c/a\u003e\u0026nbsp;.\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eLet’s continue with a series of ECC operations, since these certain points are maliciously chosen points on the secp256k1 elliptic curve\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=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-13-1024x596.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2364\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ca href=\"https://github.com/christianlundkvist/blog/blob/master/2020_05_26_secp256k1_twist_attacks/secp256k1_twist_attacks.md\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://github.com/christianlundkvist/blog/blob/master/2020_05_26_secp256k1_twist_attacks/secp256k1_twist_attacks.md\u003c/a\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003eAccording to Paulo Barreto tweet:\u0026nbsp;\u003ca href=\"https://twitter.com/pbarreto/status/825703772382908416?s=21\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://twitter.com/pbarreto/status/825703772382908416?s=21\u003c/a\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-2-1024x706.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2079\"\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\u003eThe cofactor is 3^2*13^2*3319*22639\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-3-1024x710.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2082\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003eE1: 20412485227\nE2: 3319, 22639\nE3: 109903, 12977017, 383229727\nE4: 18979\nE6: 10903, 5290657, 10833080827, 22921299619447\n\nprod = 20412485227 * 3319 * 22639 *109903 * 12977017 * 383229727 * 18979 * 10903 * 5290657 * 10833080827 * 22921299619447\n\n38597363079105398474523661669562635951234135017402074565436668291433169282997 = 3 * 13^2 * 3319 * 22639 * 1013176677300131846900870239606035638738100997248092069256697437031\n\nHEX:0x55555555555555555555555555555555C1C5B65DC59275416AB9E07B0FEDE7B5\n\n\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\"\u003e\n\u003cp\u003eWhen running\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/twist-attack/\"\u003ea Twist Attack\u003c/a\u003e\u0026nbsp;, the “private key” can be obtained by a certain choice of the “public key” (selected point of the secp256k1 elliptic curve), that is, the value in the transaction is revealed.After that, information about the private key will also be revealed, but for this you need to perform several ECC operations.\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003eE1: y^2 = x^3 + 1\nE2: y^2 = x^3 + 2\nE3: y^2 = x^3 + 3\nE4: y^2 = x^3 + 4\nE6: y^2 = x^3 + 6\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003ca href=\"https://attacksafe.ru/twist-attack-on-bitcoin/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-4-1.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2086\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ccode\u003e\u003ca href=\"https://attacksafe.ru/twist-attack-on-bitcoin/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://attacksafe.ru/twist-attack-on-bitcoin\u003c/a\u003e\u003c/code\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003ey² = x³ + ax + b. In the Koblitz curve,\ny² = x³ + 0x + 7. In the Koblitz curve,\n0  = x³ + 0  + 7\nb '= -x ^ 3 - ax.\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eAll points\u0026nbsp;\u003ccode\u003e(x, 0)\u0026nbsp;\u003c/code\u003efall on invalid curves with\u0026nbsp;\u003ccode\u003eb '= -x ^ 3 - ax\u003c/code\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\u003eLet’s move on to the experimental part:\u003c/h2\u003e\n\n\n\n\u003cp\u003e\u003cem\u003e(Consider a Bitcoin Address)\u003c/em\u003e\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003e\u003ca href=\"https://btc1.trezor.io/address/1L7vTvRwmWENJm4g15rAxAtGcXjrFsWcBx\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e1L7vTvRwmWENJm4g15rAxAtGcXjrFsWcBx\u003c/strong\u003e\u003c/a\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\u003cp\u003e\u003cem\u003e(Now consider critical vulnerable transactions)\u003c/em\u003e\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003e\u003ca href=\"https://btc1.trezor.io/tx/60918fd82894eb94c71a9c10057ffe9d8a82074426f596dcbc759d676c886ae9\"\u003ehttps://btc1.trezor.io/tx/60918fd82894eb94c71a9c10057ffe9d8a82074426f596dcbc759d676c886ae9\u003c/a\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=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-1-1024x196.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2325\"\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\u003eOpen\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/TerminalGoogleColab\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e[TerminalGoogleColab]\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;.\u003c/p\u003e\n\n\n\n\u003cp\u003eImplementing the\u0026nbsp;\u003ca href=\"https://attacksafe.ru/twist-attack-on-bitcoin/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eTwist Attack\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;algorithm using our\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/tree/main/18TwistAttack\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e18TwistAttack repository\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003egit clone https://github.com/demining/CryptoDeepTools.git\n\ncd CryptoDeepTools/18TwistAttack/\n\nls\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-6-1024x477.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2108\"\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\u003eInstall all the packages we need\u003c/h2\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-11.png\" alt=\"Implement Frey-Rück Attack to get the secret key \u0026quot;K\u0026quot; (NONCE)\" class=\"wp-image-687\"\u003e\u003c/figure\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ccode\u003erequirements.txt\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\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003esudo apt install python2-minimal\n\nwget https://bootstrap.pypa.io/pip/2.7/get-pip.py\n\nsudo python2 get-pip.py\n\npip2 install -r requirements.txt\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-7-1024x445.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2113\"\u003e\u003c/figure\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-8-1024x440.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2115\"\u003e\u003c/figure\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-9-1024x340.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2116\"\u003e\u003c/figure\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-10-1024x452.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2117\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e,\u003c/figcaption\u003e\u003c/figure\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-11-1024x453.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2118\"\u003e\u003c/figure\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2\u003ePrepare RawTX for the attack\u003c/h2\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003e\u003ca href=\"https://btc1.trezor.io/address/1L7vTvRwmWENJm4g15rAxAtGcXjrFsWcBx\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e1L7vTvRwmWENJm4g15rAxAtGcXjrFsWcBx\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://btc1.trezor.io/tx/60918fd82894eb94c71a9c10057ffe9d8a82074426f596dcbc759d676c886ae9\"\u003ehttps://btc1.trezor.io/tx/60918fd82894eb94c71a9c10057ffe9d8a82074426f596dcbc759d676c886ae9\u003c/a\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=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-2-1024x286.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2328\"\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\u003eRawTX = 01000000013edba424d1b614ec2182c8ac6856215afb803bcb9748c1888eecd35fffad67730e0000006b483045022100bbabd1cb2097e0053b3da453b15fd195a2bc1e8dbe00cfd60aee95b404d2abfa02201af66956a7ea158d32b0a56a46a83fe27f9e544387c8d0ce13cd2a54dba9a747012102912cd095d2c20e4fbdb20a8710971dd040a067dba45899b7156e9347efc20312ffffffff01a8020000000000001976a914154813f71552c59487efa3b16d62bfb009dc5f1e88ac00000000\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003ch2\u003eSave in file: RawTX.txt\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-14-1024x227.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2369\"\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\u003c/strong\u003e\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://attacksafe.ru/software/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTo implement the attack, we will use the “ATTACKSAFE SOFTWARE”\u003c/a\u003e\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;software\u003c/strong\u003e\u003cstrong\u003e\u003ca href=\"https://attacksafe.ru/software/\" 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\u003ca href=\"https://attacksafe.ru/software/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-14.png\" alt=\"Implement Frey-Rück Attack to get the secret key \u0026quot;K\u0026quot; (NONCE)\" class=\"wp-image-705\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cstrong\u003e\u003ccode\u003ewww.attacksafe.ru/software\u003c/code\u003e\u003c/strong\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003ch2\u003eAccess rights:\u003c/h2\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003echmod +x attacksafe\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-14(1).png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2134\"\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\u003eApplication:\u003c/h2\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e./attacksafe -help\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-15.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2136\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e  -version:  software version \n  -list:     list of bitcoin attacks\n  -tool:     indicate the attack\n  -gpu:      enable gpu\n  -time:     work timeout\n  -server:   server mode\n  -port:     server port\n  -open:     open file\n  -save:     save file\n  -search:   vulnerability search\n  -stop:     stop at mode\n  -max:      maximum quantity in mode\n  -min:      minimum quantity per mode\n  -speed:    boost speed for mode\n  -range:    specific range\n  -crack:    crack mode\n  -field:    starting field\n  -point:    starting point\n  -inject:   injection regimen\n  -decode:   decoding mode\u003c/code\u003e\u003c/pre\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./attacksafe -version\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-17.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2144\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ccode\u003eVersion 5.3.2. [ATTACKSAFE SOFTWARE, © 2023]\u003c/code\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003ccode\u003e\"ATTACKSAFE SOFTWARE\"\u003c/code\u003e\u0026nbsp;includes all popular attacks on Bitcoin.\u003c/p\u003e\n\n\n\n\u003ch2\u003eLet’s run a list of all attacks:\u003c/h2\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e./attacksafe -list\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-18.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2147\"\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=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-19.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2149\"\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=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-20.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2151\"\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=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-21.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2154\"\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 choose\u003ccode\u003e\u0026nbsp;-tool: twist_attack\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eTo get specific secp256k1 points from the vulnerable ECDSA signature transaction, we added the data\u0026nbsp;\u0026nbsp;\u003ccode\u003eRawTX\u003c/code\u003e\u0026nbsp;to a text document and saved it as a file\u0026nbsp;\u003ccode\u003eRawTX.txt\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e01000000013edba424d1b614ec2182c8ac6856215afb803bcb9748c1888eecd35fffad67730e0000006b483045022100bbabd1cb2097e0053b3da453b15fd195a2bc1e8dbe00cfd60aee95b404d2abfa02201af66956a7ea158d32b0a56a46a83fe27f9e544387c8d0ce13cd2a54dba9a747012102912cd095d2c20e4fbdb20a8710971dd040a067dba45899b7156e9347efc20312ffffffff01a8020000000000001976a914154813f71552c59487efa3b16d62bfb009dc5f1e88ac00000000\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\u003eLaunch\u0026nbsp;\u0026nbsp;\u003ccode\u003e-tool twist_attack\u003c/code\u003e\u0026nbsp;using software\u0026nbsp;\u003ccode\u003e“ATTACKSAFE SOFTWARE”\u003c/code\u003e\u003c/h2\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./attacksafe -tool twist_attack -open RawTX.txt -save SecretPoints.txt\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-3-1024x304.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2330\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-4-1024x262.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2332\"\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 launched this attack from\u0026nbsp;\u0026nbsp;\u003ccode\u003e-tool twist_attack\u003c/code\u003e\u0026nbsp;and the result was saved to a file\u0026nbsp;\u003ccode\u003eSecretPoints.txt\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eNow to see the successful result, open the file\u0026nbsp;\u003ccode\u003eSecretPoints.txt\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003ecat SecretPoints.txt\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\u003eResult:\u003c/h2\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003eElliptic Curve Secret Points:\n\nQ11 = E1([97072073026593516785986136148833105674452542501015145216961054272876839453879, 107567253371779495307521678088935176637661904239924771700494716430774957820966])\nQ21 = E2([3350296768277877304391506547616361976369787138559008027651808311357100316617, 72988900267653266243491077449097157591503403928437340215197819240911749073070])\nQ22 = E2([112520741232779465095566100761481226712887911875949213866586208031790667764851, 67821409607391406974451792678186486803604797717916857589728259410989018828088])\nQ31 = E3([19221018445349571002768878066568778104356611670224206148889744255553888839368, 51911948202474460182474729837629287426170495064721963100930541018009108314113])\nQ32 = E3([41890177480111283990531243647299980511217563319657594412233172058507418746086, 50666391602993122126388747247624601309616370399604218474818855509093287774278])\nQ33 = E3([42268931450354181048145324837791859216268206183479474730830244807012122440868, 106203099208900270966718494579849900683595613889332211248945862977592813439569])\nQ41 = E4([54499795016623216633513895020095562919782606390420118477101689814601700532150, 105485166437855743326869509276555834707863666622073705127774354124823038313021])\nQ61 = E6([62124953527279820718051689027867102514830975577976669973362563656149003510557, 100989088237897158673340534473118617341737987866593944452056172771683426720481])\nQ62 = E6([86907281605062616221251901813989896824116536666883529138776205878798949076805, 19984923138198085750026187300638434023309806045826685297245727280111269894421])\nQ63 = E6([66063410534588649374156935204077330523666149907425414249132071271750455781006, 25315648259518110320341360730017389015499807179224601293064633820188666088920])\nQ64 = E6([109180854384525934106792159822888807664445139819154775748567618515646342974321, 102666617356998521143219293179463920284010473849613907153669896702897252016986])\n\n\nRawTX = 01000000013edba424d1b614ec2182c8ac6856215afb803bcb9748c1888eecd35fffad67730e0000006b483045022100bbabd1cb2097e0053b3da453b15fd195a2bc1e8dbe00cfd60aee95b404d2abfa02201af66956a7ea158d32b0a56a46a83fe27f9e544387c8d0ce13cd2a54dba9a747012102912cd095d2c20e4fbdb20a8710971dd040a067dba45899b7156e9347efc20312ffffffff01a8020000000000001976a914154813f71552c59487efa3b16d62bfb009dc5f1e88ac00000000\n\n\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003ch2\u003eNow let’s add the received secp256k1 points\u003c/h2\u003e\n\n\n\n\u003cp\u003eTo do this, open\u0026nbsp;\u003ccode\u003e\u003cem\u003ePython\u003c/em\u003e-script:\u003c/code\u003e\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/bbd83042e7405508cd2e646ad1b0819da0f9c58d/18TwistAttack/discrete.py#L51\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ediscrete.py\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-5-1024x371.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2334\"\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\u003eTo run\u0026nbsp;\u003ccode\u003e\u003cem\u003ePython\u003c/em\u003e-script:\u003c/code\u003e\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/bbd83042e7405508cd2e646ad1b0819da0f9c58d/18TwistAttack/discrete.py#L51\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ediscrete.py\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;install\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://www.sagemath.org/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSageMath\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\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-27.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2188\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-28-1024x445.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2189\"\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\u003eInstallation command:\u003c/h2\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003esudo apt-get update\nsudo apt-get install -y python3-gmpy2\nyes '' | sudo env DEBIAN_FRONTEND=noninteractive apt-get -y -o DPkg::options::=\"--force-confdef\" -o DPkg::options::=\"--force-confold\" install sagemath\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=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-31-1024x422.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2201\"\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=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-32-1024x406.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2202\"\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=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-33-1024x401.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2204\"\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\u003eCheck the installation of\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://www.sagemath.org/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSageMath\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;by command:\u0026nbsp;\u003ca href=\"https://cryptodeep.ru/twist-attack/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003esage -v\u003c/a\u003e\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\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-34.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2208\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ccode\u003eSageMath\u0026nbsp;version\u0026nbsp;9.0\u003c/code\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\u003eTo solve the discrete logarithm\u0026nbsp;\u003cem\u003e\u003ccode\u003e(Pollard's rho algorithm for logarithms)\u003c/code\u003e\u003c/em\u003erun\u0026nbsp;\u003ccode\u003ePython-script:\u003c/code\u003e\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/bbd83042e7405508cd2e646ad1b0819da0f9c58d/18TwistAttack/discrete.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ediscrete.py\u003c/a\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-35-1024x520.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2210\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003ch2\u003eRun command:\u003c/h2\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003esage -python3 discrete.py\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-7.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2339\"\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\u003eResult:\u003c/h2\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003eDiscrete_log_rho:\n\n14996641256\n1546\n19575\n31735\n9071789\n145517682\n11552\n7151\n3370711\n10797447604\n10120546250224\n\nPRIVATE KEY:\n\n3160389728152122137789469305939632411648887242506549174582525524562820572318\u003c/code\u003e\u003c/pre\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\u003eprivkey = crt([x11, x21, x22, x31, x32, x33, x41, x61, x62, x63, x64], [ord11, ord21, ord22, ord31, ord32, ord33, ord41, ord61, ord62, ord63, ord64])\n\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\"\u003e\n\u003cp\u003eWe solved the discrete logarithm and using the “\u0026nbsp;\u003cem\u003eChinese Remainder Theorem\u003c/em\u003e\u0026nbsp;\u003ccode\u003e(Chinese remainder theorem)\u003c/code\u003e\u0026nbsp;” got the private key in decimal format.\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003ch2\u003eConvert private key to HEX format\u003c/h2\u003e\n\n\n\n\u003cp\u003e\u003cem\u003eThe decimal format of the private key has been saved to a file:\u003c/em\u003e\u0026nbsp;\u003ccode\u003eprivkey.txt\u003c/code\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-8.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2342\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003ch2\u003eRun Python-script:\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/18TwistAttack/privkey2hex.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eprivkey2hex.py\u003c/a\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-38.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2230\"\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\u003epython3 privkey2hex.py\ncat privkey2hex.txt\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-9.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2344\"\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\u003eLet’s open the resulting file:\u003c/em\u003e\u0026nbsp;\u003ccode\u003eprivkey2hex.txt\u003c/code\u003e\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\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-10.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2345\"\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\u003ePrivate key in HEX format:\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003ccode\u003ePrivKey = 06fcb79a2eabffa519509e43b7de95bc2df15ca48fe6be29f9160bcd6ac1a49e\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eLet’s open\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://cryptodeep.ru/bitaddress.html\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ebitaddress\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;and check:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003eADDR: 1L7vTvRwmWENJm4g15rAxAtGcXjrFsWcBx\nWIF:  KwTHx3AhV8qiN6qyfG1D85TGEeUBiaMUjnQ11eVLP5NAfiVNLLmS\nHEX:  06FCB79A2EABFFA519509E43B7DE95BC2DF15CA48FE6BE29F9160BCD6AC1A49E\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-41-2.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2348\"\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\"\u003e\u003ciframe src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/saved_resource.html\" style=\"overflow:hidden;\" frameborder=\"0\"\u003e\u003c/iframe\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://live.blockcypher.com/btc/address/1L7vTvRwmWENJm4g15rAxAtGcXjrFsWcBx/\"\u003ehttps://live.blockcypher.com/btc/address/1L7vTvRwmWENJm4g15rAxAtGcXjrFsWcBx/\u003c/a\u003e\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\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-11-1024x521.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2350\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/image-12-1024x182.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2352\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003ccode\u003e\u003cstrong\u003eBALANCE: $ 902.52\u003c/strong\u003e\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/tree/main/18TwistAttack\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSource\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://attacksafe.ru/software\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eATTACKSAFE SOFTWARE\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://t.me/cryptodeeptech\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTelegram: https://t.me/cryptodeeptech\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://youtu.be/pOviZOYItv4\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eVideo: https://youtu.be/pOviZOYItv4\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://cryptodeeptech.ru/twist-attack-2\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSource: https://cryptodeeptech.ru/twist-attack-2\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\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./Twist Attack example - 2 continue a series of ECC operations to get the value of Private Key to the Bitcoin Wallet - CRYPTO DEEP TECH_files/034-1-1024x576.png\" alt=\"Twist Attack example #2 continue a series of ECC operations to get the value of the private key to the Bitcoin Wallet\" class=\"wp-image-2359\"\u003e\u003c/figure\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\t\u003c/div\u003e\u003c!-- .entry-content --\u003e\n\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdemining%2Ftwist-attack-2","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdemining%2Ftwist-attack-2","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdemining%2Ftwist-attack-2/lists"}