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bips/bip-0032.mediawiki at master · bitcoin/bips · GitHub
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8.351a1.312 1.312 0 0 1-1.146 1.954H1.33A1.313 1.313 0 0 1 .183 9.058ZM7 7V3H5v4Zm-1 3a1 1 0 1 0 0-2 1 1 0 0 0 0 2Z"></path> </svg> </span> <span></span> </div> </div> <div data-target="query-builder.screenReaderFeedback" aria-live="polite" aria-atomic="true" class="sr-only"></div> </query-builder></form> <div class="d-flex flex-row color-fg-muted px-3 text-small color-bg-default search-feedback-prompt"> <a target="_blank" href="https://docs.github.com/search-github/github-code-search/understanding-github-code-search-syntax" data-view-component="true" class="Link color-fg-accent text-normal ml-2"> Search syntax tips </a> <div class="d-flex flex-1"></div> </div> </div> </div> </div> </modal-dialog></div> </div> <div data-action="click:qbsearch-input#retract" class="dark-backdrop position-fixed" hidden data-target="qbsearch-input.darkBackdrop"></div> <div class="color-fg-default"> <dialog-helper> <dialog data-target="qbsearch-input.feedbackDialog" 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3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path> </svg></button> </div> </div> </div> <scrollable-region data-labelled-by="feedback-dialog-title"> <div data-view-component="true" class="Overlay-body"> <!-- '"` --><!-- </textarea></xmp> --></option></form><form id="code-search-feedback-form" data-turbo="false" action="/search/feedback" accept-charset="UTF-8" method="post"><input type="hidden" data-csrf="true" name="authenticity_token" value="LVtW+WUeuygn7utaNchGtF5FrbblFKA2vcLVvhGLFm+/yz4i0UAiV0gtUrLxk6+Ybt/JNMg1IYQNYAl2kCScyw==" /> <p>We read every piece of feedback, and take your input very seriously.</p> <textarea name="feedback" class="form-control width-full mb-2" style="height: 120px" id="feedback"></textarea> <input name="include_email" id="include_email" aria-label="Include my email address so I can be contacted" class="form-control mr-2" type="checkbox"> <label for="include_email" style="font-weight: normal">Include my email address so I can be contacted</label> </form></div> </scrollable-region> <div data-view-component="true" class="Overlay-footer Overlay-footer--alignEnd"> <button data-close-dialog-id="feedback-dialog" type="button" data-view-component="true" class="btn"> Cancel </button> <button form="code-search-feedback-form" data-action="click:qbsearch-input#submitFeedback" type="submit" data-view-component="true" class="btn-primary btn"> Submit feedback </button> </div> </dialog></dialog-helper> <custom-scopes data-target="qbsearch-input.customScopesManager"> <dialog-helper> <dialog data-target="custom-scopes.customScopesModalDialog" data-action="close:qbsearch-input#handleDialogClose cancel:qbsearch-input#handleDialogClose" id="custom-scopes-dialog" aria-modal="true" aria-labelledby="custom-scopes-dialog-title" aria-describedby="custom-scopes-dialog-description" data-view-component="true" class="Overlay Overlay-whenNarrow Overlay--size-medium Overlay--motion-scaleFade Overlay--disableScroll"> <div data-view-component="true" class="Overlay-header Overlay-header--divided"> <div class="Overlay-headerContentWrap"> <div class="Overlay-titleWrap"> <h1 class="Overlay-title " id="custom-scopes-dialog-title"> Saved searches </h1> <h2 id="custom-scopes-dialog-description" class="Overlay-description">Use saved searches to filter your results more quickly</h2> </div> <div class="Overlay-actionWrap"> <button data-close-dialog-id="custom-scopes-dialog" aria-label="Close" type="button" data-view-component="true" class="close-button Overlay-closeButton"><svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-x"> <path d="M3.72 3.72a.75.75 0 0 1 1.06 0L8 6.94l3.22-3.22a.749.749 0 0 1 1.275.326.749.749 0 0 1-.215.734L9.06 8l3.22 3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path> </svg></button> </div> </div> </div> <scrollable-region data-labelled-by="custom-scopes-dialog-title"> <div data-view-component="true" class="Overlay-body"> <div data-target="custom-scopes.customScopesModalDialogFlash"></div> <div hidden class="create-custom-scope-form" data-target="custom-scopes.createCustomScopeForm"> <!-- '"` --><!-- </textarea></xmp> --></option></form><form id="custom-scopes-dialog-form" data-turbo="false" action="/search/custom_scopes" accept-charset="UTF-8" method="post"><input type="hidden" data-csrf="true" name="authenticity_token" value="q0/43WzFGfXfa0mikPP3j10wAIxqIAvmYomAjujm36Xt83Ym8zfDaIbTx7EaJenw50AGeE/Bj36y57C1geAT9Q==" /> <div data-target="custom-scopes.customScopesModalDialogFlash"></div> <input type="hidden" id="custom_scope_id" name="custom_scope_id" data-target="custom-scopes.customScopesIdField"> <div class="form-group"> <label for="custom_scope_name">Name</label> <auto-check src="/search/custom_scopes/check_name" required> <input type="text" name="custom_scope_name" id="custom_scope_name" data-target="custom-scopes.customScopesNameField" class="form-control" autocomplete="off" placeholder="github-ruby" required maxlength="50"> <input type="hidden" data-csrf="true" value="DAq1ln2lEf07kLfzKwpwlo3K2i1S4mKAHnKURsHAffQ1L9s8Jm6Vi5Z6LkBoIhOdTN4/tMfmqw9e4AQpj+yrXA==" /> </auto-check> </div> <div class="form-group"> <label for="custom_scope_query">Query</label> <input type="text" name="custom_scope_query" id="custom_scope_query" data-target="custom-scopes.customScopesQueryField" class="form-control" autocomplete="off" placeholder="(repo:mona/a OR repo:mona/b) AND lang:python" required maxlength="500"> </div> <p class="text-small color-fg-muted"> To see all available qualifiers, see our <a class="Link--inTextBlock" href="https://docs.github.com/search-github/github-code-search/understanding-github-code-search-syntax">documentation</a>. </p> </form> </div> <div data-target="custom-scopes.manageCustomScopesForm"> <div data-target="custom-scopes.list"></div> </div> </div> </scrollable-region> <div data-view-component="true" class="Overlay-footer Overlay-footer--alignEnd Overlay-footer--divided"> <button data-action="click:custom-scopes#customScopesCancel" type="button" data-view-component="true" class="btn"> Cancel </button> <button form="custom-scopes-dialog-form" data-action="click:custom-scopes#customScopesSubmit" data-target="custom-scopes.customScopesSubmitButton" type="submit" data-view-component="true" class="btn-primary btn"> Create saved search </button> </div> </dialog></dialog-helper> </custom-scopes> </div> </qbsearch-input> <div class="position-relative HeaderMenu-link-wrap d-lg-inline-block"> <a href="/login?return_to=https%3A%2F%2Fgithub.com%2Fbitcoin%2Fbips%2Fblob%2Fmaster%2Fbip-0032.mediawiki" class="HeaderMenu-link HeaderMenu-link--sign-in HeaderMenu-button flex-shrink-0 no-underline d-none d-lg-inline-flex border border-lg-0 rounded rounded-lg-0 px-2 py-1" style="margin-left: 12px;" data-hydro-click="{"event_type":"authentication.click","payload":{"location_in_page":"site header menu","repository_id":null,"auth_type":"SIGN_UP","originating_url":"https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki","user_id":null}}" data-hydro-click-hmac="80066983389830f7138a756d1882db5800e33939bab0f0f6b85988fdbef92b67" data-analytics-event="{"category":"Marketing nav","action":"click to go to homepage","label":"ref_page:Marketing;ref_cta:Sign in;ref_loc:Header"}" > Sign in </a> </div> <a href="/signup?ref_cta=Sign+up&ref_loc=header+logged+out&ref_page=%2F%3Cuser-name%3E%2F%3Crepo-name%3E%2Fblob%2Fshow&source=header-repo&source_repo=bitcoin%2Fbips" class="HeaderMenu-link HeaderMenu-link--sign-up HeaderMenu-button flex-shrink-0 d-flex d-lg-inline-flex no-underline border color-border-default rounded px-2 py-1" data-hydro-click="{"event_type":"authentication.click","payload":{"location_in_page":"site header menu","repository_id":null,"auth_type":"SIGN_UP","originating_url":"https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki","user_id":null}}" data-hydro-click-hmac="80066983389830f7138a756d1882db5800e33939bab0f0f6b85988fdbef92b67" data-analytics-event="{"category":"Sign up","action":"click to sign up for account","label":"ref_page:/<user-name>/<repo-name>/blob/show;ref_cta:Sign up;ref_loc:header logged out"}" > Sign up </a> <button type="button" class="sr-only js-header-menu-focus-trap d-block d-lg-none">Reseting focus</button> </div> </div> </div> </div> </header> <div hidden="hidden" data-view-component="true" class="js-stale-session-flash stale-session-flash flash flash-warn flash-full"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-alert"> <path d="M6.457 1.047c.659-1.234 2.427-1.234 3.086 0l6.082 11.378A1.75 1.75 0 0 1 14.082 15H1.918a1.75 1.75 0 0 1-1.543-2.575Zm1.763.707a.25.25 0 0 0-.44 0L1.698 13.132a.25.25 0 0 0 .22.368h12.164a.25.25 0 0 0 .22-.368Zm.53 3.996v2.5a.75.75 0 0 1-1.5 0v-2.5a.75.75 0 0 1 1.5 0ZM9 11a1 1 0 1 1-2 0 1 1 0 0 1 2 0Z"></path> </svg> <span class="js-stale-session-flash-signed-in" hidden>You signed in with another tab or window. <a class="Link--inTextBlock" href="">Reload</a> to refresh your session.</span> <span class="js-stale-session-flash-signed-out" hidden>You signed out in another tab or window. <a class="Link--inTextBlock" href="">Reload</a> to refresh your session.</span> <span class="js-stale-session-flash-switched" hidden>You switched accounts on another tab or window. <a class="Link--inTextBlock" href="">Reload</a> to refresh your session.</span> <button id="icon-button-6897a55c-35fa-41f1-92c9-974c6e9e1275" aria-labelledby="tooltip-e3cf086a-93db-4967-aafc-fbe36e56a135" type="button" data-view-component="true" class="Button Button--iconOnly Button--invisible Button--medium flash-close js-flash-close"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-x Button-visual"> <path d="M3.72 3.72a.75.75 0 0 1 1.06 0L8 6.94l3.22-3.22a.749.749 0 0 1 1.275.326.749.749 0 0 1-.215.734L9.06 8l3.22 3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path> </svg> </button><tool-tip id="tooltip-e3cf086a-93db-4967-aafc-fbe36e56a135" for="icon-button-6897a55c-35fa-41f1-92c9-974c6e9e1275" popover="manual" data-direction="s" data-type="label" data-view-component="true" class="sr-only position-absolute">Dismiss alert</tool-tip> </div> </div> <div id="start-of-content" class="show-on-focus"></div> <div id="js-flash-container" class="flash-container" data-turbo-replace> <template class="js-flash-template"> <div class="flash flash-full {{ className }}"> <div > <button autofocus class="flash-close js-flash-close" type="button" aria-label="Dismiss this message"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-x"> <path d="M3.72 3.72a.75.75 0 0 1 1.06 0L8 6.94l3.22-3.22a.749.749 0 0 1 1.275.326.749.749 0 0 1-.215.734L9.06 8l3.22 3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path> </svg> </button> <div aria-atomic="true" role="alert" class="js-flash-alert"> <div>{{ message }}</div> </div> </div> </div> </template> </div> <div class="application-main " data-commit-hovercards-enabled data-discussion-hovercards-enabled data-issue-and-pr-hovercards-enabled > <div itemscope itemtype="http://schema.org/SoftwareSourceCode" class=""> <main id="js-repo-pjax-container" > <div id="repository-container-header" class="pt-3 hide-full-screen" style="background-color: var(--page-header-bgColor, var(--color-page-header-bg));" data-turbo-replace> <div class="d-flex flex-nowrap flex-justify-end mb-3 px-3 px-lg-5" style="gap: 1rem;"> <div class="flex-auto min-width-0 width-fit"> <div class=" d-flex flex-wrap flex-items-center wb-break-word f3 text-normal"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-repo color-fg-muted mr-2"> <path d="M2 2.5A2.5 2.5 0 0 1 4.5 0h8.75a.75.75 0 0 1 .75.75v12.5a.75.75 0 0 1-.75.75h-2.5a.75.75 0 0 1 0-1.5h1.75v-2h-8a1 1 0 0 0-.714 1.7.75.75 0 1 1-1.072 1.05A2.495 2.495 0 0 1 2 11.5Zm10.5-1h-8a1 1 0 0 0-1 1v6.708A2.486 2.486 0 0 1 4.5 9h8ZM5 12.25a.25.25 0 0 1 .25-.25h3.5a.25.25 0 0 1 .25.25v3.25a.25.25 0 0 1-.4.2l-1.45-1.087a.249.249 0 0 0-.3 0L5.4 15.7a.25.25 0 0 1-.4-.2Z"></path> </svg> <span class="author flex-self-stretch" itemprop="author"> <a class="url fn" rel="author" data-hovercard-type="organization" data-hovercard-url="/orgs/bitcoin/hovercard" data-octo-click="hovercard-link-click" data-octo-dimensions="link_type:self" href="/bitcoin"> bitcoin </a> </span> <span class="mx-1 flex-self-stretch color-fg-muted">/</span> <strong itemprop="name" class="mr-2 flex-self-stretch"> <a data-pjax="#repo-content-pjax-container" data-turbo-frame="repo-content-turbo-frame" href="/bitcoin/bips">bips</a> </strong> <span></span><span class="Label Label--secondary v-align-middle mr-1">Public</span> </div> </div> <div id="repository-details-container" class="flex-shrink-0" data-turbo-replace style="max-width: 70%;"> <ul class="pagehead-actions flex-shrink-0 d-none d-md-inline" style="padding: 2px 0;"> <li> <a href="/login?return_to=%2Fbitcoin%2Fbips" rel="nofollow" id="repository-details-watch-button" data-hydro-click="{"event_type":"authentication.click","payload":{"location_in_page":"notification subscription menu watch","repository_id":null,"auth_type":"LOG_IN","originating_url":"https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki","user_id":null}}" data-hydro-click-hmac="aa08083ec9ea90d1d01c3eaed35dae67f7339d977bc6b7afbba42d9e33f9a8b1" aria-label="You must be signed in to change notification settings" data-view-component="true" class="btn-sm btn"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-bell mr-2"> <path d="M8 16a2 2 0 0 0 1.985-1.75c.017-.137-.097-.25-.235-.25h-3.5c-.138 0-.252.113-.235.25A2 2 0 0 0 8 16ZM3 5a5 5 0 0 1 10 0v2.947c0 .05.015.098.042.139l1.703 2.555A1.519 1.519 0 0 1 13.482 13H2.518a1.516 1.516 0 0 1-1.263-2.36l1.703-2.554A.255.255 0 0 0 3 7.947Zm5-3.5A3.5 3.5 0 0 0 4.5 5v2.947c0 .346-.102.683-.294.97l-1.703 2.556a.017.017 0 0 0-.003.01l.001.006c0 .002.002.004.004.006l.006.004.007.001h10.964l.007-.001.006-.004.004-.006.001-.007a.017.017 0 0 0-.003-.01l-1.703-2.554a1.745 1.745 0 0 1-.294-.97V5A3.5 3.5 0 0 0 8 1.5Z"></path> </svg>Notifications </a> <tool-tip id="tooltip-022c6d47-070b-4ade-bf99-2de07471f302" for="repository-details-watch-button" popover="manual" data-direction="s" data-type="description" data-view-component="true" class="sr-only position-absolute">You must be signed in to change notification settings</tool-tip> </li> <li> <a icon="repo-forked" id="fork-button" href="/login?return_to=%2Fbitcoin%2Fbips" rel="nofollow" data-hydro-click="{"event_type":"authentication.click","payload":{"location_in_page":"repo details fork button","repository_id":14531737,"auth_type":"LOG_IN","originating_url":"https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki","user_id":null}}" data-hydro-click-hmac="7d59bc63fe669c1e64e525520e1a782f14d7163468f065fcb1d82ea479b9b0cd" data-view-component="true" class="btn-sm btn"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-repo-forked mr-2"> <path d="M5 5.372v.878c0 .414.336.75.75.75h4.5a.75.75 0 0 0 .75-.75v-.878a2.25 2.25 0 1 1 1.5 0v.878a2.25 2.25 0 0 1-2.25 2.25h-1.5v2.128a2.251 2.251 0 1 1-1.5 0V8.5h-1.5A2.25 2.25 0 0 1 3.5 6.25v-.878a2.25 2.25 0 1 1 1.5 0ZM5 3.25a.75.75 0 1 0-1.5 0 .75.75 0 0 0 1.5 0Zm6.75.75a.75.75 0 1 0 0-1.5.75.75 0 0 0 0 1.5Zm-3 8.75a.75.75 0 1 0-1.5 0 .75.75 0 0 0 1.5 0Z"></path> </svg>Fork <span id="repo-network-counter" data-pjax-replace="true" data-turbo-replace="true" title="5,392" data-view-component="true" class="Counter">5.4k</span> </a> </li> <li> <div data-view-component="true" class="BtnGroup d-flex"> <a href="/login?return_to=%2Fbitcoin%2Fbips" rel="nofollow" data-hydro-click="{"event_type":"authentication.click","payload":{"location_in_page":"star button","repository_id":14531737,"auth_type":"LOG_IN","originating_url":"https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki","user_id":null}}" data-hydro-click-hmac="0660269d2eee6cbec22ea18bafd70d4dcceedad7ea78efdee9eb41716479e822" aria-label="You must be signed in to star a repository" data-view-component="true" class="tooltipped tooltipped-sw 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data-view-component="true" class="Counter js-social-count">9.5k</span> </a></div> </li> </ul> </div> </div> <div id="responsive-meta-container" data-turbo-replace> </div> <nav data-pjax="#js-repo-pjax-container" aria-label="Repository" data-view-component="true" class="js-repo-nav js-sidenav-container-pjax js-responsive-underlinenav overflow-hidden UnderlineNav px-3 px-md-4 px-lg-5"> <ul data-view-component="true" class="UnderlineNav-body list-style-none"> <li data-view-component="true" class="d-inline-flex"> <a id="code-tab" href="/bitcoin/bips" data-tab-item="i0code-tab" data-selected-links="repo_source repo_downloads repo_commits repo_releases repo_tags repo_branches repo_packages repo_deployments repo_attestations /bitcoin/bips" data-pjax="#repo-content-pjax-container" data-turbo-frame="repo-content-turbo-frame" data-hotkey="g c" data-analytics-event="{"category":"Underline navbar","action":"Click tab","label":"Code","target":"UNDERLINE_NAV.TAB"}" aria-current="page" 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data-selected-links="repo_pulls checks /bitcoin/bips/pulls" data-pjax="#repo-content-pjax-container" data-turbo-frame="repo-content-turbo-frame" data-hotkey="g p" data-analytics-event="{"category":"Underline navbar","action":"Click tab","label":"Pull requests","target":"UNDERLINE_NAV.TAB"}" data-view-component="true" class="UnderlineNav-item no-wrap js-responsive-underlinenav-item js-selected-navigation-item"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-git-pull-request UnderlineNav-octicon d-none d-sm-inline"> <path d="M1.5 3.25a2.25 2.25 0 1 1 3 2.122v5.256a2.251 2.251 0 1 1-1.5 0V5.372A2.25 2.25 0 0 1 1.5 3.25Zm5.677-.177L9.573.677A.25.25 0 0 1 10 .854V2.5h1A2.5 2.5 0 0 1 13.5 5v5.628a2.251 2.251 0 1 1-1.5 0V5a1 1 0 0 0-1-1h-1v1.646a.25.25 0 0 1-.427.177L7.177 3.427a.25.25 0 0 1 0-.354ZM3.75 2.5a.75.75 0 1 0 0 1.5.75.75 0 0 0 0-1.5Zm0 9.5a.75.75 0 1 0 0 1.5.75.75 0 0 0 0-1.5Zm8.25.75a.75.75 0 1 0 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class="ActionListItem-label"> Insights </span> </a> </li> </ul> </div></action-list> </div> </div></anchored-position> </focus-group> </action-menu></div> </nav> </div> <turbo-frame id="repo-content-turbo-frame" target="_top" data-turbo-action="advance" class=""> <div id="repo-content-pjax-container" class="repository-content " > <react-app app-name="react-code-view" initial-path="/bitcoin/bips/blob/master/bip-0032.mediawiki" style="display: block; min-height: calc(100vh - 64px);" data-attempted-ssr="false" data-ssr="false" data-lazy="false" data-alternate="false" > <script type="application/json" 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vector 5","anchor":"test-vector-5","htmlText":"Test vector 5"},{"level":2,"text":"Acknowledgements","anchor":"acknowledgements","htmlText":"Acknowledgements"}],"lineInfo":{"truncatedLoc":"317","truncatedSloc":"227"},"mode":"file"},"image":false,"isCodeownersFile":null,"isPlain":false,"isValidLegacyIssueTemplate":false,"issueTemplate":null,"discussionTemplate":null,"language":"Wikitext","languageID":228,"large":false,"planSupportInfo":{"repoIsFork":null,"repoOwnedByCurrentUser":null,"requestFullPath":"/bitcoin/bips/blob/master/bip-0032.mediawiki","showFreeOrgGatedFeatureMessage":null,"showPlanSupportBanner":null,"upgradeDataAttributes":null,"upgradePath":null},"publishBannersInfo":{"dismissActionNoticePath":"/settings/dismiss-notice/publish_action_from_dockerfile","releasePath":"/bitcoin/bips/releases/new?marketplace=true","showPublishActionBanner":false},"rawBlobUrl":"https://github.com/bitcoin/bips/raw/refs/heads/master/bip-0032.mediawiki","renderImageOrRaw":false,"richText":"\u003carticle class=\"markdown-body entry-content container-lg\" itemprop=\"text\"\u003e\n\u003cp dir=\"auto\"\u003eRECENT CHANGES:\n\n\n\n\n\n\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003e(16 Apr 2013) Added private derivation for i ≥ 0x80000000 (less risk of parent private key leakage)\u003c/li\u003e\u003cli\u003e(30 Apr 2013) Switched from multiplication by I\u003csub\u003eL\u003c/sub\u003e to addition of I\u003csub\u003eL\u003c/sub\u003e (faster, easier implementation)\u003c/li\u003e\u003cli\u003e(25 May 2013) Added test vectors\u003c/li\u003e\u003cli\u003e(15 Jan 2014) Rename keys with index ≥ 0x80000000 to hardened keys, and add explicit conversion functions.\u003c/li\u003e\u003cli\u003e(24 Feb 2017) Added test vectors for hardened derivation with leading zeros\u003c/li\u003e\u003cli\u003e(4 Nov 2020) Added new test vectors for hardened derivation with leading zeros\u003c/li\u003e\u003c/ul\u003e\n\u003cpre\u003e BIP: 32\n Layer: Applications\n Title: Hierarchical Deterministic Wallets\n Author: Pieter Wuille \u0026lt;pieter.wuille@gmail.com\u0026gt;\n Comments-Summary: No comments yet.\n Comments-URI: https://github.com/bitcoin/bips/wiki/Comments:BIP-0032\n Status: Final\n Type: Informational\n Created: 2012-02-11\n License: BSD-2-Clause\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\u003cmarkdown-accessiblity-table\u003e\u003ctable id=\"user-content-toc\" summary=\"Contents\"\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd\u003e\u003cdiv id=\"user-content-toctitle\" dir=\"auto\"\u003e\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eTable of Contents\u003c/h2\u003e\u003ca id=\"user-content-table-of-contents\" class=\"anchor\" aria-label=\"Permalink: Table of Contents\" href=\"#table-of-contents\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003cul dir=\"auto\"\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003e\u003ca href=\"#user-content-Abstract\"\u003eAbstract\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Copyright\"\u003eCopyright\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Motivation\"\u003eMotivation\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Specification_Key_derivation\"\u003eSpecification: Key derivation\u003c/a\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003e\u003ca href=\"#user-content-Conventions\"\u003eConventions\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Extended_keys\"\u003eExtended keys\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Child_key_derivation_CKD_functions\"\u003eChild key derivation (CKD) functions\u003c/a\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003e\u003ca href=\"#user-content-Private_parent_key_rarr_private_child_key\"\u003ePrivate parent key → private child key\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Public_parent_key_rarr_public_child_key\"\u003ePublic parent key → public child key\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Private_parent_key_rarr_public_child_key\"\u003ePrivate parent key → public child key\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Public_parent_key_rarr_private_child_key\"\u003ePublic parent key → private child key\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-The_key_tree\"\u003eThe key tree\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Key_identifiers\"\u003eKey identifiers\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Serialization_format\"\u003eSerialization format\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Master_key_generation\"\u003eMaster key generation\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Specification_Wallet_structure\"\u003eSpecification: Wallet structure\u003c/a\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003e\u003ca href=\"#user-content-The_default_wallet_layout\"\u003eThe default wallet layout\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Use_cases\"\u003eUse cases\u003c/a\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003e\u003ca href=\"#user-content-Full_wallet_sharing_m\"\u003eFull wallet sharing: m\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Audits_Nm\"\u003eAudits: N(m/*)\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Peroffice_balances_misubHsub\"\u003ePer-office balances: m/i\u003csub\u003eH\u003c/sub\u003e\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Recurrent_businesstobusiness_transactions_NmisubHsub0\"\u003eRecurrent business-to-business transactions: N(m/i\u003csub\u003eH\u003c/sub\u003e/0)\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Unsecure_money_receiver_NmisubHsub0\"\u003eUnsecure money receiver: N(m/i\u003csub\u003eH\u003c/sub\u003e/0)\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Compatibility\"\u003eCompatibility\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Security\"\u003eSecurity\u003c/a\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003e\u003ca href=\"#user-content-Implications\"\u003eImplications\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Test_Vectors\"\u003eTest Vectors\u003c/a\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003e\u003ca href=\"#user-content-Test_vector_1\"\u003eTest vector 1\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Test_vector_2\"\u003eTest vector 2\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Test_vector_3\"\u003eTest vector 3\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Test_vector_4\"\u003eTest vector 4\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Test_vector_5\"\u003eTest vector 5\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003e\u003ca href=\"#user-content-Acknowledgements\"\u003eAcknowledgements\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/ul\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Abstract\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Abstract\"\u003eAbstract\u003c/span\u003e\u003c/h2\u003e\u003ca id=\"user-content-abstract\" class=\"anchor\" aria-label=\"Permalink: Abstract\" href=\"#abstract\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eThis document describes hierarchical deterministic wallets (or \"HD Wallets\"): wallets which can be shared partially or entirely with different systems, each with or without the ability to spend coins.\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe specification is intended to set a standard for deterministic wallets that can be interchanged between different clients. Although the wallets described here have many features, not all are required by supporting clients.\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe specification consists of two parts. In the first part, a system for deriving a tree of keypairs from a single seed is presented. The second part demonstrates how to build a wallet structure on top of such a tree.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Copyright\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Copyright\"\u003eCopyright\u003c/span\u003e\u003c/h2\u003e\u003ca id=\"user-content-copyright\" class=\"anchor\" aria-label=\"Permalink: Copyright\" href=\"#copyright\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eThis BIP is licensed under the 2-clause BSD license.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Motivation\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Motivation\"\u003eMotivation\u003c/span\u003e\u003c/h2\u003e\u003ca id=\"user-content-motivation\" class=\"anchor\" aria-label=\"Permalink: Motivation\" href=\"#motivation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eThe Bitcoin reference client uses randomly generated keys. In order to avoid the necessity for a backup after every transaction, (by default) 100 keys are cached in a pool of reserve keys. Still, these wallets are not intended to be shared and used on several systems simultaneously. They support hiding their private keys by using the wallet encrypt feature and not sharing the password, but such \"neutered\" wallets lose the power to generate public keys as well.\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eDeterministic wallets do not require such frequent backups, and elliptic curve mathematics permit schemes where one can calculate the public keys without revealing the private keys. This permits for example a webshop business to let its webserver generate fresh addresses (public key hashes) for each order or for each customer, without giving the webserver access to the corresponding private keys (which are required for spending the received funds).\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eHowever, deterministic wallets typically consist of a single \"chain\" of keypairs. The fact that there is only one chain means that sharing a wallet happens on an all-or-nothing basis. However, in some cases one only wants some (public) keys to be shared and recoverable. In the example of a webshop, the webserver does not need access to all public keys of the merchant's wallet; only to those addresses which are used to receive customers' payments, and not for example the change addresses that are generated when the merchant spends money. Hierarchical deterministic wallets allow such selective sharing by supporting multiple keypair chains, derived from a single root.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Specification_Key_derivation\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Specification_Key_derivation\"\u003eSpecification: Key derivation\u003c/span\u003e\u003c/h2\u003e\u003ca id=\"user-content-specification-key-derivation\" class=\"anchor\" aria-label=\"Permalink: Specification: Key derivation\" href=\"#specification-key-derivation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Conventions\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Conventions\"\u003eConventions\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-conventions\" class=\"anchor\" aria-label=\"Permalink: Conventions\" href=\"#conventions\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eIn the rest of this text we will assume the public key cryptography used in Bitcoin, namely elliptic curve cryptography using the field and curve parameters defined by secp256k1 (\u003ca href=\"http://www.secg.org/sec2-v2.pdf\" rel=\"nofollow\"\u003ehttp://www.secg.org/sec2-v2.pdf\u003c/a\u003e). Variables below are either:\n\n\n\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eIntegers modulo the order of the curve (referred to as n).\u003c/li\u003e\u003cli\u003eCoordinates of points on the curve.\u003c/li\u003e\u003cli\u003eByte sequences.\u003c/li\u003e\u003c/ul\u003e\nAddition (+) of two coordinate pair is defined as application of the EC group operation.\nConcatenation (||) is the operation of appending one byte sequence onto another.\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eAs standard conversion functions, we assume:\n\n\n\n\n\n\n\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003epoint(p): returns the coordinate pair resulting from EC point multiplication (repeated application of the EC group operation) of the secp256k1 base point with the integer p.\u003c/li\u003e\u003cli\u003eser\u003csub\u003e32\u003c/sub\u003e(i): serialize a 32-bit unsigned integer i as a 4-byte sequence, most significant byte first.\u003c/li\u003e\u003cli\u003eser\u003csub\u003e256\u003c/sub\u003e(p): serializes the integer p as a 32-byte sequence, most significant byte first.\u003c/li\u003e\u003cli\u003eser\u003csub\u003eP\u003c/sub\u003e(P): serializes the coordinate pair P = (x,y) as a byte sequence using SEC1's compressed form: (0x02 or 0x03) || ser\u003csub\u003e256\u003c/sub\u003e(x), where the header byte depends on the parity of the omitted y coordinate.\u003c/li\u003e\u003cli\u003eparse\u003csub\u003e256\u003c/sub\u003e(p): interprets a 32-byte sequence as a 256-bit number, most significant byte first.\u003c/li\u003e\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Extended_keys\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Extended_keys\"\u003eExtended keys\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-extended-keys\" class=\"anchor\" aria-label=\"Permalink: Extended keys\" href=\"#extended-keys\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eIn what follows, we will define a function that derives a number of child keys from a parent key. In order to prevent these from depending solely on the key itself, we extend both private and public keys first with an extra 256 bits of entropy. This extension, called the chain code, is identical for corresponding private and public keys, and consists of 32 bytes.\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eWe represent an extended private key as (k, c), with k the normal private key, and c the chain code. An extended public key is represented as (K, c), with K = point(k) and c the chain code.\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eEach extended key has 2\u003csup\u003e31\u003c/sup\u003e normal child keys, and 2\u003csup\u003e31\u003c/sup\u003e hardened child keys. Each of these child keys has an index. The normal child keys use indices 0 through 2\u003csup\u003e31\u003c/sup\u003e-1. The hardened child keys use indices 2\u003csup\u003e31\u003c/sup\u003e through 2\u003csup\u003e32\u003c/sup\u003e-1. To ease notation for hardened key indices, a number i\u003csub\u003eH\u003c/sub\u003e represents i+2\u003csup\u003e31\u003c/sup\u003e.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Child_key_derivation_CKD_functions\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Child_key_derivation_CKD_functions\"\u003eChild key derivation (CKD) functions\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-child-key-derivation-ckd-functions\" class=\"anchor\" aria-label=\"Permalink: Child key derivation (CKD) functions\" href=\"#child-key-derivation-ckd-functions\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eGiven a parent extended key and an index i, it is possible to compute the corresponding child extended key. The algorithm to do so depends on whether the child is a hardened key or not (or, equivalently, whether i ≥ 2\u003csup\u003e31\u003c/sup\u003e), and whether we're talking about private or public keys.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Private_parent_key_rarr_private_child_key\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Private_parent_key_rarr_private_child_key\"\u003ePrivate parent key → private child key\u003c/span\u003e\u003c/h4\u003e\u003ca id=\"user-content-private-parent-key--private-child-key\" class=\"anchor\" aria-label=\"Permalink: Private parent key → private child key\" href=\"#private-parent-key--private-child-key\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eThe function CKDpriv((k\u003csub\u003epar\u003c/sub\u003e, c\u003csub\u003epar\u003c/sub\u003e), i) → (k\u003csub\u003ei\u003c/sub\u003e, c\u003csub\u003ei\u003c/sub\u003e) computes a child extended private key from the parent extended private key:\n\n\n\n\n\n\n\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eCheck whether i ≥ 2\u003csup\u003e31\u003c/sup\u003e (whether the child is a hardened key).\u003cul dir=\"auto\"\u003e\u003cli\u003eIf so (hardened child): let I = HMAC-SHA512(Key = c\u003csub\u003epar\u003c/sub\u003e, Data = 0x00 || ser\u003csub\u003e256\u003c/sub\u003e(k\u003csub\u003epar\u003c/sub\u003e) || ser\u003csub\u003e32\u003c/sub\u003e(i)). (Note: The 0x00 pads the private key to make it 33 bytes long.)\u003c/li\u003e\u003cli\u003eIf not (normal child): let I = HMAC-SHA512(Key = c\u003csub\u003epar\u003c/sub\u003e, Data = ser\u003csub\u003eP\u003c/sub\u003e(point(k\u003csub\u003epar\u003c/sub\u003e)) || ser\u003csub\u003e32\u003c/sub\u003e(i)).\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eSplit I into two 32-byte sequences, I\u003csub\u003eL\u003c/sub\u003e and I\u003csub\u003eR\u003c/sub\u003e.\u003c/li\u003e\u003cli\u003eThe returned child key k\u003csub\u003ei\u003c/sub\u003e is parse\u003csub\u003e256\u003c/sub\u003e(I\u003csub\u003eL\u003c/sub\u003e) + k\u003csub\u003epar\u003c/sub\u003e (mod n).\u003c/li\u003e\u003cli\u003eThe returned chain code c\u003csub\u003ei\u003c/sub\u003e is I\u003csub\u003eR\u003c/sub\u003e.\u003c/li\u003e\u003cli\u003eIn case parse\u003csub\u003e256\u003c/sub\u003e(I\u003csub\u003eL\u003c/sub\u003e) ≥ n or k\u003csub\u003ei\u003c/sub\u003e = 0, the resulting key is invalid, and one should proceed with the next value for i. (Note: this has probability lower than 1 in 2\u003csup\u003e127\u003c/sup\u003e.)\u003c/li\u003e\u003c/ul\u003e\nThe HMAC-SHA512 function is specified in \u003ca href=\"http://tools.ietf.org/html/rfc4231\" rel=\"nofollow\"\u003eRFC 4231\u003c/a\u003e.\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Public_parent_key_rarr_public_child_key\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Public_parent_key_rarr_public_child_key\"\u003ePublic parent key → public child key\u003c/span\u003e\u003c/h4\u003e\u003ca id=\"user-content-public-parent-key--public-child-key\" class=\"anchor\" aria-label=\"Permalink: Public parent key → public child key\" href=\"#public-parent-key--public-child-key\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eThe function CKDpub((K\u003csub\u003epar\u003c/sub\u003e, c\u003csub\u003epar\u003c/sub\u003e), i) → (K\u003csub\u003ei\u003c/sub\u003e, c\u003csub\u003ei\u003c/sub\u003e) computes a child extended public key from the parent extended public key. It is only defined for non-hardened child keys.\n\n\n\n\n\n\n\n\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eCheck whether i ≥ 2\u003csup\u003e31\u003c/sup\u003e (whether the child is a hardened key).\u003cul dir=\"auto\"\u003e\u003cli\u003eIf so (hardened child): return failure\u003c/li\u003e\u003cli\u003eIf not (normal child): let I = HMAC-SHA512(Key = c\u003csub\u003epar\u003c/sub\u003e, Data = ser\u003csub\u003eP\u003c/sub\u003e(K\u003csub\u003epar\u003c/sub\u003e) || ser\u003csub\u003e32\u003c/sub\u003e(i)).\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eSplit I into two 32-byte sequences, I\u003csub\u003eL\u003c/sub\u003e and I\u003csub\u003eR\u003c/sub\u003e.\u003c/li\u003e\u003cli\u003eThe returned child key K\u003csub\u003ei\u003c/sub\u003e is point(parse\u003csub\u003e256\u003c/sub\u003e(I\u003csub\u003eL\u003c/sub\u003e)) + K\u003csub\u003epar\u003c/sub\u003e.\u003c/li\u003e\u003cli\u003eThe returned chain code c\u003csub\u003ei\u003c/sub\u003e is I\u003csub\u003eR\u003c/sub\u003e.\u003c/li\u003e\u003cli\u003eIn case parse\u003csub\u003e256\u003c/sub\u003e(I\u003csub\u003eL\u003c/sub\u003e) ≥ n or K\u003csub\u003ei\u003c/sub\u003e is the point at infinity, the resulting key is invalid, and one should proceed with the next value for i.\u003c/li\u003e\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Private_parent_key_rarr_public_child_key\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Private_parent_key_rarr_public_child_key\"\u003ePrivate parent key → public child key\u003c/span\u003e\u003c/h4\u003e\u003ca id=\"user-content-private-parent-key--public-child-key\" class=\"anchor\" aria-label=\"Permalink: Private parent key → public child key\" href=\"#private-parent-key--public-child-key\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eThe function N((k, c)) → (K, c) computes the extended public key corresponding to an extended private key (the \"neutered\" version, as it removes the ability to sign transactions).\n\n\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eThe returned key K is point(k).\u003c/li\u003e\u003cli\u003eThe returned chain code c is just the passed chain code.\u003c/li\u003e\u003c/ul\u003e\nTo compute the public child key of a parent private key:\n\n\n\u003cul dir=\"auto\"\u003e\u003cli\u003eN(CKDpriv((k\u003csub\u003epar\u003c/sub\u003e, c\u003csub\u003epar\u003c/sub\u003e), i)) (works always).\u003c/li\u003e\u003cli\u003eCKDpub(N(k\u003csub\u003epar\u003c/sub\u003e, c\u003csub\u003epar\u003c/sub\u003e), i) (works only for non-hardened child keys).\u003c/li\u003e\u003c/ul\u003e\nThe fact that they are equivalent is what makes non-hardened keys useful (one can derive child public keys of a given parent key without knowing any private key), and also what distinguishes them from hardened keys. The reason for not always using non-hardened keys (which are more useful) is security; see further below for more information.\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Public_parent_key_rarr_private_child_key\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Public_parent_key_rarr_private_child_key\"\u003ePublic parent key → private child key\u003c/span\u003e\u003c/h4\u003e\u003ca id=\"user-content-public-parent-key--private-child-key\" class=\"anchor\" aria-label=\"Permalink: Public parent key → private child key\" href=\"#public-parent-key--private-child-key\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eThis is not possible.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-The_key_tree\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-The_key_tree\"\u003eThe key tree\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-the-key-tree\" class=\"anchor\" aria-label=\"Permalink: The key tree\" href=\"#the-key-tree\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eThe next step is cascading several CKD constructions to build a tree. We start with one root, the master extended key m. By evaluating CKDpriv(m,i) for several values of i, we get a number of level-1 derived nodes. As each of these is again an extended key, CKDpriv can be applied to those as well.\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eTo shorten notation, we will write CKDpriv(CKDpriv(CKDpriv(m,3\u003csub\u003eH\u003c/sub\u003e),2),5) as m/3\u003csub\u003eH\u003c/sub\u003e/2/5. Equivalently for public keys, we write CKDpub(CKDpub(CKDpub(M,3),2),5) as M/3/2/5. This results in the following identities:\n\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eN(m/a/b/c) = N(m/a/b)/c = N(m/a)/b/c = N(m)/a/b/c = M/a/b/c.\u003c/li\u003e\u003cli\u003eN(m/a\u003csub\u003eH\u003c/sub\u003e/b/c) = N(m/a\u003csub\u003eH\u003c/sub\u003e/b)/c = N(m/a\u003csub\u003eH\u003c/sub\u003e)/b/c.\u003c/li\u003e\u003c/ul\u003e\nHowever, N(m/a\u003csub\u003eH\u003c/sub\u003e) cannot be rewritten as N(m)/a\u003csub\u003eH\u003c/sub\u003e, as the latter is not possible.\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eEach leaf node in the tree corresponds to an actual key, while the internal nodes correspond to the collections of keys that descend from them. The chain codes of the leaf nodes are ignored, and only their embedded private or public key is relevant. Because of this construction, knowing an extended private key allows reconstruction of all descendant private keys and public keys, and knowing an extended public key allows reconstruction of all descendant non-hardened public keys.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Key_identifiers\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Key_identifiers\"\u003eKey identifiers\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-key-identifiers\" class=\"anchor\" aria-label=\"Permalink: Key identifiers\" href=\"#key-identifiers\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eExtended keys can be identified by the Hash160 (RIPEMD160 after SHA256) of the serialized ECDSA public key K, ignoring the chain code. This corresponds exactly to the data used in traditional Bitcoin addresses. It is not advised to represent this data in base58 format though, as it may be interpreted as an address that way (and wallet software is not required to accept payment to the chain key itself).\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe first 32 bits of the identifier are called the key fingerprint.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Serialization_format\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Serialization_format\"\u003eSerialization format\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-serialization-format\" class=\"anchor\" aria-label=\"Permalink: Serialization format\" href=\"#serialization-format\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eExtended public and private keys are serialized as follows:\n\n\n\n\n\n\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003e4 byte: version bytes (mainnet: 0x0488B21E public, 0x0488ADE4 private; testnet: 0x043587CF public, 0x04358394 private)\u003c/li\u003e\u003cli\u003e1 byte: depth: 0x00 for master nodes, 0x01 for level-1 derived keys, ....\u003c/li\u003e\u003cli\u003e4 bytes: the fingerprint of the parent's key (0x00000000 if master key)\u003c/li\u003e\u003cli\u003e4 bytes: child number. This is ser\u003csub\u003e32\u003c/sub\u003e(i) for i in x\u003csub\u003ei\u003c/sub\u003e = x\u003csub\u003epar\u003c/sub\u003e/i, with x\u003csub\u003ei\u003c/sub\u003e the key being serialized. (0x00000000 if master key)\u003c/li\u003e\u003cli\u003e32 bytes: the chain code\u003c/li\u003e\u003cli\u003e33 bytes: the public key or private key data (ser\u003csub\u003eP\u003c/sub\u003e(K) for public keys, 0x00 || ser\u003csub\u003e256\u003c/sub\u003e(k) for private keys)\u003c/li\u003e\u003c/ul\u003e\nThis 78 byte structure can be encoded like other Bitcoin data in Base58, by first adding 32 checksum bits (derived from the double SHA-256 checksum), and then converting to the Base58 representation. This results in a Base58-encoded string of up to 112 characters. Because of the choice of the version bytes, the Base58 representation will start with \"xprv\" or \"xpub\" on mainnet, \"tprv\" or \"tpub\" on testnet.\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eNote that the fingerprint of the parent only serves as a fast way to detect parent and child nodes in software, and software must be willing to deal with collisions. Internally, the full 160-bit identifier could be used.\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eWhen importing a serialized extended public key, implementations must verify whether the X coordinate in the public key data corresponds to a point on the curve. If not, the extended public key is invalid.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Master_key_generation\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Master_key_generation\"\u003eMaster key generation\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-master-key-generation\" class=\"anchor\" aria-label=\"Permalink: Master key generation\" href=\"#master-key-generation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eThe total number of possible extended keypairs is almost 2\u003csup\u003e512\u003c/sup\u003e, but the produced keys are only 256 bits long, and offer about half of that in terms of security. Therefore, master keys are not generated directly, but instead from a potentially short seed value.\n\u003c/p\u003e\n\n\n\n\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eGenerate a seed byte sequence S of a chosen length (between 128 and 512 bits; 256 bits is advised) from a (P)RNG.\u003c/li\u003e\u003cli\u003eCalculate I = HMAC-SHA512(Key = \"Bitcoin seed\", Data = S)\u003c/li\u003e\u003cli\u003eSplit I into two 32-byte sequences, I\u003csub\u003eL\u003c/sub\u003e and I\u003csub\u003eR\u003c/sub\u003e.\u003c/li\u003e\u003cli\u003eUse parse\u003csub\u003e256\u003c/sub\u003e(I\u003csub\u003eL\u003c/sub\u003e) as master secret key, and I\u003csub\u003eR\u003c/sub\u003e as master chain code.\u003c/li\u003e\u003c/ul\u003e\nIn case parse\u003csub\u003e256\u003c/sub\u003e(I\u003csub\u003eL\u003c/sub\u003e) is 0 or parse\u003csub\u003e256\u003c/sub\u003e(I\u003csub\u003eL\u003c/sub\u003e) ≥ n, the master key is invalid.\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/bitcoin/bips/blob/master/bip-0032/derivation.png\"\u003e\u003cimg src=\"/bitcoin/bips/raw/master/bip-0032/derivation.png\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Specification_Wallet_structure\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Specification_Wallet_structure\"\u003eSpecification: Wallet structure\u003c/span\u003e\u003c/h2\u003e\u003ca id=\"user-content-specification-wallet-structure\" class=\"anchor\" aria-label=\"Permalink: Specification: Wallet structure\" href=\"#specification-wallet-structure\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eThe previous sections specified key trees and their nodes. The next step is imposing a wallet structure on this tree. The layout defined in this section is a default only, though clients are encouraged to mimic it for compatibility, even if not all features are supported.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-The_default_wallet_layout\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-The_default_wallet_layout\"\u003eThe default wallet layout\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-the-default-wallet-layout\" class=\"anchor\" aria-label=\"Permalink: The default wallet layout\" href=\"#the-default-wallet-layout\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eAn HDW is organized as several 'accounts'. Accounts are numbered, the default account (\"\") being number 0. Clients are not required to support more than one account - if not, they only use the default account.\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eEach account is composed of two keypair chains: an internal and an external one. The external keychain is used to generate new public addresses, while the internal keychain is used for all other operations (change addresses, generation addresses, ..., anything that doesn't need to be communicated). Clients that do not support separate keychains for these should use the external one for everything.\n\n\n\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003em/i\u003csub\u003eH\u003c/sub\u003e/0/k corresponds to the k'th keypair of the external chain of account number i of the HDW derived from master m.\u003c/li\u003e\u003cli\u003em/i\u003csub\u003eH\u003c/sub\u003e/1/k corresponds to the k'th keypair of the internal chain of account number i of the HDW derived from master m.\u003c/li\u003e\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Use_cases\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Use_cases\"\u003eUse cases\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-use-cases\" class=\"anchor\" aria-label=\"Permalink: Use cases\" href=\"#use-cases\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Full_wallet_sharing_m\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Full_wallet_sharing_m\"\u003eFull wallet sharing: m\u003c/span\u003e\u003c/h4\u003e\u003ca id=\"user-content-full-wallet-sharing-m\" class=\"anchor\" aria-label=\"Permalink: Full wallet sharing: m\" href=\"#full-wallet-sharing-m\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eIn cases where two systems need to access a single shared wallet, and both need to be able to perform spendings, one needs to share the master private extended key. Nodes can keep a pool of N look-ahead keys cached for external chains, to watch for incoming payments. The look-ahead for internal chains can be very small, as no gaps are to be expected here. An extra look-ahead could be active for the first unused account's chains - triggering the creation of a new account when used. Note that the name of the account will still need to be entered manually and cannot be synchronized via the block chain.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Audits_Nm\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Audits_Nm\"\u003eAudits: N(m/*)\u003c/span\u003e\u003c/h4\u003e\u003ca id=\"user-content-audits-nm\" class=\"anchor\" aria-label=\"Permalink: Audits: N(m/*)\" href=\"#audits-nm\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eIn case an auditor needs full access to the list of incoming and outgoing payments, one can share all account public extended keys. This will allow the auditor to see all transactions from and to the wallet, in all accounts, but not a single secret key.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Peroffice_balances_misubHsub\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Peroffice_balances_misubHsub\"\u003ePer-office balances: m/i\u003csub\u003eH\u003c/sub\u003e\u003c/span\u003e\u003c/h4\u003e\u003ca id=\"user-content-per-office-balances-mih\" class=\"anchor\" aria-label=\"Permalink: Per-office balances: m/iH\" href=\"#per-office-balances-mih\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eWhen a business has several independent offices, they can all use wallets derived from a single master. This will allow the headquarters to maintain a super-wallet that sees all incoming and outgoing transactions of all offices, and even permit moving money between the offices.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Recurrent_businesstobusiness_transactions_NmisubHsub0\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Recurrent_businesstobusiness_transactions_NmisubHsub0\"\u003eRecurrent business-to-business transactions: N(m/i\u003csub\u003eH\u003c/sub\u003e/0)\u003c/span\u003e\u003c/h4\u003e\u003ca id=\"user-content-recurrent-business-to-business-transactions-nmih0\" class=\"anchor\" aria-label=\"Permalink: Recurrent business-to-business transactions: N(m/iH/0)\" href=\"#recurrent-business-to-business-transactions-nmih0\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eIn case two business partners often transfer money, one can use the extended public key for the external chain of a specific account (M/i h/0) as a sort of \"super address\", allowing frequent transactions that cannot (easily) be associated, but without needing to request a new address for each payment.\nSuch a mechanism could also be used by mining pool operators as a variable payout address.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Unsecure_money_receiver_NmisubHsub0\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Unsecure_money_receiver_NmisubHsub0\"\u003eUnsecure money receiver: N(m/i\u003csub\u003eH\u003c/sub\u003e/0)\u003c/span\u003e\u003c/h4\u003e\u003ca id=\"user-content-unsecure-money-receiver-nmih0\" class=\"anchor\" aria-label=\"Permalink: Unsecure money receiver: N(m/iH/0)\" href=\"#unsecure-money-receiver-nmih0\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eWhen an unsecure webserver is used to run an e-commerce site, it needs to know public addresses that are used to receive payments. The webserver only needs to know the public extended key of the external chain of a single account. This means someone illegally obtaining access to the webserver can at most see all incoming payments but will not be able to steal the money, will not (trivially) be able to distinguish outgoing transactions, nor be able to see payments received by other webservers if there are several.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Compatibility\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Compatibility\"\u003eCompatibility\u003c/span\u003e\u003c/h2\u003e\u003ca id=\"user-content-compatibility\" class=\"anchor\" aria-label=\"Permalink: Compatibility\" href=\"#compatibility\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eTo comply with this standard, a client must at least be able to import an extended public or private key, to give access to its direct descendants as wallet keys. The wallet structure (master/account/chain/subchain) presented in the second part of the specification is advisory only, but is suggested as a minimal structure for easy compatibility - even when no separate accounts or distinction between internal and external chains is made. However, implementations may deviate from it for specific needs; more complex applications may call for a more complex tree structure.\n\u003c/p\u003e\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Security\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Security\"\u003eSecurity\u003c/span\u003e\u003c/h2\u003e\u003ca id=\"user-content-security\" class=\"anchor\" aria-label=\"Permalink: Security\" href=\"#security\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eIn addition to the expectations from the EC public-key cryptography itself:\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eGiven a public key K, an attacker cannot find the corresponding private key more efficiently than by solving the EC discrete logarithm problem (assumed to require 2\u003csup\u003e128\u003c/sup\u003e group operations).\u003c/li\u003e\u003c/ul\u003e\nthe intended security properties of this standard are:\n\n\n\u003cul dir=\"auto\"\u003e\u003cli\u003eGiven a child extended private key (k\u003csub\u003ei\u003c/sub\u003e,c\u003csub\u003ei\u003c/sub\u003e) and the integer i, an attacker cannot find the parent private key k\u003csub\u003epar\u003c/sub\u003e more efficiently than a 2\u003csup\u003e256\u003c/sup\u003e brute force of HMAC-SHA512.\u003c/li\u003e\u003cli\u003eGiven any number (2 ≤ N ≤ 2\u003csup\u003e32\u003c/sup\u003e-1) of (index, extended private key) tuples (i\u003csub\u003ej\u003c/sub\u003e,(k\u003csub\u003ei\u003csub\u003ej\u003c/sub\u003e\u003c/sub\u003e,c\u003csub\u003ei\u003csub\u003ej\u003c/sub\u003e\u003c/sub\u003e)), with distinct i\u003csub\u003ej\u003c/sub\u003e's, determining whether they are derived from a common parent extended private key (i.e., whether there exists a (k\u003csub\u003epar\u003c/sub\u003e,c\u003csub\u003epar\u003c/sub\u003e) such that for each j in (0..N-1) CKDpriv((k\u003csub\u003epar\u003c/sub\u003e,c\u003csub\u003epar\u003c/sub\u003e),i\u003csub\u003ej\u003c/sub\u003e)=(k\u003csub\u003ei\u003csub\u003ej\u003c/sub\u003e\u003c/sub\u003e,c\u003csub\u003ei\u003csub\u003ej\u003c/sub\u003e\u003c/sub\u003e)), cannot be done more efficiently than a 2\u003csup\u003e256\u003c/sup\u003e brute force of HMAC-SHA512.\u003c/li\u003e\u003c/ul\u003e\nNote however that the following properties do not exist:\n\n\n\n\n\u003cul dir=\"auto\"\u003e\u003cli\u003eGiven a parent extended public key (K\u003csub\u003epar\u003c/sub\u003e,c\u003csub\u003epar\u003c/sub\u003e) and a child public key (K\u003csub\u003ei\u003c/sub\u003e), it is hard to find i.\u003c/li\u003e\u003cli\u003eGiven a parent extended public key (K\u003csub\u003epar\u003c/sub\u003e,c\u003csub\u003epar\u003c/sub\u003e) and a non-hardened child private key (k\u003csub\u003ei\u003c/sub\u003e), it is hard to find k\u003csub\u003epar\u003c/sub\u003e.\u003c/li\u003e\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Implications\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Implications\"\u003eImplications\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-implications\" class=\"anchor\" aria-label=\"Permalink: Implications\" href=\"#implications\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003ePrivate and public keys must be kept safe as usual. Leaking a private key means access to coins - leaking a public key can mean loss of privacy.\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eSomewhat more care must be taken regarding extended keys, as these correspond to an entire (sub)tree of keys.\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eOne weakness that may not be immediately obvious, is that knowledge of a parent extended public key plus any non-hardened private key descending from it is equivalent to knowing the parent extended private key (and thus every private and public key descending from it). This means that extended public keys must be treated more carefully than regular public keys.\nIt is also the reason for the existence of hardened keys, and why they are used for the account level in the tree. This way, a leak of account-specific (or below) private keys never risks compromising the master or other accounts.\n\u003c/p\u003e\n\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Test_Vectors\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Test_Vectors\"\u003eTest Vectors\u003c/span\u003e\u003c/h2\u003e\u003ca id=\"user-content-test-vectors\" class=\"anchor\" aria-label=\"Permalink: Test Vectors\" href=\"#test-vectors\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Test_vector_1\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Test_vector_1\"\u003eTest vector 1\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-test-vector-1\" class=\"anchor\" aria-label=\"Permalink: Test vector 1\" href=\"#test-vector-1\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eSeed (hex): 000102030405060708090a0b0c0d0e0f\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eChain m\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub661MyMwAqRbcFtXgS5sYJABqqG9YLmC4Q1Rdap9gSE8NqtwybGhePY2gZ29ESFjqJoCu1Rupje8YtGqsefD265TMg7usUDFdp6W1EGMcet8\u003c/li\u003e\u003cli\u003eext prv: xprv9s21ZrQH143K3QTDL4LXw2F7HEK3wJUD2nW2nRk4stbPy6cq3jPPqjiChkVvvNKmPGJxWUtg6LnF5kejMRNNU3TGtRBeJgk33yuGBxrMPHi\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eChain m/0\u003csub\u003eH\u003c/sub\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub68Gmy5EdvgibQVfPdqkBBCHxA5htiqg55crXYuXoQRKfDBFA1WEjWgP6LHhwBZeNK1VTsfTFUHCdrfp1bgwQ9xv5ski8PX9rL2dZXvgGDnw\u003c/li\u003e\u003cli\u003eext prv: xprv9uHRZZhk6KAJC1avXpDAp4MDc3sQKNxDiPvvkX8Br5ngLNv1TxvUxt4cV1rGL5hj6KCesnDYUhd7oWgT11eZG7XnxHrnYeSvkzY7d2bhkJ7\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eChain m/0\u003csub\u003eH\u003c/sub\u003e/1\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub6ASuArnXKPbfEwhqN6e3mwBcDTgzisQN1wXN9BJcM47sSikHjJf3UFHKkNAWbWMiGj7Wf5uMash7SyYq527Hqck2AxYysAA7xmALppuCkwQ\u003c/li\u003e\u003cli\u003eext prv: xprv9wTYmMFdV23N2TdNG573QoEsfRrWKQgWeibmLntzniatZvR9BmLnvSxqu53Kw1UmYPxLgboyZQaXwTCg8MSY3H2EU4pWcQDnRnrVA1xe8fs\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eChain m/0\u003csub\u003eH\u003c/sub\u003e/1/2\u003csub\u003eH\u003c/sub\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub6D4BDPcP2GT577Vvch3R8wDkScZWzQzMMUm3PWbmWvVJrZwQY4VUNgqFJPMM3No2dFDFGTsxxpG5uJh7n7epu4trkrX7x7DogT5Uv6fcLW5\u003c/li\u003e\u003cli\u003eext prv: xprv9z4pot5VBttmtdRTWfWQmoH1taj2axGVzFqSb8C9xaxKymcFzXBDptWmT7FwuEzG3ryjH4ktypQSAewRiNMjANTtpgP4mLTj34bhnZX7UiM\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eChain m/0\u003csub\u003eH\u003c/sub\u003e/1/2\u003csub\u003eH\u003c/sub\u003e/2\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub6FHa3pjLCk84BayeJxFW2SP4XRrFd1JYnxeLeU8EqN3vDfZmbqBqaGJAyiLjTAwm6ZLRQUMv1ZACTj37sR62cfN7fe5JnJ7dh8zL4fiyLHV\u003c/li\u003e\u003cli\u003eext prv: xprvA2JDeKCSNNZky6uBCviVfJSKyQ1mDYahRjijr5idH2WwLsEd4Hsb2Tyh8RfQMuPh7f7RtyzTtdrbdqqsunu5Mm3wDvUAKRHSC34sJ7in334\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eChain m/0\u003csub\u003eH\u003c/sub\u003e/1/2\u003csub\u003eH\u003c/sub\u003e/2/1000000000\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub6H1LXWLaKsWFhvm6RVpEL9P4KfRZSW7abD2ttkWP3SSQvnyA8FSVqNTEcYFgJS2UaFcxupHiYkro49S8yGasTvXEYBVPamhGW6cFJodrTHy\u003c/li\u003e\u003cli\u003eext prv: xprvA41z7zogVVwxVSgdKUHDy1SKmdb533PjDz7J6N6mV6uS3ze1ai8FHa8kmHScGpWmj4WggLyQjgPie1rFSruoUihUZREPSL39UNdE3BBDu76\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Test_vector_2\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Test_vector_2\"\u003eTest vector 2\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-test-vector-2\" class=\"anchor\" aria-label=\"Permalink: Test vector 2\" href=\"#test-vector-2\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eSeed (hex): fffcf9f6f3f0edeae7e4e1dedbd8d5d2cfccc9c6c3c0bdbab7b4b1aeaba8a5a29f9c999693908d8a8784817e7b7875726f6c696663605d5a5754514e4b484542\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eChain m\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub661MyMwAqRbcFW31YEwpkMuc5THy2PSt5bDMsktWQcFF8syAmRUapSCGu8ED9W6oDMSgv6Zz8idoc4a6mr8BDzTJY47LJhkJ8UB7WEGuduB\u003c/li\u003e\u003cli\u003eext prv: xprv9s21ZrQH143K31xYSDQpPDxsXRTUcvj2iNHm5NUtrGiGG5e2DtALGdso3pGz6ssrdK4PFmM8NSpSBHNqPqm55Qn3LqFtT2emdEXVYsCzC2U\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eChain m/0\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub69H7F5d8KSRgmmdJg2KhpAK8SR3DjMwAdkxj3ZuxV27CprR9LgpeyGmXUbC6wb7ERfvrnKZjXoUmmDznezpbZb7ap6r1D3tgFxHmwMkQTPH\u003c/li\u003e\u003cli\u003eext prv: xprv9vHkqa6EV4sPZHYqZznhT2NPtPCjKuDKGY38FBWLvgaDx45zo9WQRUT3dKYnjwih2yJD9mkrocEZXo1ex8G81dwSM1fwqWpWkeS3v86pgKt\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eChain m/0/2147483647\u003csub\u003eH\u003c/sub\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub6ASAVgeehLbnwdqV6UKMHVzgqAG8Gr6riv3Fxxpj8ksbH9ebxaEyBLZ85ySDhKiLDBrQSARLq1uNRts8RuJiHjaDMBU4Zn9h8LZNnBC5y4a\u003c/li\u003e\u003cli\u003eext prv: xprv9wSp6B7kry3Vj9m1zSnLvN3xH8RdsPP1Mh7fAaR7aRLcQMKTR2vidYEeEg2mUCTAwCd6vnxVrcjfy2kRgVsFawNzmjuHc2YmYRmagcEPdU9\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eChain m/0/2147483647\u003csub\u003eH\u003c/sub\u003e/1\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub6DF8uhdarytz3FWdA8TvFSvvAh8dP3283MY7p2V4SeE2wyWmG5mg5EwVvmdMVCQcoNJxGoWaU9DCWh89LojfZ537wTfunKau47EL2dhHKon\u003c/li\u003e\u003cli\u003eext prv: xprv9zFnWC6h2cLgpmSA46vutJzBcfJ8yaJGg8cX1e5StJh45BBciYTRXSd25UEPVuesF9yog62tGAQtHjXajPPdbRCHuWS6T8XA2ECKADdw4Ef\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eChain m/0/2147483647\u003csub\u003eH\u003c/sub\u003e/1/2147483646\u003csub\u003eH\u003c/sub\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub6ERApfZwUNrhLCkDtcHTcxd75RbzS1ed54G1LkBUHQVHQKqhMkhgbmJbZRkrgZw4koxb5JaHWkY4ALHY2grBGRjaDMzQLcgJvLJuZZvRcEL\u003c/li\u003e\u003cli\u003eext prv: xprvA1RpRA33e1JQ7ifknakTFpgNXPmW2YvmhqLQYMmrj4xJXXWYpDPS3xz7iAxn8L39njGVyuoseXzU6rcxFLJ8HFsTjSyQbLYnMpCqE2VbFWc\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eChain m/0/2147483647\u003csub\u003eH\u003c/sub\u003e/1/2147483646\u003csub\u003eH\u003c/sub\u003e/2\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub6FnCn6nSzZAw5Tw7cgR9bi15UV96gLZhjDstkXXxvCLsUXBGXPdSnLFbdpq8p9HmGsApME5hQTZ3emM2rnY5agb9rXpVGyy3bdW6EEgAtqt\u003c/li\u003e\u003cli\u003eext prv: xprvA2nrNbFZABcdryreWet9Ea4LvTJcGsqrMzxHx98MMrotbir7yrKCEXw7nadnHM8Dq38EGfSh6dqA9QWTyefMLEcBYJUuekgW4BYPJcr9E7j\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Test_vector_3\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Test_vector_3\"\u003eTest vector 3\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-test-vector-3\" class=\"anchor\" aria-label=\"Permalink: Test vector 3\" href=\"#test-vector-3\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eThese vectors test for the retention of leading zeros. See \u003ca href=\"https://github.com/bitpay/bitcore-lib/issues/47\" data-hovercard-type=\"issue\" data-hovercard-url=\"/bitpay/bitcore-lib/issues/47/hovercard\"\u003ebitpay/bitcore-lib#47\u003c/a\u003e and \u003ca href=\"https://github.com/iancoleman/bip39/issues/58\" data-hovercard-type=\"issue\" data-hovercard-url=\"/iancoleman/bip39/issues/58/hovercard\"\u003eiancoleman/bip39#58\u003c/a\u003e for more information.\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eSeed (hex): 4b381541583be4423346c643850da4b320e46a87ae3d2a4e6da11eba819cd4acba45d239319ac14f863b8d5ab5a0d0c64d2e8a1e7d1457df2e5a3c51c73235be\n\n\n\n\n\n\n\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eChain m\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub661MyMwAqRbcEZVB4dScxMAdx6d4nFc9nvyvH3v4gJL378CSRZiYmhRoP7mBy6gSPSCYk6SzXPTf3ND1cZAceL7SfJ1Z3GC8vBgp2epUt13\u003c/li\u003e\u003cli\u003eext prv: xprv9s21ZrQH143K25QhxbucbDDuQ4naNntJRi4KUfWT7xo4EKsHt2QJDu7KXp1A3u7Bi1j8ph3EGsZ9Xvz9dGuVrtHHs7pXeTzjuxBrCmmhgC6\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eChain m/0\u003csub\u003eH\u003c/sub\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub68NZiKmJWnxxS6aaHmn81bvJeTESw724CRDs6HbuccFQN9Ku14VQrADWgqbhhTHBaohPX4CjNLf9fq9MYo6oDaPPLPxSb7gwQN3ih19Zm4Y\u003c/li\u003e\u003cli\u003eext prv: xprv9uPDJpEQgRQfDcW7BkF7eTya6RPxXeJCqCJGHuCJ4GiRVLzkTXBAJMu2qaMWPrS7AANYqdq6vcBcBUdJCVVFceUvJFjaPdGZ2y9WACViL4L\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Test_vector_4\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Test_vector_4\"\u003eTest vector 4\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-test-vector-4\" class=\"anchor\" aria-label=\"Permalink: Test vector 4\" href=\"#test-vector-4\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eThese vectors test for the retention of leading zeros. See \u003ca href=\"https://github.com/btcsuite/btcutil/issues/172\" data-hovercard-type=\"issue\" data-hovercard-url=\"/btcsuite/btcutil/issues/172/hovercard\"\u003ebtcsuite/btcutil#172\u003c/a\u003e for more information.\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eSeed (hex): 3ddd5602285899a946114506157c7997e5444528f3003f6134712147db19b678\n\n\n\n\n\n\n\n\n\n\n\n\u003c/p\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eChain m\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub661MyMwAqRbcGczjuMoRm6dXaLDEhW1u34gKenbeYqAix21mdUKJyuyu5F1rzYGVxyL6tmgBUAEPrEz92mBXjByMRiJdba9wpnN37RLLAXa\u003c/li\u003e\u003cli\u003eext prv: xprv9s21ZrQH143K48vGoLGRPxgo2JNkJ3J3fqkirQC2zVdk5Dgd5w14S7fRDyHH4dWNHUgkvsvNDCkvAwcSHNAQwhwgNMgZhLtQC63zxwhQmRv\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eChain m/0\u003csub\u003eH\u003c/sub\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub69AUMk3qDBi3uW1sXgjCmVjJ2G6WQoYSnNHyzkmdCHEhSZ4tBok37xfFEqHd2AddP56Tqp4o56AePAgCjYdvpW2PU2jbUPFKsav5ut6Ch1m\u003c/li\u003e\u003cli\u003eext prv: xprv9vB7xEWwNp9kh1wQRfCCQMnZUEG21LpbR9NPCNN1dwhiZkjjeGRnaALmPXCX7SgjFTiCTT6bXes17boXtjq3xLpcDjzEuGLQBM5ohqkao9G\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003cli\u003eChain m/0\u003csub\u003eH\u003c/sub\u003e/1\u003csub\u003eH\u003c/sub\u003e\u003cul dir=\"auto\"\u003e\u003cli\u003eext pub: xpub6BJA1jSqiukeaesWfxe6sNK9CCGaujFFSJLomWHprUL9DePQ4JDkM5d88n49sMGJxrhpjazuXYWdMf17C9T5XnxkopaeS7jGk1GyyVziaMt\u003c/li\u003e\u003cli\u003eext prv: xprv9xJocDuwtYCMNAo3Zw76WENQeAS6WGXQ55RCy7tDJ8oALr4FWkuVoHJeHVAcAqiZLE7Je3vZJHxspZdFHfnBEjHqU5hG1Jaj32dVoS6XLT1\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003e\u003c/p\u003e\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Test_vector_5\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Test_vector_5\"\u003eTest vector 5\u003c/span\u003e\u003c/h3\u003e\u003ca id=\"user-content-test-vector-5\" class=\"anchor\" aria-label=\"Permalink: Test vector 5\" href=\"#test-vector-5\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\u003cp dir=\"auto\"\u003eThese vectors test that invalid extended keys are recognized as invalid.\n\u003c/p\u003e\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\u003cul dir=\"auto\"\u003e\u003cli\u003expub661MyMwAqRbcEYS8w7XLSVeEsBXy79zSzH1J8vCdxAZningWLdN3zgtU6LBpB85b3D2yc8sfvZU521AAwdZafEz7mnzBBsz4wKY5fTtTQBm (pubkey version / prvkey mismatch)\u003c/li\u003e\u003cli\u003exprv9s21ZrQH143K24Mfq5zL5MhWK9hUhhGbd45hLXo2Pq2oqzMMo63oStZzFGTQQD3dC4H2D5GBj7vWvSQaaBv5cxi9gafk7NF3pnBju6dwKvH (prvkey version / pubkey mismatch)\u003c/li\u003e\u003cli\u003expub661MyMwAqRbcEYS8w7XLSVeEsBXy79zSzH1J8vCdxAZningWLdN3zgtU6Txnt3siSujt9RCVYsx4qHZGc62TG4McvMGcAUjeuwZdduYEvFn (invalid pubkey prefix 04)\u003c/li\u003e\u003cli\u003exprv9s21ZrQH143K24Mfq5zL5MhWK9hUhhGbd45hLXo2Pq2oqzMMo63oStZzFGpWnsj83BHtEy5Zt8CcDr1UiRXuWCmTQLxEK9vbz5gPstX92JQ (invalid prvkey prefix 04)\u003c/li\u003e\u003cli\u003expub661MyMwAqRbcEYS8w7XLSVeEsBXy79zSzH1J8vCdxAZningWLdN3zgtU6N8ZMMXctdiCjxTNq964yKkwrkBJJwpzZS4HS2fxvyYUA4q2Xe4 (invalid pubkey prefix 01)\u003c/li\u003e\u003cli\u003exprv9s21ZrQH143K24Mfq5zL5MhWK9hUhhGbd45hLXo2Pq2oqzMMo63oStZzFAzHGBP2UuGCqWLTAPLcMtD9y5gkZ6Eq3Rjuahrv17fEQ3Qen6J (invalid prvkey prefix 01)\u003c/li\u003e\u003cli\u003exprv9s2SPatNQ9Vc6GTbVMFPFo7jsaZySyzk7L8n2uqKXJen3KUmvQNTuLh3fhZMBoG3G4ZW1N2kZuHEPY53qmbZzCHshoQnNf4GvELZfqTUrcv (zero depth with non-zero parent fingerprint)\u003c/li\u003e\u003cli\u003expub661no6RGEX3uJkY4bNnPcw4URcQTrSibUZ4NqJEw5eBkv7ovTwgiT91XX27VbEXGENhYRCf7hyEbWrR3FewATdCEebj6znwMfQkhRYHRLpJ (zero depth with non-zero parent fingerprint)\u003c/li\u003e\u003cli\u003exprv9s21ZrQH4r4TsiLvyLXqM9P7k1K3EYhA1kkD6xuquB5i39AU8KF42acDyL3qsDbU9NmZn6MsGSUYZEsuoePmjzsB3eFKSUEh3Gu1N3cqVUN (zero depth with non-zero index)\u003c/li\u003e\u003cli\u003expub661MyMwAuDcm6CRQ5N4qiHKrJ39Xe1R1NyfouMKTTWcguwVcfrZJaNvhpebzGerh7gucBvzEQWRugZDuDXjNDRmXzSZe4c7mnTK97pTvGS8 (zero depth with non-zero index)\u003c/li\u003e\u003cli\u003eDMwo58pR1QLEFihHiXPVykYB6fJmsTeHvyTp7hRThAtCX8CvYzgPcn8XnmdfHGMQzT7ayAmfo4z3gY5KfbrZWZ6St24UVf2Qgo6oujFktLHdHY4 (unknown extended key version)\u003c/li\u003e\u003cli\u003eDMwo58pR1QLEFihHiXPVykYB6fJmsTeHvyTp7hRThAtCX8CvYzgPcn8XnmdfHPmHJiEDXkTiJTVV9rHEBUem2mwVbbNfvT2MTcAqj3nesx8uBf9 (unknown extended key version)\u003c/li\u003e\u003cli\u003exprv9s21ZrQH143K24Mfq5zL5MhWK9hUhhGbd45hLXo2Pq2oqzMMo63oStZzF93Y5wvzdUayhgkkFoicQZcP3y52uPPxFnfoLZB21Teqt1VvEHx (private key 0 not in 1..n-1)\u003c/li\u003e\u003cli\u003exprv9s21ZrQH143K24Mfq5zL5MhWK9hUhhGbd45hLXo2Pq2oqzMMo63oStZzFAzHGBP2UuGCqWLTAPLcMtD5SDKr24z3aiUvKr9bJpdrcLg1y3G (private key n not in 1..n-1)\u003c/li\u003e\u003cli\u003expub661MyMwAqRbcEYS8w7XLSVeEsBXy79zSzH1J8vCdxAZningWLdN3zgtU6Q5JXayek4PRsn35jii4veMimro1xefsM58PgBMrvdYre8QyULY (invalid pubkey 020000000000000000000000000000000000000000000000000000000000000007)\u003c/li\u003e\u003cli\u003exprv9s21ZrQH143K3QTDL4LXw2F7HEK3wJUD2nW2nRk4stbPy6cq3jPPqjiChkVvvNKmPGJxWUtg6LnF5kejMRNNU3TGtRBeJgk33yuGBxrMPHL (invalid checksum)\u003c/li\u003e\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-Acknowledgements\"\u003e\u003c/a\u003e\u003cspan id=\"user-content-Acknowledgements\"\u003eAcknowledgements\u003c/span\u003e\u003c/h2\u003e\u003ca id=\"user-content-acknowledgements\" class=\"anchor\" aria-label=\"Permalink: Acknowledgements\" href=\"#acknowledgements\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\n\n\n\n\n\n\u003cul dir=\"auto\"\u003e\u003cli\u003eGregory Maxwell for the original idea of type-2 deterministic wallets, and many discussions about it.\u003c/li\u003e\u003cli\u003eAlan Reiner for the implementation of this scheme in Armory, and the suggestions that followed from that.\u003c/li\u003e\u003cli\u003eEric Lombrozo for reviewing and revising this BIP.\u003c/li\u003e\u003cli\u003eMike Caldwell for the version bytes to obtain human-recognizable Base58 strings.\u003c/li\u003e\u003c/ul\u003e\n\u003c/article\u003e","renderedFileInfo":null,"shortPath":null,"symbolsEnabled":true,"tabSize":8,"topBannersInfo":{"overridingGlobalFundingFile":false,"globalPreferredFundingPath":null,"showInvalidCitationWarning":false,"citationHelpUrl":"https://docs.github.com/github/creating-cloning-and-archiving-repositories/creating-a-repository-on-github/about-citation-files","actionsOnboardingTip":null},"truncated":false,"viewable":true,"workflowRedirectUrl":null,"symbols":{"timed_out":false,"not_analyzed":true,"symbols":[]}},"copilotInfo":null,"copilotAccessAllowed":false,"csrf_tokens":{"/bitcoin/bips/branches":{"post":"C6MNqVL6WfE1MxN2e4QPGxUTdGKRh8taVgIreYjMMAcQ2W5wIVb6HdCivSn6pzh9jXVfluApgl0Jtoa4RV5USA"},"/repos/preferences":{"post":"z0TznvG1AUWIFBDjRKeDNTbjMHjNoGak-GkKVnT-1xe3gixMtzQT9YLvfvyelAJFixKodSolDakuITbie3c3IA"}}},"title":"bips/bip-0032.mediawiki at master · 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