{"id":19915490,"url":"https://github.com/demining/lattice-attack-249bits","last_synced_at":"2025-09-10T12:38:02.998Z","repository":{"id":197551542,"uuid":"698872670","full_name":"demining/lattice-attack-249bits","owner":"demining","description":"LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA","archived":false,"fork":false,"pushed_at":"2023-10-01T12:57:57.000Z","size":15042,"stargazers_count":5,"open_issues_count":0,"forks_count":2,"subscribers_count":3,"default_branch":"main","last_synced_at":"2025-03-01T09:24:19.220Z","etag":null,"topics":["attack","attacker","bitcoin","cryptocurrency","cryptography","ecdsa","ecdsa-cryptography","ecdsa-signature","hack","hacking","lattice","lattice-attack"],"latest_commit_sha":null,"homepage":"https://cryptodeeptech.ru/lattice-attack-249bits","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":"2023-10-01T08:29:35.000Z","updated_at":"2024-12-07T15:29:21.000Z","dependencies_parsed_at":null,"dependency_job_id":"e899c356-deb0-4826-9b31-93a7f86bcaa5","html_url":"https://github.com/demining/lattice-attack-249bits","commit_stats":null,"previous_names":["demining/lattice-attack-249bits"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/demining/lattice-attack-249bits","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2Flattice-attack-249bits","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2Flattice-attack-249bits/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2Flattice-attack-249bits/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2Flattice-attack-249bits/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/demining","download_url":"https://codeload.github.com/demining/lattice-attack-249bits/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2Flattice-attack-249bits/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":274463425,"owners_count":25290113,"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","status":"online","status_checked_at":"2025-09-10T02:00:12.551Z","response_time":83,"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":["attack","attacker","bitcoin","cryptocurrency","cryptography","ecdsa","ecdsa-cryptography","ecdsa-signature","hack","hacking","lattice","lattice-attack"],"created_at":"2024-11-12T21:40:18.780Z","updated_at":"2025-09-10T12:38:02.959Z","avatar_url":"https://github.com/demining.png","language":"HTML","funding_links":[],"categories":[],"sub_categories":[],"readme":"\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/039-1024x576.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3344\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n---\n\n\n* Tutorial: https://youtu.be/CzaHitewN-4\n* Tutorial: https://cryptodeeptech.ru/lattice-attack-249bits\n\n\n---\n\n\u003cp\u003eIn our earliest work, we published an article on the topic\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/lattice-attack\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e“LATTICE ATTACK”\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;as a complete solution\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://cryptodeep.ru//doc/Hidden-Number-Problems.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eto the HNP [Hidden Number Problem]\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;, but with the recent emergence of a new attack\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/polynonce-attack\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e“POLYNONCE ATTACK”\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;, we decided to supplement the article using\u0026nbsp;\u003ccode\u003e79 signatures ECDSA\u003c/code\u003e.\u003c/p\u003e\n\n\n\n\u003cp\u003eBased on the previous article, where we took the polynomial\u0026nbsp;\u003ccode\u003e128 bits\u003c/code\u003eand with the actual increase in the number of signatures, we will bring the value of the polynomial to\u0026nbsp;\u003ccode\u003e249 bits\u003c/code\u003e.\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eAll we need is to solve the problem of hidden numbers.\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-285.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3357\" style=\"width:839px;height:878px\" width=\"839\" height=\"878\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eIn this article, we will analyze five independent examples of cryptanalysis of the Bitcoin blockchain.\u0026nbsp;All examples will be uploaded to the\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/tree/main/21LatticeAttack\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eGitHub\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;repository .\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\"\u003eFor a theoretical basis, we will take materials:\u003c/h2\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://attacksafe.ru/lattice-attack-on-bitcoin/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e“Lattice Attack on Bitcoin”\u003c/a\u003e\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-284.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3352\" style=\"width:841px;height:1016px\" width=\"841\" height=\"1016\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ccode\u003e\u003ca href=\"https://attacksafe.ru/lattice-attack-on-bitcoin\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://attacksafe.ru/lattice-attack-on-bitcoin\u003c/a\u003e\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\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eConsider an example with a Bitcoin Address:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://btc1.trezor.io/address/19mJofzRwwwx4VmXuAXgX6pgM3qzJqi25z\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e19mJofzRwwwx4VmXuAXgX6pgM3qzJqi25z\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-160.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3074\"\u003e\u003c/figure\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://btc1.trezor.io/tx/6a941396b28a72ac834d922165995e6685a760f884dbb9e8b6dea95b01f0aae8\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e6a941396b28a72ac834d922165995e6685a760f884dbb9e8b6dea95b01f0aae8\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-165-1024x638.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3079\"\u003e\u003c/figure\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eRawTX\u003c/h2\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-166-1024x371.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3080\"\u003e\u003c/figure\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\"hex\": 010000000afa0765dc83c2e04b53a03ad9f5e7603f974c5a70e7a486bc957e72809facab7b2d0000006a4730440220746bd0443317a77c069bddae306dc658ec740bb1a6312bdcb4ce666bae42e988022066c34dd48f0e34ae4aefd28564f46fb7473d0b49d55adb716b9f04e663d0a9890121033ee89b98b1d6e71285314e1d1c753003a7a80c17f46146a91077006c76e25e7affffffff................................\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\u003eLet’s go to the official website:\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://colab.research.google.com/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://colab.research.google.com\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003e\u003cem\u003eSelect the option\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003cstrong\u003e“Upload notebook”\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-50.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-2709\" style=\"width:832px;height:1428px\" width=\"832\" height=\"1428\"\u003e\u003c/figure\u003e\u003c/div\u003e\u003c/blockquote\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp class=\"has-text-align-center\"\u003eDownload the file:\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/LATTICE_ATTACK_249bits.ipynb\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eLATTICE_ATTACK_249bits.ipynb\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-52.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-2711\"\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\u003eDownload\u0026nbsp;\u003ccode\u003eHEX\u003c/code\u003ethe data through the utility\u0026nbsp;\u003ccode\u003ewget\u003c/code\u003e\u0026nbsp;and save it to a file:\u0026nbsp;\u003cstrong\u003eRawTX.txt\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!wget https://raw.githubusercontent.com/demining/CryptoDeepTools/main/21LatticeAttack/example1/HEX.txt\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-167-1024x279.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3081\"\u003e\u003c/figure\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\u003eLet’s run the code and get the bits we need\u003ccode\u003e\u003cstrong\u003eRawTX\u003c/strong\u003e\u003c/code\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003ewith open(\"HEX.txt\") as myfile:\n\n    listfile=\"\\n\".join(f'{line.rstrip()[:+298]}' for line in myfile)\n\n\nf = open(\"RawTX.txt\", 'w')\nf.write(\"\" + listfile + \"\" + \"\\n\")\nf.close()\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-169-1024x346.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3083\"\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\u003cstrong\u003eTo implement the attack, we will use the software\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp class=\"has-text-align-center\"\u003e\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://attacksafe.ru/software/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e“ATTACKSAFE SOFTWARE”\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - 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 class=\"wp-block-heading\"\u003eAccess rights:\u003c/h2\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!chmod +x attacksafe\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\u003els\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-172.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3089\"\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\"\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-173.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3091\"\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-174.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3093\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003eVersion 5.3.4. [ATTACKSAFE SOFTWARE, © 2023]\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003e\u003ccode\u003e\"ATTACKSAFE SOFTWARE\"\u003c/code\u003e\u0026nbsp;includes all popular attacks on Bitcoin.\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-175.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3097\"\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: lattice_attack\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eTo get a specific\u0026nbsp;\u003ccode\u003eHEX\u003c/code\u003evalue\u0026nbsp;\u003ccode\u003eR,S,Z\u003c/code\u003efor the signature\u0026nbsp;\u003ccode\u003eECDSA\u003c/code\u003e, we previously added data\u0026nbsp;\u0026nbsp;\u003ccode\u003eRawTX\u003c/code\u003e\u0026nbsp;through the utility\u0026nbsp;\u003ccode\u003eecho\u003c/code\u003eto a text document and saved it as a file\u0026nbsp;\u003ccode\u003eRawTX.txt\u003c/code\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-176-1024x140.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3101\"\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\"\u003eLaunch\u0026nbsp;\u0026nbsp;\u003ccode\u003e-tool lattice_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 lattice_attack -open RawTX.txt -save SignatureRSZ.csv\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-179-1024x462.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3104\"\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 lattice_attack\u003c/code\u003e\u0026nbsp;and the result was saved to a file\u0026nbsp;\u003ccode\u003eSignatureRSZ.csv\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eNow to see the successful result, open the file\u0026nbsp;\u003ccode\u003eSignatureRSZ.csv\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-181-1024x445.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3108\"\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\u003eIn order to calculate the private key to a Bitcoin Wallet from a file,\u0026nbsp;\u0026nbsp;\u003ccode\u003eSignatureRSZ.csv\u003c/code\u003ewe will install\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://cryptodeeptech.ru/install-sagemath-in-google-colab/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSageMath\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-27.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-2188\" style=\"width:835px;height:237px\" width=\"835\" height=\"237\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-28-1024x445.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" 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\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eEarlier we published\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/install-sagemath-in-google-colab/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ean article\u003c/a\u003e\u0026nbsp;, download\u0026nbsp;\u0026nbsp;\u003ccode\u003etar-file\u003c/code\u003e:\u0026nbsp;\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/sage-9.3-Ubuntu_20.04-x86_64.tar.bz2\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003esage-9.3-Ubuntu_20.04-x86_64.tar.bz2\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\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!wget https://cryptodeeptech.ru/sage-9.3-Ubuntu_20.04-x86_64.tar.bz2\n!tar -xf sage-9.3-Ubuntu_20.04-x86_64.tar.bz2\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-184-1024x330.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3114\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eLet’s go through the directory:\u003c/em\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003ecd SageMath/\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\u003els\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-186-1024x594.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3118\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eRun\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003cstrong\u003erelocate-once.py\u0026nbsp;\u003c/strong\u003e\u003cem\u003e\u0026nbsp;with the command:\u003c/em\u003e\u003ccode\u003ePython-script:\u003c/code\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003cstrong\u003e\u003c/strong\u003e\u003cem\u003e\u003c/em\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!python3 relocate-once.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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-187-1024x461.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3119\"\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\"\u003e\n\u003cp\u003eMove\u0026nbsp;\u003ccode\u003e\"AttackSafe\"\u003c/code\u003eto\u0026nbsp;\u003ccode\u003e\"SignatureRSZ.csv\"\u003c/code\u003efolder\u003ccode\u003e\"SageMath\"\u003c/code\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!mv '/content/attacksafe' '/content/SageMath/attacksafe'\n!mv '/content/SignatureRSZ.csv' '/content/SageMath/SignatureRSZ.csv'\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-190-1024x717.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3124\"\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\u003els\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-191-1024x386.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3125\"\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\"\u003e\n\u003cp\u003eDownload the script\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/crack_weak_ECDSA_nonces_with_LLL.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ecrack_weak_ECDSA_nonces_with_LLL.py\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;from Dario Clavijo through the utility\u0026nbsp;\u003ccode\u003ewget\u003c/code\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!wget https://raw.githubusercontent.com/demining/CryptoDeepTools/main/21LatticeAttack/crack_weak_ECDSA_nonces_with_LLL.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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-193-1024x359.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3130\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eNow let’s run\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003eSageMath\u003c/code\u003e\u003cem\u003e\u0026nbsp;the command:\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\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!./sage -sh\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-194-1024x389.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3132\"\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\"\u003e\n\u003cp\u003eTo calculate the private key to the Bitcoin Wallet, run the script\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/crack_weak_ECDSA_nonces_with_LLL.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ecrack_weak_ECDSA_nonces_with_LLL.py\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;specifying the parameters\u003cstrong\u003e\u003ccode\u003e249 bits 79 sign\u003c/code\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003epython3 crack_weak_ECDSA_nonces_with_LLL.py SignatureRSZ.csv 249 79 \u0026gt; PrivateKey.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\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003ecat PrivateKey.txt\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-195-1024x532.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3136\"\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\"\u003e\n\u003cp\u003eLet’s open the file:\u003ccode\u003ePrivateKey.txt\u003c/code\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003cem\u003eWe received the private key to the Bitcoin Wallet in\u0026nbsp;\u003ccode\u003eHEX\u003c/code\u003ethe format\u003c/em\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-197.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3139\" style=\"width:843px;height:934px\" width=\"843\" height=\"934\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e\u003cstrong\u003ePrivKey = 0x9a52a4dbcc148f1480a6fb5311252524fc498eb508c7cb8f63bbee4b9af37941\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\"\u003eCheck POLYNONCE for each ECDSA signature\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eTo do this, use the code from\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example1/POLYNONCE.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eGITHUB\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-200.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3142\" style=\"width:838px;height:1148px\" width=\"838\" height=\"1148\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example1/POLYNONCE.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003ccode\u003ehttps://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example1/POLYNONCE.py\u003c/code\u003e\u003c/a\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eResult:\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-201.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3143\" style=\"width:834px;height:1041px\" width=\"834\" height=\"1041\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eWe got 79 identical original bits from\u003ccode\u003e249\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\u003cp\u003eThanks to the value on the secp256k1 curve from\u0026nbsp;\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Hal_Finney_(computer_scientist)\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eHal Finney,\u0026nbsp;\u003c/a\u003e\u0026nbsp;\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/endomorphism/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eLAMBDA and BETA\u003c/a\u003e\u0026nbsp;revealed the same initial bits to us.\u0026nbsp;The value\u0026nbsp;\u003ccode\u003ePOLYNONCE\u003c/code\u003ein the format\u0026nbsp;\u003ccode\u003eHEX\u003c/code\u003eallows us to fully solve the problem of hidden numbers, get a private key and restore a Bitcoin Wallet.\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 check the HEX of the private key:\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eInstall the module\u003ccode\u003ebitcoin\u003c/code\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!pip3 install bitcoin\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-86-1024x219.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-2799\"\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\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s run the code:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003efrom bitcoin import *\n\nwith open(\"PrivateKey.txt\",\"r\") as f:\n    content = f.readlines()\n\ncontent = [x.strip() for x in content]\nf.close()\n\n\noutfile = open(\"PrivateKeyAddr.txt\",\"w\")\nfor x in content:\n  outfile.write(x+\":\"+pubtoaddr(encode_pubkey(privtopub(x), \"bin_compressed\"))+\"\\n\")\n \noutfile.close()\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-87.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-2800\"\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\"\u003e\n\u003cp\u003eLet’s open the file:\u003ccode\u003ePrivateKeyAddr.txt\u003c/code\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-202-1024x651.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3144\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ccode\u003e9a52a4dbcc148f1480a6fb5311252524fc498eb508c7cb8f63bbee4b9af37941:19mJofzRwwwx4VmXuAXgX6pgM3qzJqi25z\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\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: 19mJofzRwwwx4VmXuAXgX6pgM3qzJqi25z\nWIF:  L2PhDrYZw6fWqeLZMnMeAXvxZ47MEnepaQVLL2EazbRhqesytoQB\nHEX:  9a52a4dbcc148f1480a6fb5311252524fc498eb508c7cb8f63bbee4b9af37941\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-bitaddress-4.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3147\"\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://www.blockchain.com/en/explorer/addresses/btc/19mJofzRwwwx4VmXuAXgX6pgM3qzJqi25z\"\u003ehttps://www.blockchain.com/en/explorer/addresses/btc/19mJofzRwwwx4VmXuAXgX6pgM3qzJqi25z\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 is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-205.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3153\" style=\"width:830px;height:237px\" width=\"830\" height=\"237\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-206.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3154\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-207-1024x136.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3155\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp class=\"has-large-font-size\"\u003e\u003ccode\u003e\u003cstrong\u003eBALANCE: $ 1015.58\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\u003ch2 class=\"wp-block-heading\"\u003eLet’s look at other examples:\u003c/h2\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp class=\"has-text-align-center has-large-font-size\"\u003e\u003ccode\u003e№\u003cstrong\u003e2\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\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eConsider example #2 with a Bitcoin Address:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://btc1.trezor.io/address/1GPZVDUyPM6qxCsJQrpJeo14WDRVLvTZ2Z\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e1GPZVDUyPM6qxCsJQrpJeo14WDRVLvTZ2Z\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-82.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-2788\"\u003e\u003c/figure\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://btc1.trezor.io/tx/9130c5b8e92f37d3a58dcae16daa27625cc52b698a83af7c8b891f01bfa0b2af\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e9130c5b8e92f37d3a58dcae16daa27625cc52b698a83af7c8b891f01bfa0b2af\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-208.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3159\"\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\"\u003eRawTX\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-209-1024x379.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3160\"\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\"hex\": 0100000041e981df9d37a7af6f5ee77abade3ec58acbf864f942bdecb63ea2efa593e2c3391f0000006b4830450221009d8ceef05e2fa0a623811df57265a3678f902e81dc82c3862d12bbb07b90de18022036bbed961b4f8665eb3fb3047a1398a1aeae519a8e2a1a97de57863fc0cc4a380121029755a17bf76237cde9e05fc333a255b926d526a7763abe725a4f6253ebdae109ffffffff..............................\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\u003eLet’s remove the files from the first example:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!rm HEX.txt\n!rm RawTX.txt\n!rm NoncesHEX.txt\n!rm PrivateKey.txt\n!rm SignatureRSZ.csv\n!rm PrivateKeyAddr.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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-210.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3162\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eDownload\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003eHEX\u003c/code\u003e\u003cem\u003ethe data through the utility\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003ewget\u003c/code\u003e\u003cem\u003e\u0026nbsp;and save it to a file:\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003cstrong\u003eRawTX.txt\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!wget https://raw.githubusercontent.com/demining/CryptoDeepTools/main/21LatticeAttack/example2/HEX.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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-211.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3167\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eLet’s run the code and get the bits we need\u0026nbsp;\u003c/em\u003e\u003ccode\u003e\u003cstrong\u003eRawTX\u003c/strong\u003e\u003c/code\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003ewith open(\"HEX.txt\") as myfile:\n\n    listfile=\"\\n\".join(f'{line.rstrip()[:+298]}' for line in myfile)\n\n\nf = open(\"RawTX.txt\", 'w')\nf.write(\"\" + listfile + \"\" + \"\\n\")\nf.close()\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-212-1024x376.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3175\"\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\"\u003eLaunch\u0026nbsp;\u0026nbsp;\u003ccode\u003e-tool lattice_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 lattice_attack -open RawTX.txt -save SignatureRSZ.csv\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-213-1024x458.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3178\"\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 lattice_attack\u003c/code\u003e\u0026nbsp;and the result was saved to a file\u0026nbsp;\u003ccode\u003eSignatureRSZ.csv\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eNow to see the successful result, open the file\u0026nbsp;\u003ccode\u003eSignatureRSZ.csv\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-214.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3180\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eLet’s run\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003eSageMath\u003c/code\u003e\u003cem\u003e\u0026nbsp;the command:\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\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!./sage -sh\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-215.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3182\"\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\"\u003e\n\u003cp\u003eTo calculate the private key to the Bitcoin Wallet, run the script\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/crack_weak_ECDSA_nonces_with_LLL.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ecrack_weak_ECDSA_nonces_with_LLL.py\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;specifying the parameters\u0026nbsp;\u003cstrong\u003e\u003ccode\u003e249 bits 79 sign\u003c/code\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003epython3 crack_weak_ECDSA_nonces_with_LLL.py SignatureRSZ.csv 249 79 \u0026gt; PrivateKey.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\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003ecat PrivateKey.txt\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-216-1024x509.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3185\"\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\"\u003e\n\u003cp\u003eLet’s open the file:\u0026nbsp;\u003ccode\u003ePrivateKey.txt\u003c/code\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003cem\u003eWe received the private key to the Bitcoin Wallet in\u0026nbsp;\u0026nbsp;\u003ccode\u003eHEX\u003c/code\u003e\u0026nbsp;the format\u003c/em\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-222.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3196\" style=\"width:838px;height:853px\" width=\"838\" height=\"853\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e\u003cstrong\u003ePrivKey = 0x00db251a1ab7cfa7679dfe61271d0af4bb9c68595178cf4c9237478eab2dba1d\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\"\u003eCheck POLYNONCE for each ECDSA signature\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eTo do this, use the code from\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example2/POLYNONCE.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eGITHUB\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-218.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3190\" style=\"width:842px;height:1155px\" width=\"842\" height=\"1155\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ccode\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example2/POLYNONCE.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example2/POLYNONCE.py\u003c/a\u003e\u003c/code\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eResult:\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-219.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3192\" style=\"width:844px;height:1245px\" width=\"844\" height=\"1245\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003e\u003cem\u003eWe got 79 identical original bits from\u003c/em\u003e\u003ccode\u003e249\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\u003cp\u003eThanks to the value on the secp256k1 curve from\u0026nbsp;\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Hal_Finney_(computer_scientist)\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eHal Finney,\u0026nbsp;\u003c/a\u003e\u0026nbsp;\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/endomorphism/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eLAMBDA and BETA\u003c/a\u003e\u0026nbsp;revealed the same initial bits to us.\u0026nbsp;The value\u0026nbsp;\u003ccode\u003ePOLYNONCE\u003c/code\u003ein the format\u0026nbsp;\u003ccode\u003eHEX\u003c/code\u003eallows us to fully solve the problem of hidden numbers, get a private key and restore a Bitcoin Wallet.\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 check the HEX of the private key:\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s run the code:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003efrom bitcoin import *\n\nwith open(\"PrivateKey.txt\",\"r\") as f:\n    content = f.readlines()\n\ncontent = [x.strip() for x in content]\nf.close()\n\n\noutfile = open(\"PrivateKeyAddr.txt\",\"w\")\nfor x in content:\n  outfile.write(x+\":\"+pubtoaddr(encode_pubkey(privtopub(x), \"bin_compressed\"))+\"\\n\")\n \noutfile.close()\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-220-1024x533.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3193\"\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\"\u003e\n\u003cp\u003eLet’s open the file:\u0026nbsp;\u003ccode\u003ePrivateKeyAddr.txt\u003c/code\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-221-1024x657.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3194\"\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 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: 1GPZVDUyPM6qxCsJQrpJeo14WDRVLvTZ2Z\nWIF:  KwFNhRPDpgD5X77T8x5oL628aHh9UtscwwrLjGBKE8NeLshYvAqC\nHEX:  00db251a1ab7cfa7679dfe61271d0af4bb9c68595178cf4c9237478eab2dba1d\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-bitaddress-6.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3202\"\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://www.blockchain.com/en/explorer/addresses/btc/1GPZVDUyPM6qxCsJQrpJeo14WDRVLvTZ2Z\"\u003ehttps://www.blockchain.com/en/explorer/addresses/btc/1GPZVDUyPM6qxCsJQrpJeo14WDRVLvTZ2Z\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 is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-224.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3204\" style=\"width:842px;height:271px\" width=\"842\" height=\"271\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-225.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3205\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-226-1024x149.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3206\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp class=\"has-large-font-size\"\u003e\u003ccode\u003e\u003cstrong\u003eBALANCE: $ 999.10\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\u003ch2 class=\"wp-block-heading\"\u003eLet’s look at other examples:\u003c/h2\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp class=\"has-text-align-center has-large-font-size\"\u003e\u003ccode\u003e№\u003cstrong\u003e3\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\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eConsider example #3 with a Bitcoin Address:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://btc1.trezor.io/address/18Y9nUpdtxAKTh6yaN299jfUxcpJ2ApHz\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e18Y9nUpdtxAKTh6yaN299jfUxcpJ2ApHz\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-227.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3209\"\u003e\u003c/figure\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://btc1.trezor.io/tx/0b21368bb6e6658adf4079b5ca6e7286c6e13471acef879168e7c17809476c76\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e0b21368bb6e6658adf4079b5ca6e7286c6e13471acef879168e7c17809476c76\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-228.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3210\"\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\"\u003eRawTX\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-229-1024x378.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3211\"\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\"hex\": 0100000041c7a8d97168ee154550f5e43b9074e5f357a4dc6b2350c96f75e377df0a39b9fa210000006b48304502210097d6b896929d77634b8d9430bc2842209cad42bb236c408e18470b9fd86b3d6a0220684ac14228c4adaa9df819e7fc8e82cf3c4242b74e27f5dd190d63231e8a058a012102990a280aef14e545b9b076b6548a4e886476d967e447bb69efcf0b725efda04effffffff..............................\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\u003eLet’s remove the files from the second example:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!rm HEX.txt\n!rm RawTX.txt\n!rm NoncesHEX.txt\n!rm PrivateKey.txt\n!rm SignatureRSZ.csv\n!rm PrivateKeyAddr.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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-231.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3219\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eDownload\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003eHEX\u003c/code\u003e\u003cem\u003e the data through the utility\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003ewget\u003c/code\u003e\u003cem\u003e\u0026nbsp;and save it to a file:\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003cstrong\u003eRawTX.txt\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!wget https://raw.githubusercontent.com/demining/CryptoDeepTools/main/21LatticeAttack/example3/HEX.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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-232-1024x418.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3221\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eLet’s run the code and get the bits we need\u0026nbsp;\u003c/em\u003e\u003ccode\u003e\u003cstrong\u003eRawTX\u003c/strong\u003e\u003c/code\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003ewith open(\"HEX.txt\") as myfile:\n\n    listfile=\"\\n\".join(f'{line.rstrip()[:+298]}' for line in myfile)\n\n\nf = open(\"RawTX.txt\", 'w')\nf.write(\"\" + listfile + \"\" + \"\\n\")\nf.close()\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-233.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3225\"\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\"\u003eLaunch\u0026nbsp;\u0026nbsp;\u003ccode\u003e-tool lattice_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 lattice_attack -open RawTX.txt -save SignatureRSZ.csv\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-234.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3226\"\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 lattice_attack\u003c/code\u003e\u0026nbsp;and the result was saved to a file\u0026nbsp;\u003ccode\u003eSignatureRSZ.csv\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eNow to see the successful result, open the file\u0026nbsp;\u003ccode\u003eSignatureRSZ.csv\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-235.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3227\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eLet’s run\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003eSageMath\u003c/code\u003e\u003cem\u003e\u0026nbsp;the command:\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\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!./sage -sh\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-236-1024x451.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3228\"\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\"\u003e\n\u003cp\u003eTo calculate the private key to the Bitcoin Wallet, run the script\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/crack_weak_ECDSA_nonces_with_LLL.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ecrack_weak_ECDSA_nonces_with_LLL.py\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;specifying the parameters\u0026nbsp;\u003cstrong\u003e\u003ccode\u003e249 bits 79 sign\u003c/code\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003epython3 crack_weak_ECDSA_nonces_with_LLL.py SignatureRSZ.csv 249 79 \u0026gt; PrivateKey.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\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003ecat PrivateKey.txt\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-237.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3231\"\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\"\u003e\n\u003cp\u003eLet’s open the file:\u0026nbsp;\u003ccode\u003ePrivateKey.txt\u003c/code\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003cem\u003eWe received the private key to the Bitcoin Wallet in\u0026nbsp;\u0026nbsp;\u003ccode\u003eHEX\u003c/code\u003e\u0026nbsp;the format\u003c/em\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-238.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3234\" style=\"width:838px;height:961px\" width=\"838\" height=\"961\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e\u003cstrong\u003ePrivKey = 0x80e3052532356bc701189818c095fb8a7f035fd7a5a96777df4162205e945aa5\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\"\u003eCheck POLYNONCE for each ECDSA signature\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eTo do this, use the code from\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example3/POLYNONCE.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eGITHUB\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-239.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3235\" style=\"width:840px;height:1178px\" width=\"840\" height=\"1178\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ccode\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example3/POLYNONCE.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example3/POLYNONCE.py\u003c/a\u003e\u003c/code\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eResult:\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-240.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3236\" style=\"width:840px;height:1376px\" width=\"840\" height=\"1376\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003e\u003cem\u003eWe got 79 identical original bits from\u003c/em\u003e\u003ccode\u003e249\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\u003cp\u003eThanks to the value on the secp256k1 curve from\u0026nbsp;\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Hal_Finney_(computer_scientist)\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eHal Finney,\u0026nbsp;\u003c/a\u003e\u0026nbsp;\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/endomorphism/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eLAMBDA and BETA\u003c/a\u003e\u0026nbsp;revealed the same initial bits to us.\u0026nbsp;The value\u0026nbsp;\u003ccode\u003ePOLYNONCE\u003c/code\u003ein the format\u0026nbsp;\u003ccode\u003eHEX\u003c/code\u003eallows us to fully solve the problem of hidden numbers, get a private key and restore a Bitcoin Wallet.\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 check the HEX of the private key:\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s run the code:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003efrom bitcoin import *\n\nwith open(\"PrivateKey.txt\",\"r\") as f:\n    content = f.readlines()\n\ncontent = [x.strip() for x in content]\nf.close()\n\n\noutfile = open(\"PrivateKeyAddr.txt\",\"w\")\nfor x in content:\n  outfile.write(x+\":\"+pubtoaddr(encode_pubkey(privtopub(x), \"bin_compressed\"))+\"\\n\")\n \noutfile.close()\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-103-1024x451.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-2848\"\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\"\u003e\n\u003cp\u003eLet’s open the file:\u0026nbsp;\u003ccode\u003ePrivateKeyAddr.txt\u003c/code\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-241.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3237\"\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 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: 18Y9nUpdtxAKTh6yaN299jfUxcpJ2ApHz\nWIF:  L1YFTAP2X6jhi9W6ZVy2xX8H89TYwZcgSKcPLX7NmAx3n8PjqDkU\nHEX:  80e3052532356bc701189818c095fb8a7f035fd7a5a96777df4162205e945aa5\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-bitaddress-7.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3242\"\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://www.blockchain.com/en/explorer/addresses/btc/18Y9nUpdtxAKTh6yaN299jfUxcpJ2ApHz\"\u003ehttps://www.blockchain.com/en/explorer/addresses/btc/18Y9nUpdtxAKTh6yaN299jfUxcpJ2ApHz\u003c/a\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 is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-243.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3246\" style=\"width:840px;height:248px\" width=\"840\" height=\"248\"\u003e\u003c/figure\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-244.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3247\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-245-1024x146.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3248\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp class=\"has-large-font-size\"\u003e\u003ccode\u003e\u003cstrong\u003eBALANCE: $ 1023.25\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 class=\"has-text-align-center has-large-font-size\"\u003e\u003cstrong\u003e\u003ccode\u003e№4\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\"\u003e\n\u003cp\u003eConsider example #4 with a Bitcoin Address:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://btc1.trezor.io/address/12fqNTJc1wj2xfNscYHAzehD6f6sRjWBor\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e12fqNTJc1wj2xfNscYHAzehD6f6sRjWBor\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-246.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3253\"\u003e\u003c/figure\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://btc1.trezor.io/tx/6e6d84bc92cd79fba2d1eee5fb47e393896d44f666a50d4948a022751e3f0989\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e6e6d84bc92cd79fba2d1eee5fb47e393896d44f666a50d4948a022751e3f0989\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-247.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3254\"\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\"\u003eRawTX\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-248-1024x371.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3255\"\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\"hex\": 01000000418ff67c7d3309211ab9d9629d97bbac7730d3cbb419df4ec43d2c5fc4f81bbefb1b0000006b4830450221008c223861acf1f265547eddb04a7cf98d206643a05824e56e97c70beddd18eaf20220139a34bf077a1fdb15e716d765955203e746616dfe8bf536b86d259b5c8a09b8012103c50b5619a40a23ff6a5510238405b8efd3f8f1bc442e1a415b25078b4cbd88e3ffffffff..............................\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\u003eLet’s remove the files from the second example:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!rm HEX.txt\n!rm RawTX.txt\n!rm NoncesHEX.txt\n!rm PrivateKey.txt\n!rm SignatureRSZ.csv\n!rm PrivateKeyAddr.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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-249.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3258\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eDownload\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003eHEX\u003c/code\u003e\u003cem\u003e-data through the utility\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003eecho\u003c/code\u003e\u003cem\u003e\u0026nbsp;and save to file:\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003cstrong\u003eRawTX.txt\u0026nbsp;\u003c/strong\u003e\u003cem\u003eDownload\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003eHEX\u003c/code\u003e\u003cem\u003e-data through the utility\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003ewget\u003c/code\u003e\u003cem\u003e\u0026nbsp;and save to file:\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003cstrong\u003eRawTX.txt\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!wget https://raw.githubusercontent.com/demining/CryptoDeepTools/main/21LatticeAttack/example4/HEX.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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-250.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3260\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eLet’s run the code and get the bits we need\u0026nbsp;\u003c/em\u003e\u003ccode\u003e\u003cstrong\u003eRawTX\u003c/strong\u003e\u003c/code\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003ewith open(\"HEX.txt\") as myfile:\n\n    listfile=\"\\n\".join(f'{line.rstrip()[:+298]}' for line in myfile)\n\n\nf = open(\"RawTX.txt\", 'w')\nf.write(\"\" + listfile + \"\" + \"\\n\")\nf.close()\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-251.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3262\"\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\"\u003eLaunch\u0026nbsp;\u0026nbsp;\u003ccode\u003e-tool lattice_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 lattice_attack -open RawTX.txt -save SignatureRSZ.csv\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-252-1024x451.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3263\"\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 lattice_attack\u003c/code\u003e\u0026nbsp;and the result was saved to a file\u0026nbsp;\u003ccode\u003eSignatureRSZ.csv\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eNow to see the successful result, open the file\u0026nbsp;\u003ccode\u003eSignatureRSZ.csv\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-253-1024x444.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3265\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eLet’s run\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003eSageMath\u003c/code\u003e\u003cem\u003e\u0026nbsp;the command:\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\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!./sage -sh\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-254.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3267\"\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\"\u003e\n\u003cp\u003eTo calculate the private key to the Bitcoin Wallet, run the script\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/crack_weak_ECDSA_nonces_with_LLL.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ecrack_weak_ECDSA_nonces_with_LLL.py\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;specifying the parameters\u0026nbsp;\u003cstrong\u003e\u003ccode\u003e249 bits 79 sign\u003c/code\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003epython3 crack_weak_ECDSA_nonces_with_LLL.py SignatureRSZ.csv 249 79 \u0026gt; PrivateKey.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\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003ecat PrivateKey.txt\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-255-1024x531.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3268\"\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\"\u003e\n\u003cp\u003eLet’s open the file:\u0026nbsp;\u003ccode\u003ePrivateKey.txt\u003c/code\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003cem\u003eWe received the private key to the Bitcoin Wallet in\u0026nbsp;\u0026nbsp;\u003ccode\u003eHEX\u003c/code\u003e\u0026nbsp;the format\u003c/em\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-256.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3269\" style=\"width:841px;height:979px\" width=\"841\" height=\"979\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e\u003cstrong\u003ePrivKey = 0x9e636a4ef1a63c4bd385b8d26d29f6394a29963f12109dbf34fef74377866a32\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\"\u003eCheck POLYNONCE for each ECDSA signature\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eTo do this, use the code from\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example4/POLYNONCE.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eGITHUB\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-257.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3272\" style=\"width:841px;height:1190px\" width=\"841\" height=\"1190\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example4/POLYNONCE.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003ccode\u003ehttps://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example4/POLYNONCE.py\u003c/code\u003e\u003c/a\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eResult:\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-258.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3278\" style=\"width:841px;height:1399px\" width=\"841\" height=\"1399\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003e\u003cem\u003eWe got 79 identical original bits from\u003c/em\u003e\u003ccode\u003e249\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\u003cp\u003eThanks to the value on the secp256k1 curve from\u0026nbsp;\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Hal_Finney_(computer_scientist)\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eHal Finney,\u0026nbsp;\u003c/a\u003e\u0026nbsp;\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/endomorphism/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eLAMBDA and BETA\u003c/a\u003e\u0026nbsp;revealed the same initial bits to us.\u0026nbsp;The value\u0026nbsp;\u003ccode\u003ePOLYNONCE\u003c/code\u003ein the format\u0026nbsp;\u003ccode\u003eHEX\u003c/code\u003eallows us to fully solve the problem of hidden numbers, get a private key and restore a Bitcoin Wallet.\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 check the HEX of the private key:\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s run the code:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003efrom bitcoin import *\n\nwith open(\"PrivateKey.txt\",\"r\") as f:\n    content = f.readlines()\n\ncontent = [x.strip() for x in content]\nf.close()\n\n\noutfile = open(\"PrivateKeyAddr.txt\",\"w\")\nfor x in content:\n  outfile.write(x+\":\"+pubtoaddr(encode_pubkey(privtopub(x), \"bin_compressed\"))+\"\\n\")\n \noutfile.close()\u003c/code\u003e\u003c/pre\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-259-1024x385.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3281\"\u003e\u003c/figure\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\u003eLet’s open the file:\u0026nbsp;\u003ccode\u003ePrivateKeyAddr.txt\u003c/code\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-260.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3283\"\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 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: 12fqNTJc1wj2xfNscYHAzehD6f6sRjWBor\nWIF:  L2Xbaxg8QFoLn5URp7GKMyLwEN9dV5TtgpdbXYo7WDJsHZLcT898\nHEX:  9e636a4ef1a63c4bd385b8d26d29f6394a29963f12109dbf34fef74377866a32\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-bitaddress-8.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3286\"\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://www.blockchain.com/en/explorer/addresses/btc/12fqNTJc1wj2xfNscYHAzehD6f6sRjWBor\"\u003ehttps://www.blockchain.com/en/explorer/addresses/btc/12fqNTJc1wj2xfNscYHAzehD6f6sRjWBor\u003c/a\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 is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-262.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3290\" style=\"width:841px;height:253px\" width=\"841\" height=\"253\"\u003e\u003c/figure\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-263.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3291\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-264-1024x141.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3292\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp class=\"has-large-font-size\"\u003e\u003ccode\u003e\u003cstrong\u003eBALANCE: $ 406.03\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\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003cstrong\u003e\u003ccode\u003e№5\u003c/code\u003e\u003c/strong\u003e\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\u003eConsider example #5 with a Bitcoin Address:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://btc1.trezor.io/address/1L8v5aUZRzYbGKWcj9Yt6mGdd95Sy9bXjN\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e1L8v5aUZRzYbGKWcj9Yt6mGdd95Sy9bXjN\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-265.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3297\"\u003e\u003c/figure\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://btc1.trezor.io/tx/8a00ad0cc10d768d6d2b407f99879e556e5fc2917b619cb9a551675b7682a791\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e8a00ad0cc10d768d6d2b407f99879e556e5fc2917b619cb9a551675b7682a791\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-266.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3298\"\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\"\u003eRawTX\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-267-1024x378.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3300\"\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\n\"hex\": \"01000000fdf4014f7e4a72ecb9a3ed21a82a42b3127da87bdfee7c10779688dd8a38977cb80ece000000006a4730440220423f7cffadd494fb0148d509e67598b3c8d7f54695ee3830184adc2af234d5cf022005ebe83773bc81c7131fd0580350a998adde20fee6fd2d1da40a0191fea8242c0121027a2250a80a31965e928afff97d1c713e7ce70e6eb7c7491404a79991bfc6b5c1ffffffff...........................\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\u003eLet’s remove the files from the second example:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!rm HEX.txt\n!rm RawTX.txt\n!rm NoncesHEX.txt\n!rm PrivateKey.txt\n!rm SignatureRSZ.csv\n!rm PrivateKeyAddr.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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-268.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3302\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eDownload\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003eHEX\u003c/code\u003e\u003cem\u003ethe data through the utility\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003ewget\u003c/code\u003e\u003cem\u003e\u0026nbsp;and save it to a file:\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003cstrong\u003eRawTX.txt\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!wget https://raw.githubusercontent.com/demining/CryptoDeepTools/main/21LatticeAttack/example5/HEX.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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-269-1024x461.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3304\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eLet’s run the code and get the bits we need\u0026nbsp;\u003c/em\u003e\u003ccode\u003e\u003cstrong\u003eRawTX\u003c/strong\u003e\u003c/code\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003ewith open(\"HEX.txt\") as myfile:\n\n    listfile=\"\\n\".join(f'{line.rstrip()[:+298]}' for line in myfile)\n\n\nf = open(\"RawTX.txt\", 'w')\nf.write(\"\" + listfile + \"\" + \"\\n\")\nf.close()\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-270-1024x511.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3308\"\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\"\u003eLaunch\u0026nbsp;\u0026nbsp;\u003ccode\u003e-tool lattice_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 lattice_attack -open RawTX.txt -save SignatureRSZ.csv\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-271-1024x446.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3309\"\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 lattice_attack\u003c/code\u003e\u0026nbsp;and the result was saved to a file\u0026nbsp;\u003ccode\u003eSignatureRSZ.csv\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eNow to see the successful result, open the file\u0026nbsp;\u003ccode\u003eSignatureRSZ.csv\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-272.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3310\"\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\"\u003e\n\u003cp\u003e\u003cem\u003eLet’s run\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ccode\u003eSageMath\u003c/code\u003e\u003cem\u003e\u0026nbsp;the command:\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\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e!./sage -sh\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-273-1024x495.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3311\"\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\"\u003e\n\u003cp\u003eTo calculate the private key to the Bitcoin Wallet, run the script\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/crack_weak_ECDSA_nonces_with_LLL.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ecrack_weak_ECDSA_nonces_with_LLL.py\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;specifying the parameters\u0026nbsp;\u003cstrong\u003e\u003ccode\u003e249 bits 79 sign\u003c/code\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003epython3 crack_weak_ECDSA_nonces_with_LLL.py SignatureRSZ.csv 249 79 \u0026gt; PrivateKey.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\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003ecat PrivateKey.txt\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-274.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3312\"\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\"\u003e\n\u003cp\u003eLet’s open the file:\u0026nbsp;\u003ccode\u003ePrivateKey.txt\u003c/code\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003cem\u003eWe received the private key to the Bitcoin Wallet in\u0026nbsp;\u0026nbsp;\u003ccode\u003eHEX\u003c/code\u003e\u0026nbsp;the format\u003c/em\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-275.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3314\" style=\"width:840px;height:982px\" width=\"840\" height=\"982\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003e\u003cstrong\u003ePrivKey = 0xe2eadbde2e6a2adb6f81864cdf574dd44959717fe095486e2c0e55585594edf2\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\"\u003eCheck POLYNONCE for each ECDSA signature\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eTo do this, use the code from\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example5/POLYNONCE.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eGITHUB\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-276.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3318\" style=\"width:843px;height:1211px\" width=\"843\" height=\"1211\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ccode\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example5/POLYNONCE.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://github.com/demining/CryptoDeepTools/blob/main/21LatticeAttack/example5/POLYNONCE.py\u003c/a\u003e\u003c/code\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eResult:\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-277.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3319\" style=\"width:838px;height:1336px\" width=\"838\" height=\"1336\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003eWe got 79 identical original bits from\u003ccode\u003e249\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\u003cp\u003eThanks to the value on the secp256k1 curve from\u0026nbsp;\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Hal_Finney_(computer_scientist)\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eHal Finney,\u0026nbsp;\u003c/a\u003e\u0026nbsp;\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/endomorphism/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eLAMBDA and BETA\u003c/a\u003e\u0026nbsp;revealed the same initial bits to us.\u0026nbsp;The value\u0026nbsp;\u003ccode\u003ePOLYNONCE\u003c/code\u003ein the format\u0026nbsp;\u003ccode\u003eHEX\u003c/code\u003eallows us to fully solve the problem of hidden numbers, get a private key and restore a Bitcoin Wallet.\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 check the HEX of the private key:\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s run the code:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code\"\u003e\u003ccode\u003efrom bitcoin import *\n\nwith open(\"PrivateKey.txt\",\"r\") as f:\n    content = f.readlines()\n\ncontent = [x.strip() for x in content]\nf.close()\n\n\noutfile = open(\"PrivateKeyAddr.txt\",\"w\")\nfor x in content:\n  outfile.write(x+\":\"+pubtoaddr(encode_pubkey(privtopub(x), \"bin_compressed\"))+\"\\n\")\n \noutfile.close()\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-278.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3321\"\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\"\u003e\n\u003cp\u003eLet’s open the file:\u0026nbsp;\u003ccode\u003ePrivateKeyAddr.txt\u003c/code\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-279-1024x700.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3323\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ccode\u003ee2eadbde2e6a2adb6f81864cdf574dd44959717fe095486e2c0e55585594edf2:1L8v5aUZRzYbGKWcj9Yt6mGdd95Sy9bXjN\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\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: 1L8v5aUZRzYbGKWcj9Yt6mGdd95Sy9bXjN\nWIF:  L4porgUmuBkMbATA6Pp7r8uqShFt2zTPNEfuPNYi1BCym4hhV8gs\nHEX:  e2eadbde2e6a2adb6f81864cdf574dd44959717fe095486e2c0e55585594edf2\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-bitaddress-9.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3332\"\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://www.blockchain.com/en/explorer/addresses/btc/1L8v5aUZRzYbGKWcj9Yt6mGdd95Sy9bXjN\"\u003ehttps://www.blockchain.com/en/explorer/addresses/btc/1L8v5aUZRzYbGKWcj9Yt6mGdd95Sy9bXjN\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 is-resized\"\u003e\u003cimg decoding=\"async\" loading=\"lazy\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-281.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3337\" style=\"width:857px;height:246px\" width=\"857\" height=\"246\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-282.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3340\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/image-283.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3342\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp class=\"has-large-font-size\"\u003e\u003ccode\u003e\u003cstrong\u003eBALANCE: $ 995.39\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\u003ch2 class=\"wp-block-heading\"\u003eLiterature:\u003c/h2\u003e\n\n\n\n\u003cul\u003e\n\u003cli\u003e\u003cem\u003e\u003ca href=\"https://cryptodeep.ru/doc/Lattice-Attacks-against-Elliptic-Curve-Signatures-with-Blinded-Scalar-Multiplication.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eLattice Attacks against Elliptic-Curve Signatures with Blinded Scalar Multiplication Dahmun Goudarzi , Matthieu Rivain , and Damien Vergnaud CryptoExperts, Paris, France\u003c/a\u003e\u003c/em\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cul\u003e\n\u003cli\u003e\u003cem\u003e\u003ca href=\"https://cryptodeep.ru/doc/Biased-Nonce-Sense-Lattice-Attacks-against-Weak-ECDSA-Signatures-in-Cryptocurrencies.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBiased Nonce Sense: Lattice Attacks against Weak ECDSA Signatures in Cryptocurrencies Joachim Breitner and Nadia Heninger DFINITY Foundation, Zug University of California, San Diego\u003c/a\u003e\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003ca href=\"https://cryptodeep.ru/doc/Return-of-the-Hidden-Number-ProblemA-Widespread-and-Novel-Key-Extraction-Attack-on-ECDSA-and-DSA.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eReturn of the Hidden Number Problem A Widespread and Novel Key Extraction Attack on ECDSA and DSA Keegan Ryan\u003c/a\u003e\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003ca href=\"https://cryptodeep.ru/doc/The-curse-of-ECDSA-nonces-Systematic-analysis-of-lattice-attacks-on-noisy-leakage-of-bit-length-of-ECDSA-nonces.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eMinerva: The curse of ECDSA nonces Systematic analysis of lattice attacks on noisy leakage of bit-length of ECDSA nonces Ján Jančár , Vladimír Sedláček , Petr Švenda and Marek Sýs Masaryk University, Ca’ Foscari University of Venice\u003c/a\u003e\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003ca href=\"https://cryptodeep.ru/doc/Estimating-the-Effectiveness-of-Lattice-Attacks.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eEstimating the Effectiveness of Lattice Attacks Kotaro Abe and Makoto Ikeda School of Engineering, The University of Tokyo, Tokyo, Japan\u003c/a\u003e\u003c/em\u003e\u003c/li\u003e\n\u003c/ul\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/21LatticeAttack\" 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/CzaHitewN-4\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eVideo: https://youtu.be/CzaHitewN-4\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://cryptodeeptech.ru/lattice-attack-249bits\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSource: https://cryptodeeptech.ru/lattice-attack-249bits\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=\"./LATTICE ATTACK 249bits we solve the problem of hidden numbers using 79 signatures ECDSA - CRYPTO DEEP TECH_files/039-1024x576.png\" alt=\"LATTICE ATTACK 249bits solve the hidden number problem using 79 signatures ECDSA\" class=\"wp-image-3344\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\t\u003c/div\u003e\u003c!-- .entry-content --\u003e\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdemining%2Flattice-attack-249bits","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdemining%2Flattice-attack-249bits","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdemining%2Flattice-attack-249bits/lists"}