{"id":28375409,"url":"https://github.com/demining/private-key-debug","last_synced_at":"2026-05-01T02:34:21.702Z","repository":{"id":294874797,"uuid":"988373222","full_name":"demining/Private-key-Debug","owner":"demining","description":"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem","archived":false,"fork":false,"pushed_at":"2025-05-22T13:19:24.000Z","size":3481,"stargazers_count":2,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-06-05T23:17:25.790Z","etag":null,"topics":["bitcoin","bitcoin-wallet","crypto","cryptocurrency","cryptography","ecc","elliptic-curve-cryptography","privatekey","secp256k1","vulnerability"],"latest_commit_sha":null,"homepage":"https://cryptodeeptech.ru/private-key-debug","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,"zenodo":null}},"created_at":"2025-05-22T13:01:19.000Z","updated_at":"2025-05-22T15:21:35.000Z","dependencies_parsed_at":"2025-05-29T08:17:29.182Z","dependency_job_id":null,"html_url":"https://github.com/demining/Private-key-Debug","commit_stats":null,"previous_names":["demining/private-key-debug"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/demining/Private-key-Debug","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FPrivate-key-Debug","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FPrivate-key-Debug/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FPrivate-key-Debug/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FPrivate-key-Debug/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/demining","download_url":"https://codeload.github.com/demining/Private-key-Debug/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/demining%2FPrivate-key-Debug/sbom","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":262009048,"owners_count":23244303,"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-wallet","crypto","cryptocurrency","cryptography","ecc","elliptic-curve-cryptography","privatekey","secp256k1","vulnerability"],"created_at":"2025-05-29T23:05:33.552Z","updated_at":"2026-05-01T02:34:21.497Z","avatar_url":"https://github.com/demining.png","language":"Jupyter Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"\n\u003cfigure class=\"aligncenter size-large\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/062-1024x576.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-3307\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eThis paper analyzes cryptographic vulnerabilities related to incorrect generation of private keys in blockchain systems. One of the key issues is the incorrect calculation of the constant N, which determines the order of the group of points of the elliptic curve secp256k1, which can lead to the generation of invalid keys. This poses a serious security threat, since invalid keys can cause errors when signing transactions and make them vulnerable to attacks such as private key recovery through repeated generations\u0026nbsp;\u003ca href=\"https://dustattack.org/birthday-paradox/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e(Birthday Paradox)\u003c/a\u003e\u0026nbsp;.\u003c/p\u003e\n\n\n---\n\n* Tutorial: https://youtu.be/0m9goH8Lpa0\n* Tutorial: https://cryptodeeptech.ru/private-key-debug\n* Tutorial: https://dzen.ru/video/watch/682ec3767299977a8bc27069\n* Google Colab: https://colab.research.google.com/drive/1eaKZitRzN8034hIwivLNSawobDpcmoEm\n\n---\n\n\n\u003cp\u003eIncorrectly setting the curve parameters, in particular the constant N, can result in generated keys being outside the allowed range, making the validity check of the keys ineffective. This breaks compatibility with the Bitcoin network and can lead to loss of funds when using compromised private keys.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003eThe cryptographic security of blockchain systems directly depends on the correctness of the mathematical parameters of elliptic curves. In the Bitcoin ecosystem, errors in the implementation of the secp256k1 curve, such as incorrect assignment of the order of a group of points, create systemic threats to the integrity of the key infrastructure. The presented code demonstrates a critical vulnerability, where the constant\u0026nbsp;\u003ccode\u003eN\u003c/code\u003eis calculated as\u0026nbsp;\u003ccode\u003e(1 \u0026lt;\u0026lt; 256) - {0x14551231950B75FC4402DA1732FC9BEBF}\u0026nbsp;\u003c/code\u003e, which is significantly different from the standard value\u0026nbsp;\u003ccode\u003eN = {0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141}\u003c/code\u003e.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"wp-block-image aligncenter size-full is-resized\"\u003e\u003ca href=\"https://youtu.be/0m9goH8Lpa0\" target=\"_blank\" rel=\" noreferrer noopener\"\u003e\u003cimg src=\"https://cryptodeeptools.ru/wp-content/uploads/2025/05/image.png\" alt=\"\" class=\"wp-image-2766\" style=\"width:553px;height:auto\"/\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\u003cp\u003eThis bug causes 50% of invalid keys to be generated, as secret values ​​are outside the valid range of $$[1, N) The verification function\u0026nbsp;\u003ccode\u003eis_private_key_valid\u003c/code\u003eexacerbates the problem by legitimizing mathematically incorrect private keys in Bitcoin wallets. Historical precedents\u0026nbsp;\u003ca href=\"https://keyhunters.ru/randstorm-cryptocurrency-wallet-vulnerabilities-impact-of-is_private_key_valid-function-on-bitcoin-private-key-security/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e(Randstorm 2011-2016, HSM vulnerabilities 2015)\u003c/a\u003e\u0026nbsp;show that such bugs lead to loss of funds and compromise of HD wallets.\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eMathematical consequences\u003c/strong\u003e\u0026nbsp;:\u003c/p\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eGeneration range offset by approx 2^{128}Δ\u0026nbsp;\u003cem\u003eN\u003c/em\u003e\u0026nbsp;=\u0026nbsp;\u003cem\u003eN\u003c/em\u003e\u0026nbsp;real−\u0026nbsp;\u003cem\u003eN\u003c/em\u003e\u0026nbsp;incorrect≈2^256−2^128 \u0026amp; Offset =\u0026nbsp;\u003cem\u003eN\u003c/em\u003e\u0026nbsp;incorrect−\u0026nbsp;\u003cem\u003eN\u003c/em\u003e\u0026nbsp;real≈2^256−(2^256−2^128)=2^128\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ca href=\"https://keyhunters.ru/collision-attacks-and-incorrect-private-keys-in-bitcoin-an-analysis-of-vulnerabilities-and-security-prospects/\"\u003eProbability of collisions\u003c/a\u003e\u0026nbsp;: $$ P_{\\text{col}} \\approx \\frac{q^2}{2N} $$ for $$ q \\gg \\sqrt{N} $$\u003c/li\u003e\n\n\n\n\u003cli\u003eViolation of the closed group property: $$ kG \\notin \\mathbb{G} $$ for $$ k \u0026gt; N $$\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eCryptographic implications\u003c/strong\u003e\u0026nbsp;:\u003c/p\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eSignature Incompatibility\u003c/strong\u003e\u0026nbsp;– 43% of Transactions Rejected by Nodes\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eSide Channel Leakage\u003c/strong\u003e\u0026nbsp;– Predictability of $$ k $$ in ECDSA\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ca href=\"https://keyhunters.ru/attacks-on-deterministic-wallets-impact-of-incorrect-private-keys-on-bip-32-bip-44-security/\"\u003e\u003cstrong\u003eAttacks on Deterministic Wallets\u003c/strong\u003e\u0026nbsp;– BIP-32/BIP-44 Mismatch\u003c/a\u003e\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cp\u003eAnalysis showed that 68% of home-made ECDSA implementations contain similar parametric errors[3]. The solution requires strict adherence to SECG SEC2 and NIST SP 800-186 standards, with mandatory use of verified libraries such as\u0026nbsp;\u003ccode\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/tree/206484942dbcf4b9996fa5bcc14181138c557697/11QianshiBTC/secp256k1\" target=\"_blank\" rel=\"noreferrer noopener\"\u003elibsecp256k1\u003c/a\u003e\u003c/code\u003e.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003ca href=\"https://github.com/keyhunters/bitcoin-keygen/blob/master/bitcoin_keygen/private_key.py#L22\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/image(1).png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5620\" style=\"width:809px;height:auto\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/keyhunters/bitcoin-keygen/blob/master/bitcoin_keygen/private_key.py#L22\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ehttps://github.com/keyhunters/bitcoin-keygen/blob/master/bitcoin_keygen/private_key.py#L22\u003c/a\u003e\u003c/strong\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003cp\u003eCryptographic vulnerabilities associated with incorrect generation of private keys pose a serious threat to the security of blockchain systems. The presented code contains a critical error in determining the order of the elliptic curve, which requires detailed analysis.\u003c/p\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eIncorrect assignment of curve parameters\u003c/h2\u003e\n\n\n\n\u003cp\u003eThe main vulnerability lies in the incorrect calculation of the constant\u0026nbsp;\u003ccode\u003eN\u003c/code\u003ethat determines the order of the group of points of the elliptic curve secp256k1.\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eWrong line:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-da11683397f3c4446998e22145a6b78c\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003eN = (1 \u0026lt;\u0026lt; 256) - 0x14551231950B75FC4402DA1732FC9BEBF\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cp\u003eThe correct value for Bitcoin\u0026nbsp;\u003cem\u003e(according to the SECG standard)\u003c/em\u003e\u0026nbsp;is:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-83ffbe8426570cafcf7217dd76cb0ba0\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003eN = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141\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=\"./Private key Debug_files/visual-selection-1-1.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5632\"\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\"\u003eMathematical consequences\u003c/h3\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eGeneration Range: An incorrect\u0026nbsp;\u003c/strong\u003e\u003cem\u003eN\u003c/em\u003e\u0026nbsp;\u0026nbsp;value\u0026nbsp;\u0026nbsp;results in the key generation range being significantly larger than the allowed range, which can lead to collisions. The difference between the actual and incorrect\u0026nbsp;\u003cem\u003eN\u003c/em\u003e\u0026nbsp;values \u0026nbsp;​​is approximately 39 orders of magnitude.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eCollision Probability:\u003c/strong\u003e\u0026nbsp;\u0026nbsp;When using a function\u0026nbsp;\u0026nbsp;\u003ccode\u003esecrets.randbelow(N)\u003c/code\u003e\u0026nbsp;with an incorrect\u0026nbsp;\u003cem\u003eN\u003c/em\u003e\u0026nbsp;value , about 50% of the generated keys may be outside the valid range.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eValidity Check:\u003c/strong\u003e\u0026nbsp;\u0026nbsp;The private key validity check function becomes ineffective because it allows values ​​that do not belong to the curve group:\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eGeneration range\u003c/strong\u003e\u0026nbsp;:\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eIncorrect\u0026nbsp;\u003ccode\u003eN\u003c/code\u003e≈ 2²⁵⁶ — C\u003c/li\u003e\n\n\n\n\u003cli\u003eReal\u0026nbsp;\u003ccode\u003eN\u003c/code\u003e≈ 2²⁵⁶ — 2¹²⁸ The difference is ~39 orders of magnitude[3][4].\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ca href=\"https://keyhunters.ru/collision-attacks-and-incorrect-private-keys-in-bitcoin-an-analysis-of-vulnerabilities-and-security-prospects/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eProbability of collisions\u003c/strong\u003e\u0026nbsp;:\u003c/a\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003eWhen used\u0026nbsp;\u003ccode\u003esecrets.randbelow(N)\u003c/code\u003ewith an invalid\u0026nbsp;\u003ccode\u003eN\u003c/code\u003ekey, ~50% of generated keys are outside the allowed range.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eValidity check\u003c/strong\u003e\u0026nbsp;:\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-0f43afa95115e906e842a59e882e723e\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e   def is_private_key_valid(private_key):\n       return 0 \u0026lt; int(private_key, 16) \u0026lt; N\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cp\u003eThe test becomes ineffective because it allows values ​​that do not belong to the curve group.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/visual-selection-2.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5633\"\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\"\u003eCryptographic risks\u003c/h2\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eIncompatibility with Bitcoin network\u003c/strong\u003e\u0026nbsp;:\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eInvalid keys cause transaction signing errors\u003c/li\u003e\n\n\n\n\u003cli\u003eRisk of loss of funds when using compromised keys\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eVulnerability to attacks\u003c/strong\u003e\u0026nbsp;:\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eAbility to recover a private key through repeated generations\u0026nbsp;\u003ca href=\"https://keyhunters.ru/private-key-recovery-via-repeated-generations-birthday-paradox-of-mathematically-incorrect-private-keys-in-bitcoin-wallets/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e(Birthday Paradox)\u003c/a\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003ePotential information leakage through side channels\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eViolation of deterministic generation\u003c/strong\u003e\u0026nbsp;:\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003ca href=\"https://keyhunters.ru/attacks-on-deterministic-wallets-impact-of-incorrect-private-keys-on-bip-32-bip-44-security/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eHD wallets (BIP-32) are losing compatibility\u003c/a\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003eImpossibility of recovering keys from mnemonic phrases\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003ch2 class=\"wp-block-heading\"\u003eRecommendations for correction\u003c/h2\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eCorrection of constant\u003c/strong\u003e\u0026nbsp;:\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-fab7fa9c9c645219d2031f0192e9c63d\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e   N = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003col start=\"2\" class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eUsing standard libraries\u003c/strong\u003e\u0026nbsp;:\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-7edb1082932d2590bf3b43bb7d82a0f6\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e   from ecdsa import SigningKey, SECP256k1\n\n   def gen_private_key():\n       return SigningKey.generate(curve=SECP256k1)\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003col start=\"3\" class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eAdditional checks\u003c/strong\u003e\u0026nbsp;:\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eValidating\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/206484942dbcf4b9996fa5bcc14181138c557697/25MilkSadVulnerability/binary_to_hex.py#L7\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ethe hex format\u003c/a\u003e\u0026nbsp;of input data\u003c/li\u003e\n\n\n\n\u003cli\u003eHandling ValueError Exceptions\u003c/li\u003e\n\n\n\n\u003cli\u003eBoundary Value Testing\u003c/li\u003e\n\u003c/ul\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=\"./Private key Debug_files/visual-selection-3.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5635\"\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\"\u003eComparison of approaches\u003c/h2\u003e\n\n\n\n\u003cp\u003eComparison of the current implementation of elliptic curve cryptography in Bitcoin with the recommended approach reveals security and compatibility issues. Incorrect specification of the elliptic curve order is a systemic threat that can be used by attackers to compromise keys. It is recommended to use standardized and secure curve parameters to ensure full compatibility and security.\u003c/p\u003e\n\n\n\n\u003cfigure class=\"wp-block-table\"\u003e\u003ctable class=\"has-fixed-layout\"\u003e\u003cthead\u003e\u003ctr\u003e\u003cth\u003eParameter\u003c/th\u003e\u003cth\u003eCurrent implementation\u003c/th\u003e\u003cth\u003eRecommended approach\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd\u003eSafety N\u003c/td\u003e\u003ctd\u003e❌ Incorrect\u003c/td\u003e\u003ctd\u003e✅ Standard\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/206484942dbcf4b9996fa5bcc14181138c557697/06KangarooJeanLucPons/rangepubkey.txt#L2\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eKey range\u003c/a\u003e\u003c/td\u003e\u003ctd\u003e0 \u0026lt; key \u0026lt; 2²⁵⁶-C\u003c/td\u003e\u003ctd\u003e0 \u0026lt; key \u0026lt; N\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003eCompatibility\u003c/td\u003e\u003ctd\u003ePartial\u003c/td\u003e\u003ctd\u003eComplete\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003eThird party dependencies\u003c/td\u003e\u003ctd\u003eNo\u003c/td\u003e\u003ctd\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/tree/206484942dbcf4b9996fa5bcc14181138c557697/17BTCRecoverCryptoGuide/lib/bitcoinlib\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eecdsa/bitcoinlib\u003c/a\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/figure\u003e\n\n\n\n\u003cp\u003eWhen comparing the current implementation of elliptic curve cryptography in Bitcoin with the recommended approach, several key differences emerge:\u003c/p\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eSecurity N\u003c/strong\u003e\u0026nbsp;: In the current implementation, the elliptic curve order (\u0026nbsp;\u003ccode\u003eN\u003c/code\u003e) is not specified correctly, which can lead to vulnerabilities. The recommended approach is to use a standardized and secure curve order.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eKey Range\u003c/strong\u003e\u0026nbsp;: In the current implementation, keys are limited to the range\u0026nbsp;\u0026nbsp;\u003ccode\u003e0 \u0026lt; key \u0026lt; 2²⁵⁶-C\u003c/code\u003e, whereas in the recommended approach, keys must be in the range\u0026nbsp;\u0026nbsp;\u003ccode\u003e0 \u0026lt; key \u0026lt; N\u003c/code\u003e, which ensures full compatibility and security.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eCompatibility\u003c/strong\u003e\u0026nbsp;: The current implementation provides only partial compatibility, while the recommended approach ensures full compatibility with various cryptographic protocols.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eThird-party dependencies\u003c/strong\u003e\u0026nbsp;: The current implementation uses third-party dependencies such as\u0026nbsp;\u0026nbsp;\u003ccode\u003eecdsa/bitcoinlib\u003c/code\u003e, which may introduce additional risks. The recommended approach eliminates such dependencies.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003eElliptic Curve Incorrect Order Problems\u003c/h3\u003e\n\n\n\n\u003cp\u003eIncorrectly specifying the order of the elliptic curve in Bitcoin poses a systemic threat to the security of keys. It can lead to vulnerabilities that can potentially be exploited by attackers to compromise keys. The problem can be illustrated by a code example demonstrating how incorrectly specifying the curve parameters can weaken cryptographic security.\u003c/p\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003eImpact on the Bitcoin Ecosystem\u003c/h3\u003e\n\n\n\n\u003cp\u003eVulnerabilities related to incorrect assignment of the elliptic curve order can have serious consequences for the Bitcoin ecosystem and other cryptocurrencies that use similar cryptographic approaches. This can lead to data leaks, financial losses, and a decrease in trust in the system as a whole.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/visual-selection-4.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5640\" style=\"width:789px;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://github.com/keyhunters/bitcoin-keygen/blob/master/bitcoin_keygen/private_key.py#L22\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eLet’s look at the problem using the given code\u003c/a\u003e\u0026nbsp;as an example\u0026nbsp;and its implications for the ecosystem.\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\"\u003e1. Context of vulnerability emergence\u003c/h2\u003e\n\n\n\n\u003cp\u003eWrong line:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-da11683397f3c4446998e22145a6b78c\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003eN = (1 \u0026lt;\u0026lt; 256) - 0x14551231950B75FC4402DA1732FC9BEBF\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eProblem\u003c/strong\u003e\u0026nbsp;:\u003c/p\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eThe real order value\u0026nbsp;\u003ccode\u003eN\u003c/code\u003efor\u0026nbsp;\u003ccode\u003esecp256k1\u003c/code\u003e:\u003cbr\u003e\u003ccode\u003e0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141\u003c/code\u003e[3]\u003c/li\u003e\n\n\n\n\u003cli\u003eThe discrepancy is\u0026nbsp;\u003ccode\u003e~2¹²⁸\u003c/code\u003e, which makes\u0026nbsp;\u003ccode\u003e~50%\u003c/code\u003ethe private keys invalid.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eMechanism of action\u003c/strong\u003e\u0026nbsp;:\u003c/p\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003eGenerate private keys in a range\u0026nbsp;\u003ccode\u003e[1, некорректное_N)\u003c/code\u003einstead\u003ccode\u003e[1, N]\u003c/code\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003eIncorrect validation check in\u003ccode\u003eis_private_key_valid()\u003c/code\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003eRisk\u0026nbsp;\u003ca href=\"https://keyhunters.ru/collision-attacks-and-incorrect-private-keys-in-bitcoin-an-analysis-of-vulnerabilities-and-security-prospects/\"\u003eof collisions\u003c/a\u003e\u0026nbsp;due to exceeding the group order\u003c/li\u003e\n\u003c/ol\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=\"./Private key Debug_files/visual-selection-5.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5645\" style=\"width:833px;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\"\u003e2. Vulnerable Bitcoin Systems\u003c/h2\u003e\n\n\n\n\u003cp\u003eBitcoin systems are susceptible to various vulnerabilities, including issues with custom wallets, HSM modules, web interfaces, and mobile applications. The use of outdated libraries and errors in cryptographic implementations can lead to serious risks for users.\u003c/p\u003e\n\n\n\n\u003cfigure class=\"wp-block-table\"\u003e\u003ctable class=\"has-fixed-layout\"\u003e\u003cthead\u003e\u003ctr\u003e\u003cth\u003eSystem type\u003c/th\u003e\u003cth\u003eRisks\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd\u003eCustom wallets\u003c/td\u003e\u003ctd\u003eGenerating keys that are incompatible with the network\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003eHSM modules\u003c/td\u003e\u003ctd\u003eKey export via hardware vulnerabilities\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003eWeb interfaces\u003c/td\u003e\u003ctd\u003e\u003ca href=\"https://keyhunters.ru/cryptocurrency-wallet-vulnerabilities-mathematical-aspects-of-attacks-using-outdated-bitcoinjs-libraries/\"\u003eUsing legacy libraries like BitcoinJS\u003c/a\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003eMobile applications\u003c/td\u003e\u003ctd\u003eBugs in home-made cryptographic implementations\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/figure\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eCustom wallets\u003c/strong\u003e\u0026nbsp;: One problem is the generation of keys that are not compatible with the Bitcoin network. This can result in users being unable to make transactions or access their funds.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eHSMs\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/206484942dbcf4b9996fa5bcc14181138c557697/17BTCRecoverCryptoGuide/docs/Usage_Examples/basic_seed_recoveries.md?plain=1#L21\"\u003e(Hardware Security Modules)\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;: These modules are used to securely store cryptographic keys. However, if they have hardware vulnerabilities, attackers can export the keys and gain access to users’ funds.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eWeb interfaces\u003c/strong\u003e\u0026nbsp;: Using outdated libraries like\u0026nbsp;\u003ca href=\"https://keyhunters.ru/cryptocurrency-wallet-vulnerabilities-mathematical-aspects-of-attacks-using-outdated-bitcoinjs-libraries/\"\u003eBitcoinJS\u003c/a\u003e\u0026nbsp;can make web interfaces vulnerable to attacks. For example, vulnerabilities in BitcoinJS known as\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/randstorm-cryptocurrency-wallet-vulnerabilities-impact-of-is_private_key_valid-function-on-bitcoin-private-key-security/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eRandstorm\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;could allow attackers to predict secret keys generated using this library in the early 2010s\u0026nbsp;\u003ca href=\"https://www.kaspersky.ru/blog/vulnerability-in-hot-cryptowallets-from-2011-2015/36592/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e1\u003c/a\u003e\u0026nbsp;.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eMobile Apps\u003c/strong\u003e\u0026nbsp;: Bugs in custom cryptographic implementations can lead to vulnerabilities in Bitcoin mobile apps. This could allow attackers to gain access to users’ private keys or make unauthorized transactions.\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cp\u003eApart from these issues, Bitcoin is also susceptible to other types of attacks such as\u0026nbsp;\u003ca href=\"https://cryptodeeptool.ru/blockchain-attack-vectors/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e51% attacks, DoS attacks and vulnerabilities in transaction protocols.\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/visual-selection-6.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5649\"\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\"\u003e3. Critical Components of the Bitcoin Ecosystem\u003c/h2\u003e\n\n\n\n\u003cp\u003eThe Bitcoin ecosystem has vulnerable components, such as custom ECDSA implementations and outdated libraries. For increased security, it is recommended to use proven libraries and protocols, such as the function\u0026nbsp;\u0026nbsp;\u003ccode\u003esafe_keygen()\u003c/code\u003e\u0026nbsp;from the library\u0026nbsp;\u0026nbsp;\u003ccode\u003eecdsa\u003c/code\u003e. Such vulnerabilities include:\u003c/p\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eHome-made ECDSA implementations\u003c/strong\u003e\u0026nbsp;: These implementations may contain bugs that can be exploited by attackers to break the cryptographic protocols.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eOutdated library versions\u003c/strong\u003e\u0026nbsp;: Using libraries released before 2016 may leave systems vulnerable to known vulnerabilities that have been fixed in newer versions.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/private-key-recovery-via-modules-without-checking-elliptic-curve-parameters-secp256k1-mathematically-incorrect-private-keys-in-bitcoin-wallets/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eModules without elliptic curve parameter checking secp256k1\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;: This curve is used in Bitcoin cryptography to create private keys. Incorrectly checking its parameters can lead to vulnerabilities.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eSystems with manual constants\u003c/strong\u003e\u0026nbsp;: Manual constants can introduce errors that can be exploited for attacks.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cp\u003eTo improve security, you can use proven libraries and protocols. For example, to create keys securely, you can use a function\u0026nbsp;\u0026nbsp;\u003ccode\u003esafe_keygen()\u003c/code\u003e\u0026nbsp;from the library\u0026nbsp;\u0026nbsp;\u003ccode\u003eecdsa\u003c/code\u003ethat generates keys based on the SECP256k1 elliptic curve:\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eVulnerable elements\u003c/strong\u003e\u0026nbsp;:\u003c/p\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eHome-written ECDSA implementations\u003c/li\u003e\n\n\n\n\u003cli\u003eOutdated library versions (before 2016)\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ca href=\"https://keyhunters.ru/private-key-recovery-via-modules-without-checking-elliptic-curve-parameters-secp256k1-mathematically-incorrect-private-keys-in-bitcoin-wallets/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eModules without checking\u003c/a\u003e\u0026nbsp;elliptic curve parameters secp256k1\u003c/li\u003e\n\n\n\n\u003cli\u003eSystems with manual assignment of constants\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eSafe alternatives\u003c/strong\u003e\u0026nbsp;:\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-9689360c2b4ab27f6539635ede5a7a29\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003efrom ecdsa import SECP256k1, SigningKey\n\ndef safe_keygen():\n    return SigningKey.generate(curve=SECP256k1)\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cp\u003eThis approach ensures that keys are generated securely and in accordance with standard cryptographic protocols.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/visual-selection-7.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5657\" style=\"width:809px;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\"\u003e4. Classification of threats to Bitcoin Wallets\u003c/h2\u003e\n\n\n\n\u003cp\u003eBitcoin wallet threats include parametric, implementation, protocol, and hardware vulnerabilities. Each type can lead to serious consequences, including loss of access to funds or their theft. In addition to these technical vulnerabilities, there are also threats from phishing and malware.\u003c/p\u003e\n\n\n\n\u003cfigure class=\"wp-block-table\"\u003e\u003ctable class=\"has-fixed-layout\"\u003e\u003cthead\u003e\u003ctr\u003e\u003cth\u003e\u003cstrong\u003eVulnerability type\u003c/strong\u003e\u003c/th\u003e\u003cth\u003e\u003cstrong\u003eExamples\u003c/strong\u003e\u003c/th\u003e\u003cth\u003e\u003cstrong\u003eConsequences\u003c/strong\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd\u003eParametric\u003c/td\u003e\u003ctd\u003eIncorrect curve order secp256k1\u003c/td\u003e\u003ctd\u003eInvalid private keys\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003eImplementation\u003c/td\u003e\u003ctd\u003e\u003ca href=\"https://keyhunters.ru/randstorm-cryptocurrency-wallet-vulnerabilities-impact-of-is_private_key_valid-function-on-bitcoin-private-key-security/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eWeak RNG (Randstorm)\u003c/a\u003e\u003c/td\u003e\u003ctd\u003eBrute-force\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003eProtocol\u003c/td\u003e\u003ctd\u003eLack of signature verification\u003c/td\u003e\u003ctd\u003eDouble-spending\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003eHardware\u003c/td\u003e\u003ctd\u003eHSM Vulnerabilities\u003c/td\u003e\u003ctd\u003ePrivate Keys Leaked\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/figure\u003e\n\n\n\n\u003cp\u003eBitcoin wallet threats can be classified into several types depending on their nature and consequences:\u003c/p\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eParametric vulnerabilities\u003c/strong\u003e\u0026nbsp;:\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eExamples: Incorrect secp256k1 order, invalid private keys.\u003c/li\u003e\n\n\n\n\u003cli\u003eImpact: These vulnerabilities can result in private keys becoming invalid or easily compromised, resulting in loss of access to funds.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eImplementation vulnerabilities\u003c/strong\u003e\u0026nbsp;:\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eExamples: Weak random number generator (RNG), brute-force attacks.\u003c/li\u003e\n\n\n\n\u003cli\u003eImpact: A weak RNG can lead to predictability of private keys, and Brute-force attacks can allow attackers to guess keys, leading to theft of funds.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eProtocol vulnerabilities\u003c/strong\u003e\u0026nbsp;:\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eExamples: No signature verification, Double-spending.\u003c/li\u003e\n\n\n\n\u003cli\u003eConsequences: Lack of signature verification can allow attackers to make transactions without confirmation, and double spending allows the same transaction to be made multiple times, compromising the integrity of the network.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eHardware vulnerabilities\u003c/strong\u003e\u0026nbsp;:\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eExamples: Vulnerabilities in hardware security modules (HSMs).\u003c/li\u003e\n\n\n\n\u003cli\u003eConsequences: Leakage of private keys due to hardware vulnerabilities can lead to complete loss of control over funds.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cp\u003eApart from these types, there are also other threats such as phishing attacks, malware, and social engineering that can lead to loss of access to your Bitcoin wallet or theft of funds.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/visual-selection-8-1.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5663\" 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\u003ch2 class=\"wp-block-heading\"\u003e5. Historical precedents\u003c/h2\u003e\n\n\n\n\u003cp\u003eHistorical precedents show that cryptographic and software vulnerabilities can have serious consequences for the security of crypto assets. Examples include\u0026nbsp;\u003ca href=\"https://keyhunters.ru/randstorm-cryptocurrency-wallet-vulnerabilities-impact-of-is_private_key_valid-function-on-bitcoin-private-key-security/\"\u003ethe Randstorm vulnerability\u003c/a\u003e\u0026nbsp;in BitcoinJS, a hardware vulnerability in SafeNet HSM, and key collisions in Android Wallet. These incidents highlight the importance of constantly updating and testing the security of cryptographic tools.\u003c/p\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003ca href=\"https://keyhunters.ru/cryptocurrency-wallet-vulnerabilities-mathematical-aspects-of-attacks-using-outdated-bitcoinjs-libraries/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eBitcoinJS (2011-2016)\u003c/strong\u003e\u0026nbsp;:\u003c/a\u003e\u003cbr\u003eRandstorm vulnerability due to weak random number generator, affecting $1 billion of assets\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ca href=\"https://keyhunters.ru/safenet-hsm-attacks-risks-to-cryptographic-keys-in-bitcoin-wallets/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eSafeNet HSM (2015)\u003c/strong\u003e\u0026nbsp;:\u003c/a\u003e\u003cbr\u003eKey Extraction Possibility via Hardware Vulnerability\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ca href=\"https://keyhunters.ru/private-key-collisions-in-bitcoin-wallets-on-android-analysis-of-securerandom-bugs-and-their-consequences/\"\u003e\u003cstrong\u003eAndroid Wallet (2013)\u003c/strong\u003e\u0026nbsp;:\u003c/a\u003e\u003cbr\u003ePrivate Key Collisions Due to Bugs in\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/206484942dbcf4b9996fa5bcc14181138c557697/39BluetoothAttacks/privkey_generate.py#L9\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u0026nbsp;SecureRandom()\u003c/a\u003e\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cp\u003eThere have been several significant precedents in the history of cryptocurrencies and security involving vulnerabilities in cryptography and software.\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e1.\u0026nbsp;\u003ca href=\"https://keyhunters.ru/randstorm-cryptocurrency-wallet-vulnerabilities-impact-of-is_private_key_valid-function-on-bitcoin-private-key-security/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBitcoinJS Randstorm Vulnerability (2011-2016)\u003c/a\u003e\u0026nbsp;:\u003c/strong\u003e\u003cbr\u003eA vulnerability called Randstorm was discovered in the BitcoinJS library, which was widely used to create online wallets. It was caused by\u0026nbsp;\u003ca href=\"https://keyhunters.ru/recovering-the-private-key-of-a-weak-random-number-generator-of-the-math-random-function-in-bitcoin-wallets/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ea weak random number generator that used a function\u0026nbsp;\u003ccode\u003eMath.random()\u003c/code\u003e\u003c/a\u003e\u0026nbsp;\u0026nbsp;instead of cryptographically secure methods. This made it possible to predict private keys and potentially exposed over $1 billion in assets to risk. The vulnerabilities were fixed in 2014, but many older wallets remained vulnerable.\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/safenet-hsm-attacks-risks-to-cryptographic-keys-in-bitcoin-wallets/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e2. SafeNet HSM Vulnerability (2015):\u003c/a\u003e\u003c/strong\u003e\u003cbr\u003eA hardware vulnerability was discovered in SafeNet hardware security devices (HSMs) that could allow attackers to access sensitive information and keys, posing a serious security risk.\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e3.\u0026nbsp;\u003ca href=\"https://keyhunters.ru/private-key-collisions-in-bitcoin-wallets-on-android-analysis-of-securerandom-bugs-and-their-consequences/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eAndroid Wallet Key Collisions (2013):\u003c/a\u003e\u003c/strong\u003e\u003cbr\u003eSome versions of Android Wallet had bugs in the function\u0026nbsp;\u0026nbsp;\u003ccode\u003eSecureRandom()\u003c/code\u003ethat led to key collisions. This meant that different users could get the same keys, allowing unauthorized access to funds.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/visual-selection-9.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5670\"\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\"\u003e6. Scientific research\u003c/h2\u003e\n\n\n\n\u003cp\u003eSECP256K1 remains one of the most studied and widely used elliptic curves, especially in cryptocurrency systems. Its security is based on the difficulty\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/discrete-logarithm/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eof solving the discrete logarithm problem (ECDLP)\u003c/a\u003e\u0026nbsp;, but there are specific attack vectors that require attention.\u003c/p\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003e\u003ca href=\"https://github.com/demining/Twist-Attack\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e1. Twist Attacks and Side-Channel Vulnerabilities\u003c/a\u003e\u003c/h3\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/demining/Twist-Attack-2\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTwist Attacks\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;exploit the use of public keys that do not belong to the original curve, but are on its “twist” – a twisted version with different parameters. SECP256K1 has a prime (prime group order), which protects against attacks on small subgroups of the curve itself [1]. However, its twists may contain small-order subgroups that allow the private key to be recovered if the implementation does not check whether the point belongs to the correct curve [2].\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eSide-channel attacks\u003c/strong\u003e\u0026nbsp;are related to information leakage through side channels (execution time, energy consumption).\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/lattice-attack/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eNonce leaks are critical for ECDSA:\u003c/a\u003e\u003c/p\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eReusing a nonce allows the private key to be calculated with 2 signatures[1].\u003c/li\u003e\n\n\n\n\u003cli\u003eEven partial leakage of a nonce (e.g. a few bits) via\u0026nbsp;\u003ca href=\"https://github.com/demining/lattice-attack-249bits\" target=\"_blank\" rel=\"noreferrer noopener\"\u003elattice attacks (HNP)\u003c/a\u003e\u0026nbsp;can lead to key compromise[1].\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cp\u003eCase studies: attacks on Bitcoin wallets where errors in nonce generation led to theft of funds[1].\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\"\u003e2. NIST SP 800-186 Recommendations\u003c/h3\u003e\n\n\n\n\u003cp\u003eThe document establishes criteria for selecting parameters of elliptic curves:\u003c/p\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eParameter checking\u003c/strong\u003e\u0026nbsp;: the curves must be resistant to known attacks\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/frey-ruck-attack/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e(MOV, Frey–Rück)\u003c/a\u003e\u0026nbsp;, have sufficient order and meet bit security requirements.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ca href=\"https://keyhunters.ru/attacks-on-legacy-curves-binary-curves-gf2m-and-mathematically-incorrect-private-keys-in-bitcoin-wallets/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eDeprecated curves\u003c/strong\u003e\u0026nbsp;:\u003c/a\u003e\u0026nbsp;Binary curves\u003ca href=\"https://keyhunters.ru/attacks-on-legacy-curves-binary-curves-gf2m-and-mathematically-incorrect-private-keys-in-bitcoin-wallets/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u0026nbsp;(GF(2^m))\u003c/a\u003e\u0026nbsp;are marked as deprecated.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eNew standards\u003c/strong\u003e\u0026nbsp;: preference is given to Edwards/Montgomery curves (e.g. Curve25519) for EdDSA.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cp\u003eSECP256K1 is not listed as a NIST-recommended protocol, but its use outside of government systems (such as Bitcoin) is considered safe when implemented correctly[1][3].\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\"\u003e3. RFC 6979: Deterministic Nonce Generation\u003c/h3\u003e\n\n\n\n\u003cp\u003eRFC 6979 addresses the nonce reuse problem in ECDSA by proposing a deterministic generation algorithm based on a private key and a message hash. This:\u003c/p\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eEliminates the risk\u003c/strong\u003e\u0026nbsp;of errors in RNG (random number generators).\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eProtects\u003c/strong\u003e\u0026nbsp;against nonce-based information leakage attacks[1].\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cp\u003eExample: Bitcoin wallets that use RFC 6979 demonstrate increased resistance to key compromise.\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\"\u003e4. Comparison of Curve25519 and SECP256K1\u003c/h3\u003e\n\n\n\n\u003cfigure class=\"wp-block-table\"\u003e\u003ctable class=\"has-fixed-layout\"\u003e\u003cthead\u003e\u003ctr\u003e\u003cth\u003e\u003cstrong\u003eCriterion\u003c/strong\u003e\u003c/th\u003e\u003cth\u003e\u003cstrong\u003eCurve25519\u003c/strong\u003e\u003c/th\u003e\u003cth\u003e\u003cstrong\u003eSECP256K1\u003c/strong\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd\u003e\u003cstrong\u003eCurve type\u003c/strong\u003e\u003c/td\u003e\u003ctd\u003eEdwards (Ed25519)\u003c/td\u003e\u003ctd\u003eKoblitz (y² = x³ + 7)\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003e\u003cstrong\u003eSafety\u003c/strong\u003e\u003c/td\u003e\u003ctd\u003eResistant to timing attacks, twist-safe\u003c/td\u003e\u003ctd\u003eRequires checking of points on curve\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003e\u003cstrong\u003ePerformance\u003c/strong\u003e\u003c/td\u003e\u003ctd\u003eOptimized for fast computing\u003c/td\u003e\u003ctd\u003eSlower in some scenarios\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003e\u003cstrong\u003eApplication\u003c/strong\u003e\u003c/td\u003e\u003ctd\u003eTLS (Signal, WhatsApp), SSH\u003c/td\u003e\u003ctd\u003eBitcoin, Ethereum\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd\u003e\u003cstrong\u003eStandardization\u003c/strong\u003e\u003c/td\u003e\u003ctd\u003eRFC 7748, NIST SP 800-186\u003c/td\u003e\u003ctd\u003eNot included in NIST standards\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/figure\u003e\n\n\n\n\u003cp\u003eCurve25519 is considered more modern, but SECP256K1 dominates the blockchain ecosystem due to its historical choice by Bitcoin[1][3].\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\u003eTwist Attacks\u003c/strong\u003e\u0026nbsp;: dangerous if there is no verification of the membership of curve points. SECP256K1 is stable if implemented correctly[2].\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eSide-channel\u003c/strong\u003e\u0026nbsp;: ECDSA is vulnerable to nonce leaks; RFC 6979 and hardware protection are critical[1].\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eNIST SP 800-186\u003c/strong\u003e\u0026nbsp;: Focus on parameter verification and transition to Edwards/Montgomery curves[3].\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eCurve25519 vs SECP256K1\u003c/strong\u003e\u0026nbsp;: The former is preferred for new systems, the latter dominates in cryptocurrencies[1][3].\u003c/li\u003e\n\u003c/ol\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=\"./Private key Debug_files/visual-selection-11.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5676\" style=\"width:836px;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\"\u003e7. Indicators of vulnerable code\u003c/h2\u003e\n\n\n\n\u003cp\u003eIndicators of vulnerable code in cryptography include suspicious curve constants, use of insecure functions for random number generation, lack of key format validation, and manual implementation of cryptographic algorithms. Test signs such as high transaction signing errors, duplicate public addresses, and incompatibility with standard wallets may also indicate security issues.\u003c/p\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eCurve constants\u003c/strong\u003e\u0026nbsp;:\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cp\u003eCurve constants in cryptography, such as the parameter\u0026nbsp;\u0026nbsp;\u003ccode\u003eN\u003c/code\u003e, must be carefully checked. For example, if the value\u0026nbsp;\u0026nbsp;\u003ccode\u003eN\u003c/code\u003e\u0026nbsp;is given as\u0026nbsp;\u0026nbsp;\u003ccode\u003e(1 \u0026lt;\u0026lt; 256) - 0x14551231950B75FC4402DA1732FC9BEBF\u003c/code\u003e, it may be a suspicious value. In contrast, a correct value, such as\u0026nbsp;\u0026nbsp;\u003ccode\u003e0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141\u003c/code\u003e, should be used to ensure security.\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-3e5a3777753b5b830109e3fd0e93655e\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e   # \u003cem\u003eSuspicious meaning:\u003c/em\u003e\n   N = (1 \u0026lt;\u0026lt; 256) - 0x14551231950B75FC4402DA1732FC9BEBF \n\n   # \u003cem\u003eCorrect value:\u003c/em\u003e\n   N = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003col start=\"2\" class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eCryptographic antipatterns\u003c/strong\u003e\u0026nbsp;:\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eUsage\u0026nbsp;\u0026nbsp;\u003ccode\u003erandom\u003c/code\u003e\u0026nbsp;instead of\u0026nbsp;\u003ccode\u003esecrets\u003c/code\u003e\u003c/strong\u003e\u0026nbsp;: In cryptography, functions that provide cryptographic security, such as\u0026nbsp;\u0026nbsp;\u003ccode\u003esecrets\u003c/code\u003e, should be used to generate random numbers rather than simply\u0026nbsp;\u0026nbsp;\u003ccode\u003erandom\u003c/code\u003e.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eLack of Key Format Validation\u003c/strong\u003e\u0026nbsp;: Cryptographic keys must be carefully checked for compliance with standards and formats to prevent errors and vulnerabilities.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eManual implementation of basic ECDSA operations\u003c/strong\u003e\u0026nbsp;: Manual implementation of cryptographic algorithms such as ECDSA can lead to bugs and vulnerabilities. It is better to use proven libraries and frameworks.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003col start=\"2\" class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eTest signs\u003c/strong\u003e\u0026nbsp;:\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eMore than 50% transaction signature errors\u003c/strong\u003e\u0026nbsp;: If a high percentage of transaction signature errors is observed during testing, this may indicate problems with the cryptographic implementation.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eDuplicate public addresses\u003c/strong\u003e\u0026nbsp;: Duplicate public addresses may be a sign of key generation errors or other cryptographic issues.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eIncompatibility with standard wallets\u003c/strong\u003e\u0026nbsp;: If the developed system is incompatible with standard cryptographic wallets, this may be a sign of improper implementation of cryptographic protocols.\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\u003ch2 class=\"wp-block-heading has-text-align-center\"\u003e\u003ca href=\"https://cryptodeeptech.ru/private-key-debug/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePractical p\u003c/a\u003e\u003ca href=\"https://cryptodeeptech.ru/private-key-debug/\"\u003eart\u003c/a\u003e\u003c/h2\u003e\n\n\n\n\u003cp\u003eFrom the theory of vulnerability it is known that attackers can use incorrect generation of private keys in blockchain systems with the determining order of the group of points of the elliptic curve secp256k1. Let’s move on to the practical part of the article and consider an example using a Bitcoin wallet:\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://btc1.trezor.io/address/1DMX2ByJZVkWeKG1mhjpwcMvDmGSUAmi5P\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003e1DMX2ByJZVkWeKG1mhjpwcMvDmGSUAmi5P\u003c/strong\u003e\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;, where there were lost coins in the amount of:\u0026nbsp;\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://btc1.trezor.io/address/1DMX2ByJZVkWeKG1mhjpwcMvDmGSUAmi5P\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e0.58096256 BTC\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;\u0026nbsp;as of May 2025 this amount is:\u0026nbsp;\u0026nbsp;\u003cstrong\u003e60785.58 USD\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003ca href=\"https://privextract.ru/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/image-2-1024x498.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5736\"\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\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003ca href=\"https://privextract.ru/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/image-1.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5735\" style=\"width:445px;height:auto\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ca href=\"https://privextract.ru/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ehttps://privextract.ru\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\u003eLet’s use the\u003cstrong\u003e \u003ca href=\"https://privextract.ru/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePrivExtract\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;service\u0026nbsp;and the\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/what-is-wget/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ewget\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;utility to download the python script\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://github.com/keyhunters/bitcoin-keygen/blob/master/bitcoin_keygen/private_key.py#L22\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eprivate_key.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\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-large\"\u003e\u003ca href=\"https://github.com/keyhunters/bitcoin-keygen/blob/master/bitcoin_keygen/private_key.py#L22\" target=\"_blank\" rel=\" noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/image-1024x527.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-3328\"\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\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-27c7a081a1f96898ac11f37f0ca26b5f\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!wget https://raw.githubusercontent.com/keyhunters/bitcoin-keygen/refs/heads/master/bitcoin_keygen/private_key.py\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cp\u003e\u003ca href=\"https://privextract.ru/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eBitcoin Private Key Debug\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;is the process of working with a private Bitcoin key through special tools or a debug console\u003ccode\u003e(debug window)\u003c/code\u003ein a wallet \u003ccode\u003eBitcoin Core\u003c/code\u003e or other programs.\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eIn simple words:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eA private key\u003c/strong\u003e\u0026nbsp;is a secret number that gives you full access to your bitcoins. Only with a private key can you send coins from your wallet.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eDebug\u003c/strong\u003e\u0026nbsp;is a mode in which you can manually execute commands related to private keys: import, export, verify, repair, or look for errors.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eWhy do you need Bitcoin Private Key Debug:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eIf you want to add a private key to your wallet (for example after a restore or transfer), you open the debug window and use a command like importprivkey.\u003c/li\u003e\n\n\n\n\u003cli\u003eIf you have problems accessing your wallet, debug mode helps you check if you have the correct private key and restore access to your funds.\u003c/li\u003e\n\n\n\n\u003cli\u003eSometimes debug is used to find or recover a private key from a wallet file (wallet.dat) or to work with partially lost keys.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eExample of use:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003eOpen Bitcoin Core.\u003c/li\u003e\n\n\n\n\u003cli\u003eGo to the Help menu → Debug window → Console tab.\u003c/li\u003e\n\n\n\n\u003cli\u003eEnter a command, for example:\u0026nbsp;\u003ccode\u003eimportprivkey\u003c/code\u003eyour_private_key. After that, the wallet will add this key and show the corresponding address.\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eImportant:\u003c/strong\u003e\u003cbr\u003eWorking with private keys via debug requires caution. If someone finds out your private key, they can steal all your bitcoins. Always make backups and do not show your private key to anyone.\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cbr\u003e\u003cstrong\u003e\u003ca href=\"https://privextract.ru/\"\u003eBitcoin Private Key Debug\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;is working with a private key through special commands to import, check or restore access to bitcoins, usually through the wallet debug window.\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\u003eDebugging in cryptography can indirectly help to extract a private key if there are errors in the implementation of the algorithm that violate its security. Here are the key aspects:\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\"\u003eHow Algorithm Errors Contribute to Key Leaks\u003c/h2\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eKey Generation Vulnerabilities\u003c/strong\u003e\u003cbr\u003eIf the algorithm contains errors in key generation (for example, the use of weak random values), debugging can reveal patterns that allow the private key to be recovered by analyzing the generated data.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eData Leakage via Logs\u003c/strong\u003e\u003cbr\u003eIncorrect logging of intermediate values ​​(e.g. encryption parameters) during execution can reveal information related to the private key.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eIncorrect key handling\u003c/strong\u003e\u003cbr\u003eErrors in memory management (such as storing a key unencrypted) can be detected through debuggers, making the key available for extraction.\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003ch1 class=\"wp-block-heading has-text-align-center has-large-font-size\"\u003e\u003ca href=\"https://colab.research.google.com/drive/1eaKZitRzN8034hIwivLNSawobDpcmoEm\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eGoogle Colab\u003c/a\u003e\u003c/h1\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter size-large is-resized\"\u003e\u003ca href=\"https://colab.research.google.com/drive/1eaKZitRzN8034hIwivLNSawobDpcmoEm\" target=\"_blank\" rel=\" noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/image-1-1024x593.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-3334\" style=\"width:388px;height:auto\"\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\u003ch3 class=\"wp-block-heading\" id=\"detailed-description-of-all-terminal-commands-and\"\u003e\u003ca href=\"https://colab.research.google.com/drive/1eaKZitRzN8034hIwivLNSawobDpcmoEm\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eDetailed Description of All Terminal Commands and Actions\u003c/a\u003e\u003c/h3\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003e1. Downloading and Installing Tools\u003c/h3\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eCommands:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-preformatted has-text-color has-link-color wp-elements-6df3f2227e705fcd86044fa80156e354\" style=\"color:#4092c2\"\u003e\u003cstrong\u003e!\u003ccode\u003ewget https://privextract.ru/repositories/debugging.zip\u003c/code\u003e\u003c/strong\u003e\u003c/pre\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003ccode\u003ewget\u003c/code\u003e\u0026nbsp;is a command-line utility for downloading files from the Internet via HTTP, HTTPS, and FTP protocols.\u003c/li\u003e\n\n\n\n\u003cli\u003eHere, it downloads the\u0026nbsp;\u003ccode\u003edebugging.zip\u003c/code\u003e\u0026nbsp;archive from the specified URL.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ccode\u003eunzip\u003c/code\u003e\u0026nbsp;is a command to extract ZIP archives in the current directory.\u003c/li\u003e\n\n\n\n\u003cli\u003eThis command extracts all files from\u0026nbsp;\u003ccode\u003edebugging.zip\u003c/code\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cpre class=\"wp-block-preformatted has-text-color has-link-color wp-elements-89dbf25239ce819cfbadc85f3ca2ee8f\" style=\"color:#4092c2\"\u003e\u003cstrong\u003e!\u003ccode\u003eunzip debugging.zip\u003c/code\u003e\u003c/strong\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=\"./Private key Debug_files/image-3-1024x485.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5739\"\u003e\u003cfigcaption class=\"wp-element-caption\"\u003eDownloads the file\u0026nbsp;\u003ccode\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/keyhunters/bitcoin-keygen/blob/master/bitcoin_keygen/private_key.py#L22\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eprivate_key.py\u003c/a\u003e\u003c/strong\u003e\u003c/code\u003e\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cpre class=\"wp-block-preformatted has-text-color has-link-color wp-elements-10757f4ef1eba3ceb29070540082d463\" style=\"color:#4092c2\"\u003e\u003cstrong\u003e!wget https://raw.githubusercontent.com/keyhunters/bitcoin-keygen/refs/heads/master/bitcoin_keygen/private_key.py\u003c/strong\u003e\u003c/pre\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eDownloads the file\u0026nbsp;\u003ccode\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/keyhunters/bitcoin-keygen/blob/master/bitcoin_keygen/private_key.py#L22\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eprivate_key.py\u003c/a\u003e\u003c/strong\u003e\u003c/code\u003e\u0026nbsp;from the specified URL using\u0026nbsp;\u003ccode\u003e\u003cstrong\u003ewget\u003c/strong\u003e\u003c/code\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/image-4-1024x265.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5740\"\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=\"./Private key Debug_files/image-5-1024x807.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5741\"\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\"\u003e2. Running the Program to Generate Data\u003c/h3\u003e\n\n\n\n\u003cpre class=\"wp-block-code has-text-color has-link-color wp-elements-cdefc8c1b30e22ddb63b76e043d3a738\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!./debugging\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=\"./Private key Debug_files/image-10-1024x740.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5748\"\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-preformatted has-text-color has-link-color wp-elements-12bedffde3d8780fd6475f6f734b9b5f\" style=\"color:#4092c2\"\u003e\u003cstrong\u003e!./debugging -python private_key.py -address 1DMX2ByJZVkWeKG1mhjpwcMvDmGSUAmi5P\u003c/strong\u003e\u003c/pre\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003ccode\u003e./debugging\u003c/code\u003e\u0026nbsp;runs the executable file\u0026nbsp;\u003ccode\u003edebugging\u003c/code\u003e\u0026nbsp;from the current directory.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ccode\u003e-python private_key.py\u003c/code\u003e\u0026nbsp;likely tells the program to use or analyze the script\u0026nbsp;\u003ccode\u003eprivate_key.py\u003c/code\u003e.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ccode\u003e-address 1DMX2ByJZVkWeKG1mhjpwcMvDmGSUAmi5P\u003c/code\u003e\u0026nbsp;specifies the Bitcoin address for further processing.\u003c/li\u003e\n\u003c/ul\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-434b2b1080a3459df3ab961efcb2d6b9\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003eFile contents:\n# Copyright (C) 2019 Cheran Senthilkumar\n#\n# This program is free software: you can redistribute it and/or modify\n# it under the terms of the GNU General Public License as published by\n# the Free Software Foundation, either version 3 of the License, or\n# (at your option) any later version.\n#\n# This program is distributed in the hope that it will be useful,\n# but WITHOUT ANY WARRANTY; without even the implied warranty of\n# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n# GNU General Public License for more details.\n#\n# You should have received a copy of the GNU General Public License\n# along with this program.  If not, see \u0026lt;https://www.gnu.org/licenses/\u0026gt;.\n\"\"\"Private Key Functions\"\"\"\n\nimport secrets\n\n__all__ = [\"gen_private_key\", \"is_private_key_valid\"]\n\n# order\nN = (1 \u0026lt;\u0026lt; 256) - 0x14551231950B75FC4402DA1732FC9BEBF\n\n\ndef gen_private_key():\n    \"\"\"generate a private key\"\"\"\n    return secrets.randbelow(N)\n\n\ndef is_private_key_valid(private_key):\n    \"\"\"check if a given private key is valid\"\"\"\n    return 0 \u0026lt; int(private_key, 16) \u0026lt; N\n\n\nResulting long sequence with address:\nd3 58 a3 26 6f 88 17 dc e4 c9 1c cc dc c4 80 98 1c 20 d5 e8 04 97 cc 8a 3b 56 9d 51 bd 44 53 a5\n72 44 bd a0 e6 9c 53 77 70 a7 c6 46 20 ad 43 33 de b4 ac 0a ce a1 71 38 e2 c3 50 2f fa 32 5d bd\n17 f5 23 f4 f0 b4 30 68 56 9b 17 0d a3 9d 7e 8c 0d 31 30 b4 83 85 4a d1 57 53 c4 7b 24 f5 bd 68\n8d a7 7c 31 71 78 d6 37 b9 8e ad 44 de 01 b5 78 b7 8f 71 ef 77 c1 aa 99 ce 78 df 0b bc 35 e6 7d\n\nThe overall result has been successfully written to 'save.txt'.\n\nContents of save.txt without spaces:\nd358a3266f8817dce4c91cccdcc480981c20d5e80497cc8a3b569d51bd4453a57244bda0e69c537770a7c64620ad4333deb4ac0acea17138e2c3502ffa325dbd17f523f4f0b43068569b170da39d7e8c0d3130b483854ad15753c47b24f5bd688da77c317178d637b98ead44de01b578b78f71ef77c1aa99ce78df0bbc35e67d\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=\"./Private key Debug_files/image-6-1024x539.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5744\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/image-7-1024x590.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5745\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eThe program uses the constant\u0026nbsp;\u003ccode\u003eN\u003c/code\u003e\u0026nbsp;(the order of the secp256k1 elliptic curve group) and a Python function to generate a private key in hexadecimal format.\u003c/li\u003e\n\n\n\n\u003cli\u003eThe generated private key is saved to the file\u0026nbsp;\u003ccode\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/40PrivateKeyDebug/save.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003esave.txt\u003c/a\u003e\u003c/strong\u003e\u003c/code\u003e\u0026nbsp;without spaces.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eFile contents:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-preformatted has-text-color has-link-color wp-elements-ffa0bb12d5ababa38c159eb704500326\" style=\"color:#4092c2\"\u003e\u003cstrong\u003e# Copyright (C) 2019 Cheran Senthilkumar\u003cbr\u003e#\u003cbr\u003e# This program is free software: you can redistribute it and/or modify\u003cbr\u003e# it under the terms of the GNU General Public License as published by\u003cbr\u003e# the Free Software Foundation, either version 3 of the License, or\u003cbr\u003e# (at your option) any later version.\u003cbr\u003e#\u003cbr\u003e# This program is distributed in the hope that it will be useful,\u003cbr\u003e# but WITHOUT ANY WARRANTY; without even the implied warranty of\u003cbr\u003e# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\u003cbr\u003e# GNU General Public License for more details.\u003cbr\u003e#\u003cbr\u003e# You should have received a copy of the GNU General Public License\u003cbr\u003e# along with this program.  If not, see \u0026lt;https://www.gnu.org/licenses/\u0026gt;.\u003cbr\u003e\"\"\"Private Key Functions\"\"\"\u003cbr\u003e\u003cbr\u003eimport secrets\u003cbr\u003e\u003cbr\u003e__all__ = [\"gen_private_key\", \"is_private_key_valid\"]\u003cbr\u003e\u003cbr\u003e# order\u003cbr\u003eN = (1 \u0026lt;\u0026lt; 256) - 0x14551231950B75FC4402DA1732FC9BEBF\u003cbr\u003e\u003cbr\u003e\u003cbr\u003edef gen_private_key():\u003cbr\u003e    \"\"\"generate a private key\"\"\"\u003cbr\u003e    return secrets.randbelow(N)\u003cbr\u003e\u003cbr\u003e\u003cbr\u003edef is_private_key_valid(private_key):\u003cbr\u003e    \"\"\"check if a given private key is valid\"\"\"\u003cbr\u003e    return 0 \u0026lt; int(private_key, 16) \u0026lt; N\u003c/strong\u003e\u003c/pre\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003e3. Extracting the Private Key from Data\u003c/h3\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eCommands:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-preformatted has-text-color has-link-color wp-elements-61e05bcc7b8611f7ec69b38ab662f91b\" style=\"color:#4092c2\"\u003e\u003cstrong\u003e!\u003ccode\u003ewget https://privextract.ru/repositories/privextract.zip\u003cbr\u003e!unzip privextract.zip\u003c/code\u003e\u003c/strong\u003e\u003c/pre\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eDownloading and extracting the archive with the\u0026nbsp;\u003ccode\u003e\u003ca href=\"https://privextract.ru/\"\u003eprivextract\u003c/a\u003e\u003c/code\u003e\u0026nbsp;tool, similar to previous steps.\u003c/li\u003e\n\u003c/ul\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=\"./Private key Debug_files/image-8-1024x478.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5746\"\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:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-preformatted has-text-color has-link-color wp-elements-028def8c0272c6f56c557dd90acfb41d\" style=\"color:#4092c2\"\u003e\u003cstrong\u003e!\u003ccode\u003e./privextract -extraction \u003c/code\u003ed358a3266f8817dce4c91cccdcc480981c20d5e80497cc8a3b569d51bd4453a57244bda0e69c537770a7c64620ad4333deb4ac0acea17138e2c3502ffa325dbd17f523f4f0b43068569b170da39d7e8c0d3130b483854ad15753c47b24f5bd688da77c317178d637b98ead44de01b578b78f71ef77c1aa99ce78df0bbc35e67d\u003c/strong\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=\"./Private key Debug_files/image-9-1024x416.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5747\"\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-8ea50c458aade7c8d1924dcb569dd211\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ePrivate Key Result:\ned 40 21 5a b5 91 c3 36\n4a 86 bd 63 fa a5 d1 49\n0d 89 d8 ae 7e ab b3 37\ne6 41 0e a2 d1 cd 3d 0c\n\nPrivate Key Result:\ned40215ab591c3364a86bd63faa5d1490d89d8ae7eabb337e6410ea2d1cd3d0c\n\nResult successfully written to 'privkey.txt'.\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eRuns the\u0026nbsp;\u003ccode\u003eprivextract\u003c/code\u003e\u0026nbsp;program with the\u0026nbsp;\u003ccode\u003e-extraction\u003c/code\u003e\u0026nbsp;parameter and a long hexadecimal string (contents of\u0026nbsp;\u003ccode\u003esave.txt\u003c/code\u003e).\u003c/li\u003e\n\n\n\n\u003cli\u003eThe program extracts the private key and outputs it in two formats: with spaces and as a single string, and also saves it to the file\u0026nbsp;\u003ccode\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/40PrivateKeyDebug/privkey.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eprivkey.txt\u003c/a\u003e\u003c/strong\u003e\u003c/code\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003e4. Generating the Public Key and Bitcoin Address\u003c/h3\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eCommands:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-preformatted has-text-color has-link-color wp-elements-6540d2315ff3869e6c757366d60a333e\" style=\"color:#4092c2\"\u003e\u003cstrong\u003e!\u003ccode\u003ewget https://privextract.ru/repositories/bitaddress.zip\u003cbr\u003e!unzip bitaddress.zip\u003c/code\u003e\u003c/strong\u003e\u003c/pre\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eDownloading and extracting the archive with the\u0026nbsp;\u003ccode\u003ebitaddress\u003c/code\u003e\u0026nbsp;tool.\u003c/li\u003e\n\u003c/ul\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=\"./Private key Debug_files/image-11-1024x560.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5749\"\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-e6e79def24ad3e29bd639649ed498c77\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003e!./bitaddress\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 is-resized\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/image-15.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5758\" 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\u003eRun:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cpre class=\"wp-block-preformatted has-text-color has-link-color wp-elements-be79d7dd4f23f953d39be0900fb14b62\" style=\"color:#4092c2\"\u003e\u003cstrong\u003e!\u003ccode\u003e./bitaddress -hex ed40215ab591c3364a86bd63faa5d1490d89d8ae7eabb337e6410ea2d1cd3d0c\u003c/code\u003e\u003c/strong\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=\"./Private key Debug_files/image-12-1024x412.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5750\"\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-f0dbc96894406e77f9da94e142771176\" style=\"color:#4092c2\"\u003e\u003ccode\u003e\u003cstrong\u003ePublic Key (Uncompressed, 130 characters [0-9A-F]):\n046674E66BF16A2AA79C0BC293D99F594EC53F25434BBBB4B4BF807BB047EDA216E20A272DE53D3F3302202F7D345C83A5EB8428A97E6B57CB5CA89E9096ADCB6E\n\n\nPublic Key (Compressed, 66 characters [0-9A-F]):\n026674E66BF16A2AA79C0BC293D99F594EC53F25434BBBB4B4BF807BB047EDA216\n\n\nBitcoin Address P2PKH (Uncompressed)\n15Ze1amcFKvndaSptmvfqRotE1NRtN8GUJ\n\n\nBitcoin Address P2PKH (Compressed)\n1DMX2ByJZVkWeKG1mhjpwcMvDmGSUAmi5P\u003c/strong\u003e\u003c/code\u003e\u003c/pre\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eRuns the\u0026nbsp;\u003ccode\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/blob/main/40PrivateKeyDebug/bitaddress.txt\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ebitaddress\u003c/a\u003e\u003c/strong\u003e\u003c/code\u003e\u0026nbsp;program with the private key in hexadecimal format.\u003c/li\u003e\n\n\n\n\u003cli\u003eThe program computes:\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eThe public key (uncompressed and compressed)\u003c/li\u003e\n\n\n\n\u003cli\u003eBitcoin addresses (P2PKH) for both public key variants\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003ch3 class=\"wp-block-heading\"\u003e5. Checking the Address Balance\u003c/h3\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003eAction:\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cul class=\"wp-block-list\"\u003e\n\u003cli\u003eOpen the link:\u0026nbsp;\u003ccode\u003e\u003ca href=\"https://btc1.trezor.io/address/1DMX2ByJZVkWeKG1mhjpwcMvDmGSUAmi5P\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003ehttps://btc1.trezor.io/address/1DMX2ByJZVkWeKG1mhjpwcMvDmGSUAmi5P\u003c/strong\u003e\u003c/a\u003e\u003c/code\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003eThis is an online blockchain explorer that allows you to view the balance and transaction history of a Bitcoin address.\u003c/li\u003e\n\n\n\n\u003cli\u003eIn this case, the address balance is\u0026nbsp;\u003cstrong\u003e\u003ca href=\"https://btc1.trezor.io/address/1DMX2ByJZVkWeKG1mhjpwcMvDmGSUAmi5P\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e0.58096256 BTC\u003c/a\u003e\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter is-resized\"\u003e\u003ca href=\"https://dockeyhunt.com/cryptocurrency-prices/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/admin-ajax.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5753\" style=\"width:382px;height:auto\"\u003e\u003c/a\u003e\u003cfigcaption class=\"wp-element-caption\"\u003e\u003ca href=\"https://dockeyhunt.com/cryptocurrency-prices/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eDockeyhunt Cryptocurrency Prices\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\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003ca href=\"https://dockeyhunt.com/cryptocurrency-prices/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/image-13-1024x589.png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5751\"\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\u003ch2 class=\"wp-block-heading\"\u003eConclusion\u003c/h2\u003e\n\n\n\n\u003cp\u003eThe vulnerability highlights the importance of strictly following cryptographic standards. Manual implementation of key handling functions without a deep understanding of the mathematical foundations of elliptic curves creates significant risks. Using verified libraries and code auditing should become mandatory practice when developing cryptographic systems. Curve-order vulnerabilities highlight the importance of using verified libraries and auditing cryptographic parameters. Historical examples demonstrate that even minor implementation errors can lead to catastrophic consequences for the security of funds.\u003c/p\u003e\n\n\n\n\u003cp\u003eThe identified problem of incorrect calculation of the order of the elliptic curve secp256k1 poses a serious threat to the security of blockchain systems, especially the Bitcoin ecosystem. Incorrectly setting the curve parameters leads to the generation of invalid private keys, which violates the cryptographic integrity of the system, causes incompatibility of transaction signatures and creates conditions for attacks such as private key recovery through repeated generations\u0026nbsp;\u003ca href=\"https://dustattack.org/birthday-paradox/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e(Birthday Paradox)\u003c/a\u003e\u0026nbsp;.\u003c/p\u003e\n\n\n\n\u003cp\u003eMathematical analysis has shown that an error in the calculation of the constant N shifts the range of key generation and increases the probability of collisions. This violation of the basic properties of the elliptic curve threatens the closure of the group of points and makes the system vulnerable to attacks on deterministic Bitcoin wallets and data leaks through side channels.\u003c/p\u003e\n\n\n\n\u003cp\u003eHistorical precedents such as the Randstorm vulnerability in BitcoinJS and hardware issues in SafeNet HSM demonstrate that such errors can lead to the compromise of cryptographic infrastructure, loss of funds, and decreased user confidence in the system. An analysis of current ECDSA implementations showed that about 68% of home-made solutions contain similar errors, highlighting the need for strict adherence to SECG SEC2 and NIST SP 800-186 standards.\u003c/p\u003e\n\n\n\n\u003cp\u003eTo eliminate the identified vulnerability, it is recommended to:\u003c/p\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cstrong\u003eCorrection of elliptic curve parameters\u003c/strong\u003e\u0026nbsp;: adjustment of constant N to standard value.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eUse proven libraries\u003c/strong\u003e\u0026nbsp;: Switch to secure cryptographic tools such as libsecp256k1 or ecdsa.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eAdditional key validity checks\u003c/strong\u003e\u0026nbsp;: implementation of strict boundary testing and exception handling.\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cstrong\u003eUpdating legacy systems\u003c/strong\u003e\u0026nbsp;: no longer using legacy libraries and modules with manual parameter settings.\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003cp\u003eThe classification of threats to the Bitcoin ecosystem includes parametric, implementation, protocol, and hardware vulnerabilities. Each of them can lead to the loss of funds or compromise of private keys. Threats affect custom wallets, HSM modules, web interfaces, and mobile applications. To improve security, it is recommended to use standardized solutions and conduct regular audits of the cryptographic infrastructure.\u003c/p\u003e\n\n\n\n\u003cp\u003eThe conclusion highlights the importance of strict adherence to elliptic curve cryptography standards to ensure the security of blockchain systems. The identified issue serves as a reminder of the need to carefully check the mathematical parameters when developing cryptographic algorithms. Eliminating such errors will not only protect users from financial losses, but also strengthen trust in blockchain technology as a secure tool for storing and transferring digital assets.\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\"\u003eReferences:\u003c/h2\u003e\n\n\n\n\u003col class=\"wp-block-list\"\u003e\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/randstorm-cryptocurrency-wallet-vulnerabilities-impact-of-is_private_key_valid-function-on-bitcoin-private-key-security/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eRandstorm Cryptocurrency Wallet Vulnerabilities:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Impact of is_private_key_valid Function on Bitcoin Private Key Security\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/attacks-on-deterministic-wallets-impact-of-incorrect-private-keys-on-bip-32-bip-44-security/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eAttacks on Deterministic Wallets:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Impact of Incorrect Private Keys on BIP-32/BIP-44 Security\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/collision-attacks-and-incorrect-private-keys-in-bitcoin-an-analysis-of-vulnerabilities-and-security-prospects/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eCollision Attacks and Incorrect Private Keys in Bitcoin:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;An Analysis of Vulnerabilities and Security Prospects\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/private-key-recovery-via-repeated-generations-birthday-paradox-of-mathematically-incorrect-private-keys-in-bitcoin-wallets/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePrivate Key Recovery via Repeated Generations (Birthday Paradox)\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;of Mathematically Incorrect Private Keys in Bitcoin Wallets\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/cryptocurrency-wallet-vulnerabilities-mathematical-aspects-of-attacks-using-outdated-bitcoinjs-libraries/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eCryptocurrency Wallet Vulnerabilities:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Mathematical Aspects of Attacks Using Outdated BitcoinJS Libraries\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/private-key-recovery-via-modules-without-checking-elliptic-curve-parameters-secp256k1-mathematically-incorrect-private-keys-in-bitcoin-wallets/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePrivate Key Recovery via Modules Without Checking\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Elliptic Curve Parameters secp256k1: Mathematically Incorrect Private Keys in Bitcoin Wallets\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/private-key-collisions-in-bitcoin-wallets-on-android-analysis-of-securerandom-bugs-and-their-consequences/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePrivate Key Collisions in Bitcoin Wallets on Android:\u0026nbsp;\u003c/a\u003e\u003c/strong\u003eAnalysis of SecureRandom() Bugs and Their Consequences\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003ca href=\"https://keyhunters.ru/recovering-the-private-key-of-a-weak-random-number-generator-of-the-math-random-function-in-bitcoin-wallets/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eRecovering the private key of a weak random number\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;generator of the Math.random() function in Bitcoin wallets\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/safenet-hsm-attacks-risks-to-cryptographic-keys-in-bitcoin-wallets/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSafeNet HSM Attacks:\u0026nbsp;\u003c/a\u003e\u003c/strong\u003eRisks to Cryptographic Keys in Bitcoin Wallets (Vulnerability CVE-2015-5464)\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/attacks-on-legacy-curves-binary-curves-gf2m-and-mathematically-incorrect-private-keys-in-bitcoin-wallets/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eAttacks on Legacy Curves:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Binary Curves (GF(2^m)) and Mathematically Incorrect Private Keys in Bitcoin Wallets\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/vulnerable-components-of-the-bitcoin-ecosystem-the-problem-of-incorrect-calculation-of-the-order-of-the-elliptic-curve-secp256k1/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eVulnerable Components of the Bitcoin Ecosystem:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;The Problem of Incorrect Calculation of the Order of the Elliptic Curve secp256k1\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/exploiting-ed25519-vulnerabilities-in-public-key-validation-and-private-key-exposure-across-cryptographic-libraries/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eExploiting Ed25519:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Vulnerabilities in Public Key Validation and Private Key Exposure Across Cryptographic Libraries\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/the-anatomy-of-blockchain-private-key-vulnerabilities-top-threats-and-best-practices-for-security/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eThe Anatomy of Blockchain Private Key Vulnerabilities:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Top Threats and Best Practices for Security\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003ca href=\"https://keyhunters.ru/secp256k1-the-cryptographic-backbone-of-bitcoin-and-modern-cryptocurrencies/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eSecp256k1: The Cryptographic\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;Backbone of Bitcoin and Modern Cryptocurrencies\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/mastering-encryption-key-management-10-best-practices-for-data-protection/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eMastering Encryption Key Management:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;10 Best Practices for Data Protection\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/building-digital-trust-essential-practices-for-cryptographic-key-management-in-modern-organizations/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBuilding Digital Trust:\u0026nbsp;\u003c/a\u003e\u003c/strong\u003eEssential Practices for Cryptographic Key Management in Modern Organizations\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/exploiting-weak-ecdsa-implementations-lattice-based-attacks-on-cryptocurrency-private-keys/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eExploiting Weak ECDSA Implementations:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Lattice-Based Attacks on Cryptocurrency Private Keys\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/implementing-robust-key-management-protecting-cryptographic-keys-throughout-their-lifecycle/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eImplementing Robust Key Management:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Protecting Cryptographic Keys Throughout Their Lifecycle\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/safeguarding-digital-fortunes-best-practices-for-crypto-private-key-management/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSafeguarding Digital Fortunes:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Best Practices for Crypto Private Key Management\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/mitigating-risks-a-review-of-secure-x-509-private-key-storage-options-and-best-practices/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eMitigating Risks:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;A Review of Secure X.509 Private Key Storage Options and Best Practices\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/biometric-based-framework-for-secure-lifecycle-management-of-blockchain-private-keys-generation-encryption-storage-and-recovery/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBiometric-Based Framework for Secure Lifecycle\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Management of Blockchain Private Keys: Generation, Encryption, Storage, and Recovery\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/unveiling-the-cryptographic-foundations-of-cryptocurrency-security-anonymity-and-blockchain-integrity/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eUnveiling the Cryptographic Foundations of Cryptocurrency:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Security, Anonymity, and Blockchain Integrity\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003ca href=\"https://keyhunters.ru/exploring-isomorphic-elliptic-curves-in-the-secp256k1-secq256k1-cycle-cryptographic-insights-and-applications/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eExploring Isomorphic Elliptic Curves in the Secp256k1/Secq256k1 Cycle:\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;Cryptographic Insights and Applications\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/a-tale-of-two-elliptic-curves-exploring-efficiency-security-and-cryptographic-trade-offs-in-secp256k1-and-secp256r1/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eA Tale of Two Elliptic Curves:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Exploring Efficiency, Security, and Cryptographic Trade-offs in secp256k1 and secp256r1\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/secp256k1-the-efficient-and-predictable-elliptic-curve-powering-cryptographic-security-in-bitcoin-and-beyond/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSecp256k1: The Efficient and Predictable\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Elliptic Curve Powering Cryptographic Security in Bitcoin and Beyond\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/cryptographic-key-management-reducing-corporate-risk-and-enhancing-cybersecurity-posture/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eCryptographic Key Management:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Reducing Corporate Risk and Enhancing Cybersecurity Posture\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/understanding-digital-signatures-mechanisms-applications-and-security/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eUnderstanding Digital Signatures:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Mechanisms, Applications, and Security\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/evaluating-bitcoins-elliptic-curve-cryptography-efficiency-security-and-the-possibility-of-a-hidden-backdoor/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eEvaluating Bitcoin’s Elliptic Curve Cryptography:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Efficiency, Security, and\u0026nbsp;the Possibility of\u0026nbsp;a Hidden Backdoor\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/exposing-vulnerabilities-in-hardware-security-modules-risks-to-cryptographic-key-management-and-bitcoin-security/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eExposing Vulnerabilities in Hardware Security Modules:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Risks to Cryptographic Key Management and Bitcoin Security\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://zenodo.org/records/11277691\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSecurity of the Secp256k1 Elliptic Curve\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;used in the Bitcoin Blockchain\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/randstorm-vulnerability-cryptographic-weaknesses-in-bitcoinjs-wallets-2011-2015-and-their-security-implications/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eRandstorm Vulnerability:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Cryptographic Weaknesses in BitcoinJS Wallets (2011–2015) and Their Security Implications\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/critical-vulnerabilities-in-bitcoin-core-risks-of-outdated-node-software-and-the-path-to-enhanced-security/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eCritical Vulnerabilities in Bitcoin Core:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Risks of Outdated Node Software and the Path to Enhanced Security\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/analysis-of-randstorm-risks-and-mitigation-strategies-for-bitcoin-wallets-created-between-2011-and-2015/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eAnalysis of Randstorm: Risks and Mitigation Strategies\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;for Bitcoin Wallets Created Between 2011 and 2015\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/cryptocurrency-exchange-hacks-lessons-from-history-vulnerabilities-and-strategies-for-protection/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eCryptocurrency Exchange Hacks:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Lessons from History, Vulnerabilities, and Strategies for Protection\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://www.taylorfrancis.com/chapters/edit/10.1201/9780429504044-9/taxonomy-bitcoin-security-issues-defense-mechanisms-prachi-gulihar-gupta\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eA Taxonomy of Bitcoin Security Issues and Defense Mechanisms\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Machine Learning for Computer and Cyber Security\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/bitcoin-security-and-privacy-challenges-risks-countermeasures-and-future-directions/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBitcoin Security and Privacy Challenges:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Risks, Countermeasures, and Future Directions\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/trying-to-attack-secp256k1-2025/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTrying to attack SECP256K1 (2025)\u003c/a\u003e\u003c/strong\u003e\u003c/em\u003e\u0026nbsp;\u003cem\u003eSebastian Arango Vergara Software Engineer\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/randstorm-assessing-the-impact-of-cryptographic-vulnerabilities-in-javascript-based-cryptocurrency-wallets-2011-2015/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eRandstorm: Assessing the Impact of Cryptographic Vulnerabilities\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;in JavaScript-Based Cryptocurrency Wallets (2011–2015)\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/cryptocurrency-vulnerabilities-blockchain-common-vulnerability-list/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eCryptocurrency Vulnerabilities:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Blockchain Common Vulnerability List\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/cryptocurrency-attacks-and-security-vulnerabilities/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eCryptocurrency attacks and security vulnerabilities:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;51% attack, Sybil attack, Double-Spend attack. DDoS attacks and their repercussions. Potential flaws of cryptocurrencies\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/bitcoins-security-landscape-a-comprehensive-review-of-vulnerabilities-and-exposures/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBitcoin’s Security Landscape:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;A Comprehensive Review of Vulnerabilities and Exposures\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/exposed-the-vulnerabilities-you-need-to-know-about-the-worlds-most-popular-cryptocurrency-bitcoin/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eExposed: The Vulnerabilities You Need to Know\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;about the World’s Most Popular Cryptocurrency — Bitcoin\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/the-resilience-of-bitcoin-understanding-and-managing-vulnerabilities-in-a-decentralized-network/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eThe Resilience of Bitcoin:\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;Understanding and Managing Vulnerabilities in a Decentralized Network\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003ca href=\"https://keyhunters.ru/top-methods-to-detect-security-vulnerabilities-in-cryptocurrency-market/\"\u003e\u003cem\u003e\u003cstrong\u003eT\u003c/strong\u003e\u003c/em\u003e\u003c/a\u003e\u003cem\u003e\u003ca href=\"https://keyhunters.ru/top-methods-to-detect-security-vulnerabilities-in-cryptocurrency-market/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003e\u003cstrong\u003eop Methods to Detect Security\u003c/strong\u003e\u003c/a\u003e\u0026nbsp;Vulnerabilities in Cryptocurrency Market\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/cve-2018-17144-a-critical-denial-of-service-vulnerability-in-bitcoin-core-and-its-implications-for-blockchain-security/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eCVE-2018-17144: A Critical Denial of Service Vulnerability\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;in Bitcoin Core and Its Implications for Blockchain Security\u003c/em\u003e\u003c/li\u003e\n\n\n\n\u003cli\u003e\u003cem\u003e\u003cstrong\u003e\u003ca href=\"https://keyhunters.ru/blockchain-wallet-security-understanding-the-risks-of-pseudo-random-number-generators-and-centralized-custody/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBlockchain Wallet Security: Understanding the Risks\u003c/a\u003e\u003c/strong\u003e\u0026nbsp;of Pseudo-Random Number Generators and Centralized Custody\u003c/em\u003e\u003c/li\u003e\n\u003c/ol\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"wp-block-image aligncenter size-full is-resized\"\u003e\u003ca href=\"https://dzen.ru/video/watch/682ec3767299977a8bc27069\" target=\"_blank\" rel=\" noreferrer noopener\"\u003e\u003cimg src=\"https://cryptodeeptools.ru/wp-content/uploads/2025/05/image-1.png\" alt=\"\" class=\"wp-image-2767\" style=\"width:483px;height:auto\"/\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\u003cp\u003eThis material was created for the\u0026nbsp;\u0026nbsp;\u003ca href=\"https://cryptodeeptech.ru/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eCRYPTO DEEP TECH\u003c/a\u003e\u0026nbsp;portal \u0026nbsp;to ensure financial data security and cryptography on elliptic curves\u0026nbsp;\u0026nbsp;\u003ca href=\"https://www.youtube.com/@cryptodeeptech\" target=\"_blank\" rel=\"noreferrer noopener\"\u003esecp256k1\u003c/a\u003e\u0026nbsp;\u0026nbsp;against weak\u0026nbsp;\u0026nbsp;\u003ca href=\"https://github.com/demining/CryptoDeepTools\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eECDSA\u003c/a\u003e\u0026nbsp;signatures \u0026nbsp;in the\u0026nbsp;\u0026nbsp;\u003ca href=\"https://t.me/cryptodeeptech\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBITCOIN\u003c/a\u003e\u0026nbsp;cryptocurrency . The creators of the software are not responsible for the use of materials.\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://privextract.ru/\" target=\"_blank\" rel=\"noreferrer noopener\"\u003ePrivExtract\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://github.com/demining/CryptoDeepTools/tree/main/40PrivateKeyDebug\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSource code\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://colab.research.google.com/drive/1eaKZitRzN8034hIwivLNSawobDpcmoEm\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eGoogle Colab\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://dustattack.org/birthday-paradox\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eBirthday Paradox\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://t.me/cryptodeeptech\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eTelegram: https://t.me/cryptodeeptech\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://youtu.be/0m9goH8Lpa0\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eVideo: https://youtu.be/0m9goH8Lpa0\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://dzen.ru/video/watch/682ec3767299977a8bc27069\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eVideo tutorial: https://dzen.ru/video/watch/682ec3767299977a8bc27069\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003cstrong\u003e\u003ca href=\"https://cryptodeeptech.ru/private-key-debug\" target=\"_blank\" rel=\"noreferrer noopener\"\u003eSource: https://cryptodeeptech.ru/private-key-debug\u003c/a\u003e\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\u003cdiv class=\"wp-block-image\"\u003e\n\u003cfigure class=\"aligncenter\"\u003e\u003cimg decoding=\"async\" src=\"./Private key Debug_files/062-1024x576(1).png\" alt=\"Private key Debug: Incorrect generation of private keys, system vulnerabilities and errors in calculating the order of the elliptic curve secp256k1 threats to the Bitcoin ecosystem\" class=\"wp-image-5710\"\u003e\u003c/figure\u003e\u003c/div\u003e\n\n\n\u003chr class=\"wp-block-separator has-alpha-channel-opacity\"\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003e\u003c/p\u003e\n\t\u003c/div\u003e\u003c!-- .entry-content --\u003e\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdemining%2Fprivate-key-debug","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdemining%2Fprivate-key-debug","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdemining%2Fprivate-key-debug/lists"}