{"id":21625071,"url":"https://github.com/demining/signature-malleability","last_synced_at":"2026-02-08T21:32:30.277Z","repository":{"id":264359767,"uuid":"893147017","full_name":"demining/Signature-Malleability","owner":"demining","description":"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures","archived":false,"fork":false,"pushed_at":"2024-11-23T18:16:33.000Z","size":45073,"stargazers_count":3,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-01-24T22:32:58.655Z","etag":null,"topics":["bitcoin","bitcoin-transaction","bitcoin-wallet","btc","eth","ethereum","malleability","private-key","signature","vulnerability"],"latest_commit_sha":null,"homepage":"https://cryptodeeptech.ru/signature-malleability","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/demining.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2024-11-23T16:53:56.000Z","updated_at":"2024-12-06T09:40:45.000Z","dependencies_parsed_at":"2024-11-23T18:27:54.075Z","dependency_job_id":null,"html_url":"https://github.com/demining/Signature-Malleability","commit_stats":null,"previous_names":["demining/signature-malleability"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FSignature-Malleability","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FSignature-Malleability/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FSignature-Malleability/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FSignature-Malleability/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/demining","download_url":"https://codeload.github.com/demining/Signature-Malleability/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":244297778,"owners_count":20430344,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["bitcoin","bitcoin-transaction","bitcoin-wallet","btc","eth","ethereum","malleability","private-key","signature","vulnerability"],"created_at":"2024-11-25T01:07:43.593Z","updated_at":"2026-02-08T21:32:30.249Z","avatar_url":"https://github.com/demining.png","language":"Jupyter Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"\n\t\t\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/057-1024x576.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4928\"\u003e\u003c/figure\u003e\n\n\n\n\u003cp\u003eA vulnerability known as Signature Malleability poses a serious threat to Bitcoin and Ethereum cryptocurrencies that use the Elliptic Curve Digital Signature Algorithm (ECDSA). This vulnerability allows attackers to manipulate signatures, creating invalid but acceptable signatures for the system. This article discusses the mechanisms of exploitation of this vulnerability, its implications for the security of cryptocurrencies, and proposed measures to mitigate it. ECDSA (Elliptic Curve Digital Signature Algorithm) is an algorithm that is widely used to create digital signatures for a BTC or ETH coin transfer transaction in Bitcoin and Ethereum cryptocurrencies. The signature consists of two components:\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003er\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;\u0026nbsp;and\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003es\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;, which depend on a random nonce\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003ek\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;\u0026nbsp;(NONCE) and a private key\u0026nbsp;\u003cem\u003e\u003cstrong\u003ex\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;\u0026nbsp;(PrivKey) of the signatory.\u003c/p\u003e\n\n\n---\n\n* Tutorial: https://youtu.be/wf6QwCpP3oc\n* Tutorial: https://cryptodeeptech.ru/signature-malleability\n* Google Colab: https://colab.research.google.com/drive/1HMmeEQDL4kRKfJNQptTf3Mz4VTZmka8h\n\n---\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eHow does Signature Malleability vulnerability occur in Bitcoin transaction?\u003c/h2\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eSignature Malleability\u003c/strong\u003e\u0026nbsp;vulnerabilities\u0026nbsp;\u0026nbsp;arise because it is possible to change the value\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003es\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;\u0026nbsp;in a signature while maintaining the validity of the signature. This is possible because multiple equivalent values\u0026nbsp;\u0026nbsp;\u003cstrong\u003e​​(\u0026nbsp;\u003cem\u003er\u003c/em\u003e\u0026nbsp;,\u0026nbsp;\u003cem\u003es\u003c/em\u003e\u0026nbsp;′)\u003c/strong\u003e\u0026nbsp;can be obtained for the same signature :\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-1.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-5841\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e(where\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003en\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;\u0026nbsp;is the order of the elliptic curve group\u0026nbsp;\u003cem\u003e\u003cstrong\u003esecp256k1\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;). In this way, an attacker can create a new signature that will be accepted as valid by the system.\u0026nbsp;\u003cstrong\u003eInsufficient value checking\u003c/strong\u003e\u0026nbsp;: If the values ​​of\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003er\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;\u0026nbsp;and\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003es\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;\u0026nbsp;are not checked for valid ranges (e.g., must be between\u0026nbsp;\u003cstrong\u003e1\u003c/strong\u003e\u0026nbsp;and\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003en\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e\u0026nbsp;−1\u003c/strong\u003e\u0026nbsp;), this may allow attackers to use incorrect values ​​to create fake signatures.\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\"\u003e\u003ca href=\"https://nvd.nist.gov/vuln/detail/CVE-2024-42461\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eCVE-2024-42461: Signature Malleability in Elliptic Library for ECDSA\u003c/a\u003e\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003eOne such vulnerability is\u0026nbsp;\u003cstrong\u003eCVE-2024-42461\u003c/strong\u003e\u0026nbsp;, discovered in the\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://www.npmjs.com/package/elliptic\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eElliptic\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;library used to implement\u0026nbsp;\u003cstrong\u003ethe ECDSA\u003c/strong\u003e\u0026nbsp;(Elliptic Curve Digital Signature Algorithm) digital signature algorithm.\u0026nbsp;\u003c/em\u003e\u0026nbsp;\u003cem\u003eCVE-2024-42461 affects\u0026nbsp;\u003ca href=\"https://www.npmjs.com/package/elliptic\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eversion 6.5.6 of the Elliptic library for Node.js\u003c/a\u003e\u0026nbsp;and is classified as a low-severity vulnerability with a CVSS score of 5.3. The problem is that the library allows the use of signatures encoded in the\u0026nbsp;\u003ca href=\"https://keyhunters.ru/basic-encoding-rules/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eBER (Basic Encoding Rules)\u003c/strong\u003e\u003c/a\u003e\u003ca href=\"https://keyhunters.ru/basic-encoding-rules/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u0026nbsp;format\u003cstrong\u003e\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;. This creates an opportunity for attackers to modify signatures without invalidating them, which opens the way for various attacks.\u003c/em\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=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-2-1024x623.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-5852\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cstrong\u003e\u003ca href=\"https://nvd.nist.gov/vuln/detail/CVE-2024-42461\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://nvd.nist.gov/vuln/detail/CVE-2024-42461\u003c/a\u003e\u003c/strong\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eCVE-2024-42461 is a vulnerability found in the Elliptic library used to implement the Elliptic Curve Digital Signature Algorithm (ECDSA) in Node.js. This vulnerability is related to\u0026nbsp;\u003cstrong\u003ethe Ricci Flow\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eHidden Number Problem\u0026nbsp;\u003cem\u003e(Ricci Flow HNP)\u003c/em\u003e\u003c/strong\u003e\u0026nbsp;, which makes it particularly important for the security of cryptographic applications.\u0026nbsp;\u003cstrong\u003eThe Hidden Number Problem\u003c/strong\u003e\u0026nbsp;is a mathematical problem that consists of finding a hidden number used in the encryption process. In the context of ECDSA, if an attacker can solve the HNP, this can lead to the compromise of private keys. CVE-2024-42461 allows a potential attacker to extract information about private keys from signatures, which compromises the integrity of digital signatures and user authentication. This vulnerability opens up a wide range of attacks, as the vulnerability can be used in various attacks, including authentication and data integrity attacks. This could cause serious problems for systems that rely on ECDSA to secure Bitcoin and Ethereum cryptocurrency transactions.\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003e\u003cstrong\u003eCompromise of Private Keys\u003c/strong\u003e\u0026nbsp;: A successful\u0026nbsp;\u003cstrong\u003eRicci Flow HNP\u003c/strong\u003e\u0026nbsp;solution could allow an attacker to gain access to private keys, leading to the ability to forge Bitcoin and Ethereum transaction signatures.\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\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-full\"\u003e\u003ca href=\"https://www.youtube.com/watch?v=wf6QwCpP3oc\"\u003e\u003cimg decoding=\"async\" width=\"666\" height=\"380\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-3033\" srcset=\"https://cryptodeeptech.ru/wp-content/uploads/2024/11/image.png 666w, https://cryptodeeptech.ru/wp-content/uploads/2024/11/image-300x171.png 300w\" sizes=\"(max-width: 666px) 100vw, 666px\"\u003e\u003c/a\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\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\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/Ricci_Flow_Hidden_Number_Problem.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eRicci Flow HNP\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eThe Ricci Flow Hidden Number Problem (HNP\u0026nbsp;\u003c/strong\u003e\u003cem\u003e)\u003c/em\u003e\u0026nbsp;has become a key tool in proving theorems such as\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Thurston_elliptization_conjecture\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ethe Thurston elliptization conjecture\u003c/a\u003e\u0026nbsp;,\u0026nbsp;\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Geometrization_conjecture\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eGeometrization conjecture\u003c/a\u003e\u0026nbsp;, and\u0026nbsp;\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePoincaré conjecture\u003c/a\u003e\u0026nbsp;, which concern the topology of manifolds. Hamilton and later\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Grigori_Perelman\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eGrigori Perelman\u003c/a\u003e\u0026nbsp;used this approach to obtain deep results about the structure of manifolds, which can mean using flow to identify and analyze hidden geometric features of manifolds, allowing one to infer their topology and other properties.\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003eThe Ricci flow is closely related to curvature theory, since it uses the Ricci tensor to describe changes in the Riemannian metric on a manifold.\u003c/em\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eBasic Relationships Between Ricci Flow and Curvature\u003c/h2\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eRicci Tensor:\u003c/strong\u003e\u0026nbsp;The Ricci flow is based on the Ricci tensor, which is the average of sectional curvatures. It reflects how the shape of a manifold changes with its curvature, where it is formulated as the problem of finding a hidden number when the results of a function applied to combinations of that number with known elements are known. This can be useful in the context of cryptography, especially in public-key systems where it is important to minimize leakage of information about private keys.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eCurvature dynamics:\u003c/strong\u003e\u0026nbsp;During the Ricci flow, the metric changes in such a way that the curvature can increase or decrease. This allows us to analyze how the geometric properties of the manifold affect its topology.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eSingularities:\u003c/strong\u003e\u0026nbsp;The Ricci flow can lead to singularities, points where the curvature becomes infinite. Studying these singularities is key to understanding the long-term behavior of the flow and its application to topological problems such as the Poincaré conjecture.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eMaximum principle:\u003c/strong\u003e\u0026nbsp;The Ricci flow preserves the positivity of the scalar curvature, which allows us to use maximum principles to analyze the geometric properties of manifolds under deformation.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-12-1024x697.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4723\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003eIn the context of elliptic curves, Ricci flows can be used to analyze their geometric properties and understand the relationships between different structures on these curves\u003c/em\u003e\u0026nbsp;.\u0026nbsp;\u003cem\u003eThe indicatrix of curvature,\u003c/em\u003e\u0026nbsp;\u0026nbsp;or\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003ca href=\"https://keyhunters.ru/dupins-indicatrix/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eDupin indicatrix\u003c/a\u003e\u003c/em\u003e\u0026nbsp;,\u0026nbsp;\u003cem\u003eis constructed in the tangent plane at a given point on the surface according to the following rule. The coordinate axes in the tangent plane coincide with the principal directions. On the ray located in each direction, a segment is laid off equal to the reciprocal square root of the normal curvature of the surface in this direction\u003c/em\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003eClassification of surface points\u003c/h2\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-13-1024x574.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4724\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp class=\"has-text-align-center\"\u003e\u003cstrong\u003eThere are surfaces consisting of points of one, two or three types.\u003c/strong\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-14.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4725\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003eThis quadratic equation may have one or two roots — asymptotic directions, or no roots. The presence of a root provides an ordinary differential equation of the first order, the indication of a point on the surface sets the initial conditions for its solution. The theorem of the existence and uniqueness of the solution of the Cauchy problem for an ordinary differential equation of the first order, proved in courses on mathematical analysis, leads to the following geometric result. On a surface consisting of elliptical points, there are no real asymptotic lines; on a surface consisting of hyperbolic points, there is an asymptotic network; on a surface consisting of parabolic points that are not flattening points, a unique asymptotic line passes through each point.\u003c/em\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003cstrong\u003eOptimization of algorithms\u003c/strong\u003e\u003c/h2\u003e\n\n\n\n\u003cp\u003eThe methods developed in the framework of Ricci flow theory can be adapted to optimize computations in elliptic curve cryptography, especially in the context of operations on points on elliptic curves secp256k1. Thus, the Ricci flow not only serves as a tool for studying the evolution of metrics, but also provides a deep connection between geometry and topology through curvature analysis. Take for example the numbers\u0026nbsp;\u003cstrong\u003e“N”\u003c/strong\u003e\u0026nbsp;and\u0026nbsp;\u003cstrong\u003e“P”\u003c/strong\u003e\u0026nbsp;which are important parameters in the context of elliptic curve cryptography, especially in the secp256k1 standard, which is widely used in the Bitcoin and Ethereum blockchain and cryptocurrency.\u003c/p\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading has-text-align-center\"\u003eThe meaning of the number N\u003c/h3\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eN\u003c/strong\u003e\u0026nbsp;is the order of the group of points on the elliptic curve. It determines the maximum number of points that can be used to generate keys in cryptographic algorithms. In the case of\u0026nbsp;\u003cstrong\u003esecp256k1\u003c/strong\u003e\u0026nbsp;, the value of\u0026nbsp;\u003cstrong\u003eN\u003c/strong\u003e\u0026nbsp;is:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-26d373adbed3f86c95d4ef24545c11cb\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003eN = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003eThis number also indicates that when working with this curve, all operations must be performed within this order.\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\u003ch3 class=\"wp-block-heading has-text-align-center\"\u003eThe meaning of the number P\u003c/h3\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eP\u003c/strong\u003e\u0026nbsp;is a characteristic of the elliptic curve itself, a prime number that defines the field in which the work on the points on the curve occurs. The value of\u0026nbsp;\u003cstrong\u003eP\u003c/strong\u003e\u0026nbsp;for\u0026nbsp;\u003cstrong\u003esecp256k1\u003c/strong\u003e\u0026nbsp;is:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-58fe20cb4fe6496c83155ba97d1de2b8\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003eP = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003eThis number specifies the size of the field, which is important for determining the range of possible values ​​of the coordinates of points on the curve.\u003c/em\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003eDifference between N and P\u003c/h2\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eGroup Order (N)\u003c/strong\u003e\u0026nbsp;: Determines the number of points on the curve that can be used for cryptographic operations.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003ePrime Number (P)\u003c/strong\u003e\u0026nbsp;: Defines the field in which the curve operates. This number is important for mathematical operations on points on the curve.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cp\u003eThus, although both numbers play a key role in ensuring the security and functionality of cryptographic systems, they perform different functions:\u0026nbsp;\u003cstrong\u003eN\u003c/strong\u003e\u0026nbsp;concerns\u0026nbsp;\u003cem\u003ethe structure of a group of points\u003c/em\u003e\u0026nbsp;, and\u0026nbsp;\u003cstrong\u003eP\u003c/strong\u003e\u0026nbsp;concerns\u0026nbsp;\u003cem\u003ethe structure of a field\u003c/em\u003e\u0026nbsp;.\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\"\u003eVertical position value of N and P\u003c/h2\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading has-text-align-center\"\u003e\u003cem\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/value_n.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePython script: value_n.py\u003c/a\u003e\u003c/em\u003e\u003c/h3\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-17.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4739\" style=\"width:838px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading has-text-align-center\"\u003e\u003cem\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/value_p.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePython script: value_p.py\u003c/a\u003e\u003c/em\u003e\u003c/h3\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-18.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4740\" style=\"width:838px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eHow to exploit Signature Malleability in Bitcoin transaction?\u003c/h2\u003e\n\n\n\n\u003cp\u003eTo implement a full-fledged attack on Bitcoin using the\u0026nbsp;\u003cstrong\u003eSignature Malleability\u003c/strong\u003e\u0026nbsp;vulnerability, it is necessary to change the equivalent value\u0026nbsp;\u0026nbsp;\u003cstrong\u003e(\u0026nbsp;\u003cem\u003es\u003c/em\u003e\u0026nbsp;′)\u003c/strong\u003e\u0026nbsp;as shown in the second column of the table of components\u0026nbsp;\u003cem\u003eof the value\u0026nbsp;\u003cstrong\u003e(R, S, Z)\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;\u003cem\u003eof the digital signature in\u0026nbsp;\u003cstrong\u003eECDSA\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;.\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/Ricci_Flow_Hidden_Number_Problem.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/nonces-1024x412.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4752\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/Ricci_Flow_Hidden_Number_Problem.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e36SignatureMalleability/Ricci_Flow_Hidden_Number_Problem.txt\u003c/strong\u003e\u003c/a\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-58fe20cb4fe6496c83155ba97d1de2b8\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003eP = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cp\u003eFor a successful attack on Bitcoin,\u0026nbsp;\u003cem\u003e\u003cstrong\u003e32\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e\u0026nbsp;ECDSA\u003c/strong\u003e\u0026nbsp;signature transactions are enough\u0026nbsp;, where by changing the two initial digits\u0026nbsp;\u003cstrong\u003eof HEX\u003c/strong\u003e\u0026nbsp;to the equivalent value\u0026nbsp;\u0026nbsp;\u003cstrong\u003e(\u0026nbsp;\u003cem\u003es\u003c/em\u003e\u0026nbsp;′)\u003c/strong\u003e\u0026nbsp;we build a table to determine the range of possible values ​​of the coordinates of points on the curve, as well as optimizing the mathematical algorithms\u0026nbsp;\u003cem\u003e\u003c/em\u003edeveloped within the framework of the Ricci flow theory. Since Ricci flows are closely related to the curvature theory, we can use the average value of the sectional curvature and solve the hidden number problem, where by applying the obtained data to\u0026nbsp;\u003cem\u003e\u003cstrong\u003e32\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;Bitcoin transactions we extract from the given values\u0026nbsp;\u003cem\u003e\u003cstrong\u003e​​​​(R, S, Z)\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;the initial data for\u0026nbsp;\u003cem\u003ethe secret keys\u003c/em\u003e\u0026nbsp;:\u0026nbsp;\u003cstrong\u003e(\u0026nbsp;\u003cem\u003ek\u003c/em\u003e\u0026nbsp;′)\u003c/strong\u003e\u0026nbsp;NONCE for\u0026nbsp;\u003cem\u003e\u003cstrong\u003e32\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;Bitcoin transactions and using the\u0026nbsp;\u003cstrong\u003eRicci Flow HNP\u0026nbsp;\u003c/strong\u003e\u0026nbsp;\u003cem\u003e(Ricci Flow Hidden Number Problem)\u003c/em\u003e\u0026nbsp;tool \u0026nbsp;we find the hidden number:\u0026nbsp;\u003cstrong\u003e(\u0026nbsp;\u003cem\u003ex\u003c/em\u003e\u0026nbsp;′)\u003c/strong\u003e\u0026nbsp;PrivKey –\u0026nbsp;\u003cem\u003eprivate key\u003c/em\u003e\u0026nbsp;.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading has-text-align-center\"\u003eThe R and S values ​​are the main components of a digital signature in ECDSA\u003c/h3\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003e\u003cstrong\u003eThe R\u003c/strong\u003e\u0026nbsp;value\u0026nbsp;is the coordinate of a point on the elliptic curve that results from mathematical operations involving a private key and a random number (called a “cryptographic random number”). This value ensures that the signature is unique for each message, even if it is signed with the same private key.\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\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp class=\"has-medium-font-size\"\u003e\u003cem\u003eThe value of\u0026nbsp;\u0026nbsp;\u003cstrong\u003eS\u003c/strong\u003e\u0026nbsp;\u0026nbsp;is calculated based on the message digest (hash function) and the private key. It is related to how well the signature verifies the authenticity of the message. The value of\u0026nbsp;\u0026nbsp;\u003cstrong\u003eS\u003c/strong\u003e\u0026nbsp;\u0026nbsp;also depends on the value of\u0026nbsp;\u003cstrong\u003eR\u003c/strong\u003e\u0026nbsp;and the random number.\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\u003ch3 class=\"wp-block-heading has-text-align-center\"\u003eHow R and S are formed\u0026nbsp;\u003cem\u003e(signature verification method)\u003c/em\u003e\u003c/h3\u003e\n\n\n\n\u003cp\u003eThe process of generating R and S values ​​involves the following steps:\u003c/p\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eGenerating a message digest\u003c/strong\u003e\u0026nbsp;: First, a hash of the message is created using an algorithm such as SHA-256.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eRandom Number Selection\u003c/strong\u003e\u0026nbsp;: A random number is generated and used to create a point on the elliptic curve.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eCalculating R\u003c/strong\u003e\u0026nbsp;: Using this random number, the coordinate of a point on the curve is calculated, which becomes the R value.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eCalculation of S\u003c/strong\u003e\u0026nbsp;: The value of S is calculated given the message digest and the private key.\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cp\u003eWhen verifying a signature, the recipient uses the R and S values ​​along with the sender’s public key and the message digest to verify the authenticity of the signature. If all calculations match, this means that the message was indeed signed by the owner of the corresponding private key.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading has-text-align-center\"\u003e\u003cstrong\u003eHow to get R, S, Z\u003c/strong\u003e\u0026nbsp;value\u0026nbsp;from\u0026nbsp;\u003cstrong\u003eRawTX\u0026nbsp;\u003c/strong\u003e\u003cem\u003e(Signature Decoding Method)\u003c/em\u003e\u003c/h3\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp class=\"has-medium-font-size\"\u003e\u003cem\u003e\u003cstrong\u003eRawTX\u003c/strong\u003e\u0026nbsp;is an encoded representation of a Bitcoin transaction in hexadecimal format. It contains all the data needed to complete a Bitcoin transaction.\u003c/em\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003eExtract\u0026nbsp;\u003cstrong\u003eR, S, Z:\u003c/strong\u003e\u003c/h3\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eA signature in ECDSA consists of two components:\u0026nbsp;\u003cstrong\u003eR\u003c/strong\u003e\u0026nbsp;and\u0026nbsp;\u003cstrong\u003eS\u003c/strong\u003e\u0026nbsp;. After decoding\u0026nbsp;\u003cstrong\u003eRawTX,\u003c/strong\u003e\u0026nbsp;find the field containing the signature\u0026nbsp;\u003cem\u003e(usually part of the transaction input).\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003eThe signature will be represented as\u0026nbsp;\u003cem\u003ea\u0026nbsp;\u003c/em\u003e\u003cstrong\u003eDER\u003c/strong\u003e\u0026nbsp;encoding\u0026nbsp;. You will need to extract the\u0026nbsp;\u003cstrong\u003eR\u003c/strong\u003e\u0026nbsp;and\u0026nbsp;\u003cstrong\u003eS\u003c/strong\u003e\u0026nbsp;values ​​from this signature. They are usually represented as two integers, which can be extracted using\u0026nbsp;\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://cryptodeeptech.ru/deserialize-signature-vulnerability-bitcoin/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003edeserialization\u003c/a\u003e\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;.\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://cryptodeeptech.ru/deserialize-signature-vulnerability-bitcoin/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003c/a\u003e\u003c/strong\u003e\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eThe Z\u003c/strong\u003e\u0026nbsp;value\u0026nbsp;is a hash of the message being signed. To get Z, you have to hash the transaction data\u0026nbsp;\u003cem\u003e(usually using SHA-256)\u003c/em\u003e\u0026nbsp;that was signed.\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\u003ch3 class=\"wp-block-heading\"\u003eDecoding\u0026nbsp;\u003cstrong\u003eRawTX\u003c/strong\u003e\u0026nbsp;with\u0026nbsp;\u003ca href=\"https://github.com/smartibase/Broadcast-Bitcoin-Transaction/tree/main/decoderaw\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003edecoderaw tool\u003c/strong\u003e\u003c/a\u003e\u003c/h3\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp class=\"has-medium-font-size\"\u003e\u003cem\u003eFirst, let’s get\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/RawTX.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eRawTX,\u003c/a\u003e\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;\u003cem\u003ethe encoded Bitcoin transaction in hexadecimal format.\u0026nbsp;\u003c/em\u003e\u003cstrong\u003e\u003csup\u003e\u003ca href=\"https://cryptodeeptool.ru/signature-malleability/#aa553e57-81fe-4c3c-98dd-0d1b60ea55ee\"\u003e1\u003c/a\u003e\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp class=\"has-medium-font-size\"\u003eLet’s open a new notebook in\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://colab.research.google.com/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eGoogle Colab\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eCommand:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-183b0826bd95d2bed18a48a4922e7c75\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!git clone https://github.com/smartibase/Broadcast-Bitcoin-Transaction.git\n\ncd Broadcast-Bitcoin-Transaction/\n\n!python setup.py\n\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-26-1024x465.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4812\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eCommand:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-79920bb9f702afb9eb413dd0ec9217c5\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ecd decoderaw/\n\n!chmod +x decoderaw\n\nls\n\n!./decoderaw\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-28-1024x538.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4824\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eCommand:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-091f8661b801bef4da98d257d847fa71\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!./decoderaw 01000000010dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935000000008b48304502210097255916a3cc4f69d4fa16f68219d0b1798d392fb0dce5fb0a358510df8cabe002201014656120e0a6e7c8c4a79ee22b3cdd4f55435e3e9bf3ab7287ae16858dd9d50141049b4069d8237fae8f2417c71c5512ec1b0547b5597474480cc28ea1bbfeecaab8b90fdec161ad6ef4378f274a60b900452431533596bf3bd23e01202ebf679461ffffffff01d2040000000000001976a914d77522a2b18e0064aba02ca7f864a5bb2299825988ac00000000\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-29-1024x330.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4825\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-8cf66185109e4f0551aa843f0b1e4f1f\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003eResult:\n\n1111,0097255916a3cc4f69d4fa16f68219d0b1798d392fb0dce5fb0a358510df8cabe0,1014656120e0a6e7c8c4a79ee22b3cdd4f55435e3e9bf3ab7287ae16858dd9d5,931a52e8610cf87b6d00875f687042224c305865fd20ecb15ef76b1277ba10fd,0000\n\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003ePractical part\u003c/h2\u003e\n\n\n\n\u003cp\u003eFrom the theory of vulnerability\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://nvd.nist.gov/vuln/detail/CVE-2024-42461\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eCVE-2024-42461\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;it is known that attackers can use incorrect values ​​to create fake transaction signatures. Let’s move on to the practical part of the article and consider an example using a Bitcoin wallet:\u0026nbsp;\u0026nbsp;\u003ca href=\"https://btc1.trezor.io/address/1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;\u0026nbsp;, where there were lost coins in the amount of:\u0026nbsp;\u0026nbsp;\u003cstrong\u003e21.2529214 BTC\u003c/strong\u003e\u0026nbsp;\u0026nbsp;as of November 2024, this amount is:\u0026nbsp;\u0026nbsp;\u003cstrong\u003e1744572.51 USD\u003c/strong\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-46-1024x366.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4880\"\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\"\u003eSolution of differential equation\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003eSolutions of differential equations help to model various processes, this formula allows us to understand and predict the behavior of various systems depending on the change in variables.\u0026nbsp;\u003c/em\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=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-21.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4784\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003e\u003ca href=\"https://keyhunters.ru/differential-equations/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eGeneral solution of a differential equation\u003c/a\u003e\u0026nbsp;where the function\u0026nbsp;\u0026nbsp;\u003cstrong\u003ey\u003c/strong\u003e\u0026nbsp;\u0026nbsp;depends on the variable\u0026nbsp;\u0026nbsp;\u003cstrong\u003ex\u003c/strong\u003e\u0026nbsp;.\u003c/em\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eOriginal equation\u003c/strong\u003e\u0026nbsp;:\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eThe left side of the equation can be interpreted as the derivative of the function\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003ey\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;\u0026nbsp;with respect to\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003ex\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;, which is equal to the product of two functions:\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003cem\u003eg\u003c/em\u003e\u0026nbsp;(\u0026nbsp;\u003cem\u003ey\u003c/em\u003e\u0026nbsp;)\u003c/strong\u003e\u0026nbsp;, depending on\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003ey\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;, and\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003cem\u003eh\u003c/em\u003e\u0026nbsp;(\u0026nbsp;\u003cem\u003ex\u003c/em\u003e\u0026nbsp;)\u003c/strong\u003e\u0026nbsp;, depending on\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003ex\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eRewriting the equation\u003c/strong\u003e\u0026nbsp;:\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eThe equation can be rewritten in a form that separates the variables:\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-22.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4787\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003eThis allows both sides to be integrated separately.\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003eAfter separating the variables, we can integrate both sides exactly:\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cem\u003eLeft side relative to\u0026nbsp;\u0026nbsp;\u003cstrong\u003ey\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;:\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-23.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4788\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003cem\u003eRight side relative to\u0026nbsp;\u0026nbsp;\u003cstrong\u003ex\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;:\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-25.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4790\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003eWe will explore the relationship between variables through integration\u0026nbsp;\u003ccode\u003e\u003cstrong\u003e[ frac{dy}{dx} = g(y)h(x) quad Rightarrow quad frac{1}{g(y)} dy = h(x) dx ]\u003c/strong\u003e\u003c/code\u003eand apply a tool for mathematical analysis and solving differential equations.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch1 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://perelmanwork.com/ricci-flow-hnp\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePerelman Work\u003c/a\u003e\u003c/h1\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-full\"\u003e\u003ca href=\"https://www.youtube.com/watch?v=isWxfa3PeHU\"\u003e\u003cimg loading=\"lazy\" decoding=\"async\" width=\"666\" height=\"386\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-1(1).png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-3035\" srcset=\"https://cryptodeeptech.ru/wp-content/uploads/2024/11/image-1.png 666w, https://cryptodeeptech.ru/wp-content/uploads/2024/11/image-1-300x174.png 300w\" sizes=\"auto, (max-width: 666px) 100vw, 666px\"\u003e\u003c/a\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp class=\"has-medium-font-size\"\u003e\u003cem\u003e\u003ca href=\"https://github.com/smartibase/Broadcast-Bitcoin-Transaction/tree/main/darksignature\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eExample #1\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;using the\u003ca href=\"https://github.com/smartibase/Broadcast-Bitcoin-Transaction/tree/main/darksignature\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e\u0026nbsp;DarkSignature\u003c/strong\u003e\u003c/a\u003e\u003c/em\u003e\u0026nbsp;tool:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003eLet’s go back to the root directory of the\u0026nbsp;\u003ca href=\"https://github.com/smartibase/Broadcast-Bitcoin-Transaction\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eBroadcast Bitcoin Transaction repository\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eCommand:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-2187a86ab4b467bc62c2aa17e7f8cef3\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ecd -\n\nls\n\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-30-1024x294.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4826\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eCommand:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-f82b2299b813b390a63174e605dd5019\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ecd darksignature/\n\n!chmod +x darksignature\n\nls\n\n!./darksignature\n\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-31-1024x601.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4827\"\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-medium-font-size\"\u003eTo obtain\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/pubkey.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ethe public key\u003c/a\u003e\u0026nbsp;to the Bitcoin Address\u0026nbsp;\u003cstrong\u003e1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw,\u003c/strong\u003e\u0026nbsp;select the command:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-d65deca57e050c01691efb3ae5965429\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003edarksignature -address \u0026lt;Bitcoin Address\u0026gt;\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cp\u003eEnter the Bitcoin address and get\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/pubkey.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ethe public key\u003c/a\u003e\u0026nbsp;:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-2f75d832a49fcc1126bc2e65e68b2533\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!./darksignature -address 1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-32-1024x74.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4828\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eResult:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-e897902c49a53457167cee8c1ed405b1\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003epubkey: (HEX) = 049b4069d8237fae8f2417c71c5512ec1b0547b5597474480cc28ea1bbfeecaab8b90fdec161ad6ef4378f274a60b900452431533596bf3bd23e01202ebf679461\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp class=\"has-medium-font-size\"\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://dockeyhunt.com/dockeyhunt-lattice-attack/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eExample #2\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;using\u003cstrong\u003e\u003ca href=\"https://dockeyhunt.com/dockeyhunt-lattice-attack/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u0026nbsp;Dockeyhunt Lattice Attack\u003c/a\u003e\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;tool:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://dockeyhunt.com/dockeyhunt-lattice-attack/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eWe launch the Dockeyhunt Lattice Attack\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;software and\u0026nbsp;\u003ccode\u003e\"Input date\"\u003c/code\u003eenter the Bitcoin Address\u0026nbsp;\u003ca href=\"https://btc1.trezor.io/address/1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;in the field\u0026nbsp;and receive the public key of the wallet:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-bdb963ea4f8cda42fbf27bf644131fa6\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e049b4069d8237fae8f2417c71c5512ec1b0547b5597474480cc28ea1bbfeecaab8b90fdec161ad6ef4378f274a60b900452431533596bf3bd23e01202ebf679461\n\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=53\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-1024x544.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-190\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=53\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003cstrong\u003eLet’s use the DarkSignature\u003c/strong\u003e\u0026nbsp;tool\u0026nbsp;to get fake data\u0026nbsp;\u003cstrong\u003eR, S, Z\u003c/strong\u003e\u0026nbsp;values ​​for the ECDSA algorithm transaction. In the field,\u0026nbsp;\u003ccode\u003e\"Input date\"\u003c/code\u003eenter the public key of the Bitcoin Address\u0026nbsp;\u003cstrong\u003e\u003ccode\u003e049b4069d8237fae8f2417c71c5512ec1b0547b5597474480cc28ea1bbfeecaab8b90fdec161ad6ef4378f274a60b900452431533596bf3bd23e01202ebf679461\u003c/code\u003e\u003c/strong\u003eand get the data\u0026nbsp;\u003cstrong\u003eR, S, Z\u003c/strong\u003e\u0026nbsp;values ​​in the amount of\u0026nbsp;\u003cem\u003e32 Bitcoin transactions\u003c/em\u003e\u0026nbsp;.\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=67\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-1-1024x546.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-200\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=67\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eApply getting fake data value\u0026nbsp;\u003cstrong\u003eR, S, Z\u003c/strong\u003e\u0026nbsp;for ECDSA algorithm transaction in\u0026nbsp;\u003ca href=\"https://keyhunters.ru/google-colab-in-cryptanalysis/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eGoogle Colab\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eLet’s install the ECDSA module:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-8be306a934c87bfc04ea6164360c8f48\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003epip install ecdsa\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-33-1024x200.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4836\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eTo obtain coordinates\u0026nbsp;\u003ccode\u003e\u003cstrong\u003e(Gx, Gy)\u003c/strong\u003e\u003c/code\u003efor the public key, we will use a\u0026nbsp;\u003cem\u003ePython\u003c/em\u003e\u0026nbsp;script:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/smartibase/Broadcast-Bitcoin-Transaction/blob/main/darksignature/coordinates.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003edarksignature/coordinates.py\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-34-1024x508.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4837\"\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-medium-font-size\"\u003e\u003cstrong\u003eLet’s use the command:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp class=\"has-text-color has-link-color wp-elements-1a0e8b8da85f6d2dcb6a3f2f5ce555aa\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003edarksignature -pubkey \u0026lt;Gx Gy\u0026gt;\u003c/strong\u003e\u003c/code\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cem\u003eWe run the Python\u003c/em\u003e\u0026nbsp;script code\u0026nbsp;:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/smartibase/Broadcast-Bitcoin-Transaction/blob/main/darksignature/transactions.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003edarksignature/transactions.py\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;and get the data values\u0026nbsp;\u003cstrong\u003e​​R, S, Z\u003c/strong\u003e\u0026nbsp;in the amount will be\u0026nbsp;\u003cem\u003e32 Bitcoin transactions\u003c/em\u003e\u0026nbsp;.\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/darkmedia.gif\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003eAfter generation we get the file:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/SignatureRSZ.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSignatureRSZ.txt\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eAlso in the root directory:\u0026nbsp;\u003ccode\u003e\u003cstrong\u003ec:\\PerelmanWork\\Dockeyhunt Lattice Attack\\\u003c/strong\u003e\u003c/code\u003ewe get the file:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/Signatures.txt\"\u003eSignatures.txt\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-2-1024x546.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-206\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=94\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-3-1024x542.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-207\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=94\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp class=\"has-medium-font-size\"\u003eAs we can see the first two digits the value of\u0026nbsp;\u003cstrong\u003e\u003cem\u003eS\u003c/em\u003e\u003c/strong\u003e\u0026nbsp;is arranged as\u0026nbsp;\u003cstrong\u003ethe Order of the group (N)\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading has-text-align-center\"\u003e\u003cem\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/value_n.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePython script: value_n.py\u003c/a\u003e\u003c/em\u003e\u003c/h3\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-17.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4739\" style=\"width:840px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://perelmanwork.com/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eAs a tool for mathematical analysis and solving differential equations, we will use the Perelman Work\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;software\u0026nbsp;. We will select the option from the\u0026nbsp;\u003cstrong\u003eFunctions and Graphs\u003c/strong\u003e\u0026nbsp;section for a complete relationship between variables through the integration of\u0026nbsp;\u003cstrong\u003eFirst-order differential equations:\u003c/strong\u003e\u0026nbsp;\u003ccode\u003e\u003cstrong\u003e[ frac{dy}{dx} = g(y)h(x) quad Rightarrow quad frac{1}{g(y)} dy = h(x) dx ]\u003c/strong\u003e\u003c/code\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-4-1024x548.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-210\"\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\"\u003eRicci Flow Hidden Number Problem\u003c/h2\u003e\n\n\n\n\u003cp\u003eWe copy the values ​​from the file:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/Signatures.txt\"\u003eSignatures.txt\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;according to the list and paste them into the input field\u0026nbsp;\u003ccode\u003e\u003cstrong\u003eRicci Flow HNP\u003c/strong\u003e\u003c/code\u003eto build completely new transactions of the\u0026nbsp;\u003cstrong\u003eECDSA\u003c/strong\u003e\u0026nbsp;algorithm .\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=226\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-5-1024x542.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-211\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=226\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-11-1024x544.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-219\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-10-1024x543.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-218\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-9-1024x549.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-217\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-8-1024x545.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-216\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-6-1024x544.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-213\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003eUsing\u0026nbsp;\u003ca href=\"https://perelmanwork.com/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ePerelman Work\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;and\u0026nbsp;\u003ca href=\"https://dockeyhunt.com/dockeyhunt-lattice-attack/\"\u003e\u003cstrong\u003eDockeyhunt\u0026nbsp;\u003c/strong\u003e\u003c/a\u003e\u003ca href=\"https://dockeyhunt.com/dockeyhunt-lattice-attack/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eLattice Attack, we arbitrarily change variables to\u0026nbsp;\u003c/strong\u003e\u003c/a\u003e\u003ca href=\"https://cryptodeeptech.ru/signature-malleability/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eSignature Malleability\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;vulnerability\u0026nbsp;as we wrote at the beginning\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/signature-malleability/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eof the article\u003c/a\u003e\u0026nbsp;this vulnerability in Bitcoin transaction occurs due to the fact that it is possible to change the value of\u0026nbsp;\u0026nbsp;\u003cstrong\u003eS\u003c/strong\u003e\u0026nbsp;\u0026nbsp;in the signature, while maintaining the validity of the signature. As we reported in the arbitrary formula all this is possible due to the fact that for the same signature it is possible to obtain several equivalent values\u0026nbsp;\u0026nbsp;\u003cstrong\u003e​​(r,s′)\u003c/strong\u003e\u0026nbsp;:\u003c/em\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=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-37.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4852\"\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\u003eAs a final result of the transformation of variables in the signature value\u0026nbsp;\u003cstrong\u003eR, S′, Z\u003c/strong\u003e\u0026nbsp;we see two digits the value\u0026nbsp;\u003cstrong\u003e\u003cem\u003eS\u003c/em\u003e\u0026nbsp;′\u003c/strong\u003e\u0026nbsp;is built as\u0026nbsp;\u003cstrong\u003ea field structure (P)\u003c/strong\u003e\u0026nbsp;:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-58fe20cb4fe6496c83155ba97d1de2b8\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003eP = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cp\u003eThis number defines the field in which the\u0026nbsp;\u003cstrong\u003esecp256k1\u003c/strong\u003e\u0026nbsp;curve operates to perform mathematical operations on points on\u0026nbsp;\u003cem\u003ean elliptic curve\u003c/em\u003e\u0026nbsp;.\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=1250\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-35-1024x546.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4845\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=1250\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTime-stamped video\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003ch3 class=\"wp-block-heading has-text-align-center\"\u003e\u003cem\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/value_p.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePython script: value_p.py\u003c/a\u003e\u003c/em\u003e\u003c/h3\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-18.png\" alt=\"Signature Malleability\" class=\"wp-image-4740\" style=\"width:838px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eNow we know the signatures of the difference between the numbers\u0026nbsp;\u003cstrong\u003eN\u003c/strong\u003e\u0026nbsp;and\u0026nbsp;\u003cstrong\u003eP\u003c/strong\u003e\u0026nbsp;. When reducing, we can get a hidden number\u0026nbsp;\u003cstrong\u003eX\u003c/strong\u003e\u0026nbsp;as we know when shifting the generation of one-time numbers\u0026nbsp;\u003cstrong\u003e(NONCES)\u003c/strong\u003e\u0026nbsp;, the value of the signature variables\u0026nbsp;\u003cstrong\u003eR, S′, Z\u003c/strong\u003e\u0026nbsp;will tend to one point. This point will be a hidden number, that is,\u0026nbsp;\u003cem\u003e\u003cstrong\u003ea private key\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;.\u003c/p\u003e\n\n\n\n\u003cp\u003e(\u0026nbsp;\u003cstrong\u003eN\u003c/strong\u003e\u0026nbsp;\u0026nbsp;are\u0026nbsp;\u0026nbsp;\u003cem\u003epoint group structures\u003c/em\u003e\u0026nbsp;,\u0026nbsp;\u0026nbsp;\u003cstrong\u003eP\u003c/strong\u003e\u0026nbsp;\u0026nbsp;are\u0026nbsp;\u0026nbsp;\u003cem\u003efield structures\u003c/em\u003e\u0026nbsp;,\u0026nbsp;\u003cstrong\u003eX\u003c/strong\u003e\u0026nbsp;\u0026nbsp;is\u0026nbsp;\u0026nbsp;\u003cem\u003ea private key\u003c/em\u003e\u0026nbsp;)\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003eTo obtain a private key, we will use\u0026nbsp;\u003ca href=\"https://keyhunters.ru/lattice-reduction-algorithms/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ethe lattice reduction algorithm\u0026nbsp;\u003cstrong\u003e(theorem of large numbers)\u003c/strong\u003e\u0026nbsp;.\u003c/a\u003e\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\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-54.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4905\" style=\"width:840px;height:auto\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eReduction of a lattice basis in two-dimensional space: the lattice is represented by blue dots, the original basis by black vectors, the reduced basis by red vectors.\u003c/a\u003e\u003c/strong\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://keyhunters.ru/lattice-reduction-algorithms/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eLenstra-Lenstra-Lovasz (LLL) Lattice Reduction Algorithm\u003c/a\u003e\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s use the LLL\u003c/strong\u003e\u0026nbsp;source code\u0026nbsp;from\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://www.linkedin.com/in/darioclavijo\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eDarío Clavijo,\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;a well-known developer on\u0026nbsp;\u003cstrong\u003eGitHub:\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/daedalus\" target=\"_blank\" rel=\"noreferrer noopener\"\u003edaedalus\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\"\u003e\u003ca href=\"https://github.com/daedalus/BreakingECDSAwithLLL.git\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-38-1024x574.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4853\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cem\u003e\u003ca href=\"https://github.com/daedalus/BreakingECDSAwithLLL.git\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eRepositories\u003c/strong\u003e\u003c/a\u003e\u003c/em\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-39.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4854\" style=\"width:840px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/google-colab-in-cryptanalysis/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eInstall SageMath in Google Colab:\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-e0d1a27361252b07a508f9f06f100564\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!sudo apt-get install sagemath python3-ecdsa\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-40.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4855\" style=\"width:840px;height:auto\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eCommands:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-156bbd87720e72b7bec9cb23a1266f8f\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!wget https://raw.githubusercontent.com/demining/CryptoDeepTools/refs/heads/main/36SignatureMalleability/latticereductions.py\n!wget https://raw.githubusercontent.com/demining/CryptoDeepTools/refs/heads/main/36SignatureMalleability/Ricci_Flow_Hidden_Number_Problem.txt\n\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-41-1024x350.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4862\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eRun\u0026nbsp;\u003cem\u003ethe Python\u003c/em\u003e\u0026nbsp;script:\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/latticereductions.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003elatticereductions.py\u003c/a\u003e\u0026nbsp;and get\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/KEYFOUND.privkey\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ethe private key\u003c/a\u003e\u0026nbsp;to the Bitcoin Address:\u0026nbsp;\u003ca href=\"https://btc1.trezor.io/address/1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-d2a4406a8b0d02c9290329023c9c2858\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!cat Ricci_Flow_Hidden_Number_Problem.txt \u0026gt; nonces.csv\n!python latticereductions.py nonces.csv 243 32\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-42-1024x539.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4863\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eResult:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-2c55aab53f6ac72c07e0ffc2effaf297\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e17e96966f15a56993e13f8c19ce34a99111ad768a051d9febc24b6d48cae1951\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eInstall the Bitcoin\u003c/strong\u003e\u003cem\u003e\u0026nbsp;library\u0026nbsp;\u003c/em\u003e\u003ca href=\"https://keyhunters.ru/exploring-bitcoin-tools-in-python-a-comprehensive-guide-to-the-bitcoin-package-on-pypi/\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-e1255bbe4e58a23675fd93194c0ab266\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!pip install bitcoin\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-43-1024x286.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4866\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003eLet’s run\u0026nbsp;\u0026nbsp;\u003c/em\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/priv_addr.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ethe code\u003c/strong\u003e\u003c/a\u003e\u003cem\u003e\u0026nbsp;\u0026nbsp;to check the Bitcoin Address match:\u003c/em\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=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-44.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4867\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-1430fb02e9d1fd98d397a583059ec387\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e__________________________________________________\n\nPrivate Key WIF: 17e96966f15a56993e13f8c19ce34a99111ad768a051d9febc24b6d48cae1951\nBitcoin Address: 1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\ntotal_received \t= 21.25292140 Bitcoin\n__________________________________________________\n\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cp class=\"has-text-align-center has-text-color has-link-color wp-elements-9745838a4bc4a23a1bd341927263e00e\" style=\"color:#19684b;font-size:25px\"\u003e\u003cstrong\u003eThat’s right! The private key corresponds to the Bitcoin Wallet.\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eLet’s open\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://cryptodeeptech.ru/bitaddress.html\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ebitaddress\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;and check:\u003c/h2\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-7f3b35e89a9914cdd5555fc10db3bfa7\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003eADDR: 1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\nWIF:  5HzpNjEsxrpxPFqBKaoRSnFeq7RP57mvzwgoQFVtAJNZBpLVyur\nHEX:  17e96966f15a56993e13f8c19ce34a99111ad768a051d9febc24b6d48cae1951\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-45.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4868\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003cstrong\u003e\u003ca href=\"https://dockeyhunt.com/dockeyhunt-lattice-attack/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eDockeyhunt Lattice Attack\u003c/a\u003e\u003c/strong\u003e\u003c/h2\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eLet’s consider obtaining a private key using the\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://dockeyhunt.com/dockeyhunt-lattice-attack/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eDockeyhunt Lattice Attack software as an example\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003eTo start\u0026nbsp;\u003cem\u003e\u003ca href=\"https://keyhunters.ru/lattice-reduction-algorithms/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ethe lattice reduction algorithm,\u003c/a\u003e\u003c/em\u003e\u0026nbsp;click on the button: \u003cstrong\u003e\u003ccode\u003ePrivate Key\u003c/code\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=1279\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-47-1.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4914\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=1279\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eTime-stamped video\u003c/strong\u003e\u003c/a\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eNext we need to make sure that we have received the required private key value in\u0026nbsp;\u003cstrong\u003eHEX format.\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=1284\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-49.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4892\"\u003e\u003c/a\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp class=\"has-medium-font-size\"\u003eClick on the button\u0026nbsp;\u003cstrong\u003e\u003ccode\u003eBitcoin Address\u003c/code\u003e\u003c/strong\u003eand get the required value of the private key in\u0026nbsp;\u003cstrong\u003eHEX format\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-cbcb492145e7479db057f616dee7106e\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e17e96966f15a56993e13f8c19ce34a99111ad768a051d9febc24b6d48cae1951: 1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-50-1.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4916\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp class=\"has-medium-font-size\"\u003eWe also click on the button\u0026nbsp;\u003cstrong\u003e\u003ccode\u003eBalance BTC\u003c/code\u003e\u003c/strong\u003eand get the result of the balance amount:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-4b0ba0416f2f86bfeaabe9f873b3ec5a\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e_____________________________________________________________________________________________________\n\n17e96966f15a56993e13f8c19ce34a99111ad768a051d9febc24b6d48cae1951: 1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw: 21.2529214 BTC\n_____________________________________________________________________________________________________\n\n\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=1310\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-51-1.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4917\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cstrong\u003e\u003ca href=\"https://youtu.be/isWxfa3PeHU?t=1310\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTime-stamped video\u003c/a\u003e\u003c/strong\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-52.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4901\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-373fa05094c0e112a9fdeebb08ab3bef\" style=\"color:#187d58\"\u003e\u003cstrong\u003ePrivate key received!\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cem\u003eTo search for the\u0026nbsp;\u003cstrong\u003eSignature Malleability vulnerability, as a threat prevention for your own\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eBitcoin\u003c/strong\u003e\u0026nbsp;and\u0026nbsp;\u003cstrong\u003eEthereum\u003c/strong\u003e\u0026nbsp;cryptocurrency wallet,\u0026nbsp;we can use and apply various machine learning methods to examples\u003c/em\u003e\u0026nbsp;.\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003eLet’s use the list from\u0026nbsp;\u0026nbsp;\u003ca href=\"https://github.com/demining/Tutorials-Power-AI\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e“Tutorials Power AI”\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;\u0026nbsp;a widely used category of artificial intelligence to introduce business in various fields of cryptanalysis and cryptography in general.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eInstallation command:\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-3871e28c4f03e855cbfa67e59f0896b8\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003egit clone https://github.com/demining/Tutorials-Power-AI.git\n\ncd Tutorials-Power-AI/\n\npython tutorials.py\n\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/process.gif\" alt=\"Signature Malleability: A study of the vulnerability of a forged signature using a decodable Bitcoin Wallet file\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-1024x272.png\" alt=\"Signature Malleability: A study of the vulnerability of a forged signature using a decodable Bitcoin Wallet file\" class=\"wp-image-5654\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003ca href=\"https://bitcoinchatgpt.org/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eBitcoinChatGPT\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;\u0026nbsp;is an innovative AI-powered chatbot that helps users find vulnerabilities in Bitcoin cryptocurrency transactions. BitcoinChatGPT benefits and classifications give you the ability to check your Bitcoin address for various crypto wallet attack schemes. Machine learning based on cryptanalysis gives us the full ability to investigate various attacks on the algorithms used in the Bitcoin ecosystem. Bitcoin Wallet private key extraction tools are widely popular, where BitcoinChatGPT serves as an important and useful resource for cybersecurity.\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\"\u003eExploiting the CVE-2024-42461: Signature Malleability vulnerability in the Elliptic library to create a Raw transaction using the BitcoinChatGPT machine learning process\u003c/h2\u003e\n\n\n\n\u003cp class=\"has-medium-font-size\"\u003eLet’s consider the construction of the structure of a vulnerable\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/RawTX.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eRaw\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;transaction in which the\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://bitcoinchatgpt.org/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBitcoinChatGPT module is used\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-full\"\u003e\u003ca href=\"https://www.youtube.com/watch?v=u7vD01x8Os8\"\u003e\u003cimg loading=\"lazy\" decoding=\"async\" width=\"664\" height=\"380\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-2.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-3039\" srcset=\"https://cryptodeeptech.ru/wp-content/uploads/2024/11/image-2.png 664w, https://cryptodeeptech.ru/wp-content/uploads/2024/11/image-2-300x172.png 300w\" sizes=\"auto, (max-width: 664px) 100vw, 664px\"\u003e\u003c/a\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp class=\"has-medium-font-size\"\u003e\u003cstrong\u003eLet’s open the Google Colab version:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://colab.research.google.com/drive/1YGZiPtgY0vPQ3PwUvbAjQW8LcErVHRsT\"\u003ehttps://colab.research.google.com/drive/1YGZiPtgY0vPQ3PwUvbAjQW8LcErVHRsT\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-d67d73b1c19c14b84d2ec63394e449b0\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003eState of a vulnerable transaction in Bitcoin:\n\n01000000\n....01\n........0dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935\n............00000000\n........8b483045\n....0221\n...........00\n...........97255916a3cc4f69d4fa16f68219d0b1798d392fb0dce5fb0a358510df8cabe0\n....0220\n........1014656120e0a6e7c8c4a79ee22b3cdd4f55435e3e9bf3ab7287ae16858dd9d5\n.....0141\n.....049b4069d8237fae8f2417c71c5512ec1b0547b5597474480cc28ea1bbfeecaab8b90fdec161ad6ef4378f274a60b900452431533596bf3bd23e01202ebf679461\n....ffffffff\n01\n....d204000000000000\n........1976\n............a914\n........d77522a2b18e0064aba02ca7f864a5bb22998259\n....88ac\n00000000\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-16-1024x670.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4734\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s combine all the output values ​​into one common string using the Python script\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/combinex.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ecombinex.py\u003c/a\u003e\u0026nbsp;:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-43bf0e87707eb97a009fefbcb84c8f1d\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e01000000010dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935000000008b48304502210097255916a3cc4f69d4fa16f68219d0b1798d392fb0dce5fb0a358510df8cabe002201014656120e0a6e7c8c4a79ee22b3cdd4f55435e3e9bf3ab7287ae16858dd9d50141049b4069d8237fae8f2417c71c5512ec1b0547b5597474480cc28ea1bbfeecaab8b90fdec161ad6ef4378f274a60b900452431533596bf3bd23e01202ebf679461ffffffff01d2040000000000001976a914d77522a2b18e0064aba02ca7f864a5bb2299825988ac00000000\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp class=\"has-medium-font-size\"\u003e\u003cstrong\u003eLet’s open the BlockCypher option\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e\u003ca href=\"https://live.blockcypher.com/btc/decodetx\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e“Decode A Transaction”\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;:\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://live.blockcypher.com/btc/decodetx\"\u003ehttps://live.blockcypher.com/btc/decodetx\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-1-1024x525.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4697\"\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 is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp class=\"has-medium-font-size\"\u003e\u003cstrong\u003eAfter decoding the vulnerable Bitcoin Raw transaction we get the result:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-151e1505683a60a585cd25dd20e6800f\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e{\n    \"addresses\": [\n        \"1QiERrMcv6mtGk4F1TVz4sRp9dFfXTQpK\",\n        \"1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\"\n    ],\n    \"block_height\": -1,\n    \"block_index\": -1,\n    \"confirmations\": 0,\n    \"double_spend\": false,\n    \"fees\": 2606688996428,\n    \"hash\": \"a5828ec5775b967c36ab5c6a0184aaa52fd64e6650d07287cc7688266c6dbb28\",\n    \"inputs\": [\n        {\n            \"addresses\": [\n                \"1QiERrMcv6mtGk4F1TVz4sRp9dFfXTQpK\"\n            ],\n            \"age\": 344419,\n            \"output_index\": 0,\n            \"output_value\": 2606688997662,\u003c/strong\u003e\n\u003cstrong\u003e            \"prev_hash\": \"35591e5c7f4f1f0e4d81748042f2a4b7dcae3ae01027f361cad7c8746369bc0d\",\u003c/strong\u003e\n\u003cstrong\u003e.......\n.......\n.......\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp class=\"has-medium-font-size\"\u003e\u003cstrong\u003ePay attention to Bitcoin HASH160:\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003ed77522a2b18e0064aba02ca7f864a5bb22998259\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-9.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4710\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/dfc7da9a6b41d72253bfcb6ae6da2718de7d9b87/36SignatureMalleability/DecodeRawTX.txt#L31\"\u003ehttps://github.com/demining/CryptoDeepTools/blob/dfc7da9a6b41d72253bfcb6ae6da2718de7d9b87/36SignatureMalleability/DecodeRawTX.txt#L31\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://coinbin.ru/#verify\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTransaction Script\u003c/a\u003e\u003c/h2\u003e\n\n\n\n\u003ch5 class=\"wp-block-heading has-text-align-center\"\u003eThe above script has been decoded\u003c/h5\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eBitcoinChatGPT\u003c/strong\u003e\u0026nbsp;creates a transaction structure using\u0026nbsp;\u003ccode\u003e\u003cstrong\u003eHASH\u003c/strong\u003e\u003c/code\u003ethe public key, where we see that Bitcoin address:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://btc1.trezor.io/address/1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;sends\u0026nbsp;\u003cstrong\u003e\u003ccode\u003e1234 satoshi\u003c/code\u003e\u003c/strong\u003eto the same address within its network.\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-2-1024x377.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4699\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eBitcoin HASH160 was generated using Python Script:\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/wif_to_hash160.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ewif_to_hash160.py\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-3.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4701\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/DecodeRawTX.txt#L31\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ed77522a2b18e0064aba02ca7f864a5bb22998259\u003c/strong\u003e\u003c/a\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-4-1024x619.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4703\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/wif_to_hash160.py\"\u003ehttps://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/wif_to_hash160.py\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp class=\"has-medium-font-size\"\u003e\u003cstrong\u003eQuestion – Answer:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-5-1024x539.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4704\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-6-1024x584.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4705\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-7-1024x606.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4706\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003eFinally, the\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/BitcoinChatGPT/Signature-Malleability-Vulnerability-Algorithm/blob/main/BitcoinChatGPT_%E2%84%965_Signature_Malleability_Vulnerability_Algorithm.ipynb\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBitcoinChatGPT\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;module outputs the response to the file:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/KEYFOUND.privkey\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eKEYFOUND.privkey\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;storing the private key in two most used formats\u0026nbsp;\u003cstrong\u003eHEX \u0026amp; WIF\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-8-1024x669.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4707\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/KEYFOUND.privkey\"\u003e\u003cstrong\u003ehttps://github.com/demining/CryptoDeepTools/blob/main/36SignatureMalleability/KEYFOUND.privkey\u003c/strong\u003e\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-12acbb3a0b53da0e68297d79657e6f80\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e============================= KEYFOUND.privkey =============================\n\nPrivate Key HEX: 0x17e96966f15a56993e13f8c19ce34a99111ad768a051d9febc24b6d48cae1951\n\nPrivate Key WIF: 5HzpNjEsxrpxPFqBKaoRSnFeq7RP57mvzwgoQFVtAJNZBpLVyur\n\nBitcoin Address: 1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\n\nBalance: 21.25292140 BTC\n\n============================= KEYFOUND.privkey =============================\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 has-text-align-center\"\u003e\u003ca href=\"https://youtu.be/nWU2c2haVoA\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBitcoinChatGPT №5 Signature Malleability Vulnerability Algorithm\u003c/a\u003e\u003c/h2\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-full\"\u003e\u003ca href=\"https://www.youtube.com/watch?v=nWU2c2haVoA\"\u003e\u003cimg loading=\"lazy\" decoding=\"async\" width=\"667\" height=\"391\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-3(1).png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-3042\" srcset=\"https://cryptodeeptech.ru/wp-content/uploads/2024/11/image-3.png 667w, https://cryptodeeptech.ru/wp-content/uploads/2024/11/image-3-300x176.png 300w\" sizes=\"auto, (max-width: 667px) 100vw, 667px\"\u003e\u003c/a\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\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\"\u003eVulnerable Raw Transaction\u003c/h2\u003e\n\n\n\n\u003cp\u003eLet’s create a vulnerable Raw transaction from the received data using the\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/smartibase/Broadcast-Bitcoin-Transaction\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBroadcast Bitcoin Transaction repository\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eDownload and install the source code, open the terminal and run the command:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-ed1ed2d6bd8eb54429f361c28733fbae\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003egit clone https://github.com/smartibase/Broadcast-Bitcoin-Transaction.git\n\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eCatalog:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-37c252389923970f49833153c041c31d\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ecd Broadcast-Bitcoin-Transaction\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s install three important libraries:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003ca href=\"https://pypi.org/project/zmq/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ezmq\u003c/strong\u003e\u003c/a\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ca href=\"https://pypi.org/project/urllib3/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eurllib3\u003c/strong\u003e\u003c/a\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ca href=\"https://pypi.org/project/requests/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003erequests\u003c/strong\u003e\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cfigure class=\"wp-block-image\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-8-1024x495.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-4733\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ca href=\"https://github.com/smartibase/Broadcast-Bitcoin-Transaction/blob/main/requirements.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003erequirements.txt\u003c/strong\u003e\u003c/a\u003e\u003c/figcaption\u003e\u003c/figure\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s run the command:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-c3638457a19a8e59dfd773c6eeb0aa38\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003epip install -r requirements.txt\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eLet’s open the main file in\u0026nbsp;\u003ca href=\"https://keyhunters.ru/the-benefits-of-the-popular-notepad-program/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eNotepad\u0026nbsp;\u003c/a\u003e\u003ca href=\"https://keyhunters.ru/the-benefits-of-the-popular-notepad-program/\"\u003e++\u003c/a\u003e\u0026nbsp;and make a small change to the Python Script code:\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/smartibase/Broadcast-Bitcoin-Transaction/blob/main/main.py\" target=\"_blank\" rel=\"noreferrer noopener\"\u003emain.py\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-adceca3e50bddbaa961145a54a133425\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003efrom io import BytesIO\nfrom secp256k1 import *\nfrom sighash import *\n\npk = PrivateKey.parse(\"5HzpNjEsxrpxPFqBKaoRSnFeq7RP57mvzwgoQFVtAJNZBpLVyur\")\npk.address()\ntx = bytes.fromhex(\"35591e5c7f4f1f0e4d81748042f2a4b7dcae3ae01027f361cad7c8746369bc0d\")\nindex = 0\nsend = \"1LeEbwu667oPtQC5dKiGiysUjFM3mQaxpw\"\ntx_in = TxIn(tx, index, b'', 0xffffffff)\ntx_in._script_pubkey = Tx.get_address_data(pk.address())['script_pubkey']\ntx_in._value = 2345\ntx_ins = [ tx_in ]\ntx_outs = [\n    TxOut(1234, Tx.get_address_data(send)['script_pubkey'].serialize())\n]\ntx = Tx(1, tx_ins, tx_outs, 0, testnet=True)\nsignature(tx, 0, pk)\ntx.serialize().hex()\nprint(tx.serialize().hex())\nf = open(\"RawTX.txt\", 'w')\nf.write(\"\" + tx.serialize().hex() + \"\" + \"\\n\")\nf.close()\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s run the command:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-ba63856e6306b76b5e1e36b8e2c44d96\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003epython main.py\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp class=\"has-text-align-center has-medium-font-size\"\u003e\u003cstrong\u003e\u003ca href=\"https://www.youtube.com/watch?v=8B2LKMBsVSE\"\u003eVulnerable transaction created\u0026nbsp;\u003c/a\u003e\u003ca href=\"https://www.youtube.com/watch?v=8B2LKMBsVSE\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e!\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003cp\u003e\u003cstrong\u003eLet’s open the RawTX file in the directory:\u003c/strong\u003e\u003c/p\u003e\n\u003c/blockquote\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-43bf0e87707eb97a009fefbcb84c8f1d\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e01000000010dbc696374c8d7ca61f32710e03aaedcb7a4f2428074814d0e1f4f7f5c1e5935000000008b48304502210097255916a3cc4f69d4fa16f68219d0b1798d392fb0dce5fb0a358510df8cabe002201014656120e0a6e7c8c4a79ee22b3cdd4f55435e3e9bf3ab7287ae16858dd9d50141049b4069d8237fae8f2417c71c5512ec1b0547b5597474480cc28ea1bbfeecaab8b90fdec161ad6ef4378f274a60b900452431533596bf3bd23e01202ebf679461ffffffff01d2040000000000001976a914d77522a2b18e0064aba02ca7f864a5bb2299825988ac00000000\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 has-text-align-center\"\u003eThe order of actions in the video:\u003c/h2\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-full\"\u003e\u003ca href=\"https://www.youtube.com/watch?v=8B2LKMBsVSE\"\u003e\u003cimg loading=\"lazy\" decoding=\"async\" width=\"671\" height=\"387\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-4.png\" alt=\"Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures\" class=\"wp-image-3043\" srcset=\"https://cryptodeeptech.ru/wp-content/uploads/2024/11/image-4.png 671w, https://cryptodeeptech.ru/wp-content/uploads/2024/11/image-4-300x173.png 300w\" sizes=\"auto, (max-width: 671px) 100vw, 671px\"\u003e\u003c/a\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003e\u003cem\u003eIt was this vulnerable RawTX that we looked at at the beginning of this article:\u003c/em\u003e\u003c/strong\u003e\u0026nbsp;\u003ca href=\"https://cryptodeeptool.ru/signature-malleability/#aa553e57-81fe-4c3c-98dd-0d1b60ea55ee-link\"\u003e↩︎\u003c/a\u003e\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Research into Signature Malleability and Private Key Compromise in Bitcoin Signatures - CRYPTO DEEP TECH_files/image-20.png\" alt=\"This image has an empty alt attribute; its file name is image-19-1024x422.png\" class=\"wp-image-4773\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cstrong\u003eRawTX\u003c/strong\u003e\u0026nbsp;decoding process\u0026nbsp;\u0026nbsp;\u0026nbsp;using tool\u0026nbsp;\u003ca href=\"https://github.com/smartibase/Broadcast-Bitcoin-Transaction/tree/main/decoderaw\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003edecoderaw\u003c/strong\u003e\u003c/a\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp class=\"has-medium-font-size\"\u003e\u003cem\u003eAs we know from\u0026nbsp;\u003ca href=\"https://keyhunters.ru/what-is-prompt-answers-and-how-is-it-related-to-machine-learning-and-artificial-intelligence/\"\u003ethe prompt responses of the\u0026nbsp;\u003c/a\u003e\u003ca href=\"https://colab.research.google.com/drive/1YGZiPtgY0vPQ3PwUvbAjQW8LcErVHRsT\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eBitcoinChatGPT\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;module ,\u0026nbsp;the Signature Malleability Vulnerability Algorithm can be used to solve complex cryptographic problems.\u003c/em\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eConclusion\u003c/h2\u003e\n\n\n\n\u003cp\u003eThere are many methods to detect and prevent counterfeit signatures in the Bitcoin network. These methods range from simple solutions such as increasing the number of confirmations to more complex anomaly analysis systems and regular security protocol updates. Effective protection requires a comprehensive approach to network security and constant monitoring of new threats. Counterfeit signatures can lead to fraudulent transactions and loss of funds. The main methods used to detect and prevent such attacks are:\u003c/p\u003e\n\n\n\n\u003cblockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"\u003e\n\u003ch3 class=\"wp-block-heading\"\u003e1. Increasing the number of confirmations\u003c/h3\u003e\n\n\n\n\u003cp\u003eOne of the simplest ways to protect against counterfeit signatures is to increase the number of confirmations of a transaction before it is finally accepted. It is recommended to wait for at least six confirmations to reduce the likelihood of a successful attack. This ensures that the transaction was included in the block and cannot be reversed.\u003c/p\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003e2. Analysis of blocks and transactions\u003c/h3\u003e\n\n\n\n\u003cp\u003eMining software and network nodes analyze blocks and transactions for conflicts and anomalies. This includes checking the signature for compliance with the format, as well as checking the values ​​of\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003er\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;\u0026nbsp;and\u0026nbsp;\u0026nbsp;\u003cem\u003e\u003cstrong\u003es\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;\u0026nbsp;for acceptable ranges. If the values ​​are outside the acceptable ranges, the transaction may be rejected.\u003c/p\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003e3. Implementation of anomaly analysis systems\u003c/h3\u003e\n\n\n\n\u003cp\u003eUsing anomaly analysis systems can identify suspicious transactions and blockchains. These systems can use machine learning algorithms to detect unusual behavior in the network, which may indicate attempts to forge signatures.\u003c/p\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003e4. Network monitoring software\u003c/h3\u003e\n\n\n\n\u003cp\u003eTools such as\u0026nbsp;\u003ca href=\"https://keyhunters.ru/sybil-and-eclipse-attacks/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eWireshark\u003c/a\u003e\u0026nbsp;can be used to analyze network traffic and identify suspicious activity. Monitoring network traffic can help identify\u0026nbsp;\u003ca href=\"https://keyhunters.ru/sybil-and-eclipse-attacks/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSybil\u003c/a\u003e\u0026nbsp;or\u0026nbsp;\u003ca href=\"https://keyhunters.ru/sybil-and-eclipse-attacks/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eEclipse\u003c/a\u003e\u0026nbsp;attacks that can be used to manipulate transactions.\u003c/p\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003e5. Regularly update security protocols\u003c/h3\u003e\n\n\n\n\u003cp\u003eRegularly updating software and security protocols helps to eliminate known vulnerabilities, such as the\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/deserialize-signature-vulnerability-bitcoin/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eDeserializeSignature\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;vulnerability , which allows attackers to create invalid signatures. Updates should include fixes for all known vulnerabilities and security improvements.\u003c/p\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003e6. Multi-level confirmation\u003c/h3\u003e\n\n\n\n\u003cp\u003eUsing multiple levels of transaction confirmation can improve network security. This could include additional checks by nodes or using third-party services to verify signatures.\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\"\u003eReferences:\u003c/h2\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cem\u003e\u003ca href=\"https://cryptodeeptech.ru/doc/mertens.disproof.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eOdlyzko, Andrew; te Reile, Herman JJ «Disproving Mertens Conjecture»\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;Journal for Pure and Applied Mathematics\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://cryptodeeptech.ru/doc/lll25_Simon.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eD. Simon (2007). «Selected applications of LLL in number theory»\u003c/a\u003e\u003c/s","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdemining%2Fsignature-malleability","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdemining%2Fsignature-malleability","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdemining%2Fsignature-malleability/lists"}