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src="https://youproof.hu/wp-content/uploads/2019/04/cropped-logo_full_big-1.png" class="custom-logo" alt="YOUPROOF" decoding="async" srcset="https://youproof.hu/wp-content/uploads/2019/04/cropped-logo_full_big-1.png 467w, https://youproof.hu/wp-content/uploads/2019/04/cropped-logo_full_big-1-300x100.png 300w" sizes="(max-width: 467px) 100vw, 467px" /></a> </div> <div id="menu-container" class="menu-container"> <nav class="richprimarymenu" itemtype="http://schema.org/SiteNavigationElement" role="navigation"><ul id="menu-header-navigation-menu" class="vertical large-horizontal menu" data-responsive-menu="accordion large-dropdown"><li id="menu-item-1551" class="menu-item menu-item-type-post_type menu-item-object-page current_page_parent menu-item-1551"><a href="https://youproof.hu/blog/">Összes cikk</a></li> <li id="menu-item-1552" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-1552"><a href="https://youproof.hu/kriptografia/">Kriptográfia</a></li> </ul></nav> <ul id="iconmenu" class="menu richiconmenu"> <li id="menu-item-1073" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-1073"><a href="https://www.facebook.com/youproof.hu">Facebook</a></li> <li id="searchicon" class="icon-search menu-item"> <a> Search </a> </li> </ul> </div> </header> <div id="searchwrap"> <div class= "row"> <div class="columns"> <form role="search" method="get" id="searchform" action="https://youproof.hu/"> <div class="input-group"> <input type="text" class="input-group-field" value="" name="s" id="s" placeholder="Search"> <div class="input-group-button"> <input type="submit" id="searchsubmit" value="Search" class="button"> </div> </div> </form> </div> </div> </div> <div id="container" class="row"> <div id="primary" class="large-7 medium-8 small-11 small-centered columns"> <div class="row"> <div class="column large-8 medium-10"> <div class="archive-title-description"> <h2 class="entry-title">prím</h2>  </div> </div> </div> <article id="post-6431" class="row postbox postboxloop post-6431 post type-post status-publish format-standard has-post-thumbnail hentry category-absztrakt-algebra tag-additiv-csoport tag-csoport tag-csoport-rendje tag-csoportelem-rendje tag-izomorfizmus tag-kongruencia tag-lagrange-tetele tag-maradekosztaly tag-maradekosztalygyuru tag-mellekosztaly tag-miller-rabin-primteszt tag-modularis-aritmetika tag-multiplikativ-csoport tag-prim tag-reszcsoport tag-univerzalis-alprim yp_series-kriptografia" > <div class="medium-4 columns"> <div class="postlistthumb"> <div class="postlistthumbwrap"> <a href="https://youproof.hu/kriptografia/24-csoport-reszcsoport-mellekosztaly-lagrange-tetel-csoport-rendje-elem-rendje-miller-rabin-primteszt/" rel="bookmark"> <img width="1142" height="630" src="https://youproof.hu/wp-content/uploads/kriptografia_24_thumbnail_orig-1142x630.jpg" class="attachment-post-thumbnail size-post-thumbnail wp-post-image" alt="" decoding="async" /> </a> </div> </div> </div> <div class=" medium-8 columns"> <header class="entry-header"> <h5 class="yp-series-title yp-postbox-first-line">Episode I: Alice és Bob</h5> <a href="https://youproof.hu/kriptografia/24-csoport-reszcsoport-mellekosztaly-lagrange-tetel-csoport-rendje-elem-rendje-miller-rabin-primteszt/" rel="bookmark"> <h5 class="entry-title yp-postbox-second-line"> 24. rész: Alice és Bob komolyabb fegyverekhez nyúl </h5> </a> </header> <div class="postbox-entry-meta"><span class="screen-reader-text">Posted on</span> <time class="entry-date published" datetime="2020-07-08T22:03:41+02:00">2020.07.08.</time><time class="updated" datetime="2021-07-19T12:12:33+02:00">2021.07.19.</time><p>Mi az oka annak, hogy a Miller-Rabin-prímtesztre nézve egyáltalán nem léteznek univerzális álprímek? Milyen fegyverek állnak Alice és Bob rendelkezésére egy ilyen jellegű kérdés megválaszolásához? Mik azok a csoportok és mivel foglalkozik a csoportelmélet? Mit állít a Lagrange-tétel, és mi köze a Miller-Rabin-prímteszthez?</p> </div> </div> </a> </article> <article id="post-6204" class="row postbox postboxloop post-6204 post type-post status-publish format-standard has-post-thumbnail hentry category-elemi-szamelmelet tag-asszocialt tag-bezout-lemma tag-carmichael-szam tag-egyseg tag-euklideszi-algoritmus tag-felbonthatatlan tag-fermat-faktorizacio tag-fermat-primteszt tag-kinai-maradektetel tag-kis-fermat-tetel tag-kongruencia tag-kongruenciarendszer tag-maradekosztaly tag-miller-rabin-primteszt tag-prim tag-primteszt tag-relativ-prim tag-univerzalis-alprim yp_series-kriptografia" > <div class="medium-4 columns"> <div class="postlistthumb"> <div class="postlistthumbwrap"> <a href="https://youproof.hu/kriptografia/23-primteszteles-fermat-primteszt-miller-rabin-primteszt-carmichael-szam-univerzalis-alprim-fermat-faktorizacio/" rel="bookmark"> <img width="1142" height="630" src="https://youproof.hu/wp-content/uploads/kriptografia_23_thumbnail_orig-1-1142x630.jpg" class="attachment-post-thumbnail size-post-thumbnail wp-post-image" alt="" decoding="async" /> </a> </div> </div> </div> <div class=" medium-8 columns"> <header class="entry-header"> <h5 class="yp-series-title yp-postbox-first-line">Episode I: Alice és Bob</h5> <a href="https://youproof.hu/kriptografia/23-primteszteles-fermat-primteszt-miller-rabin-primteszt-carmichael-szam-univerzalis-alprim-fermat-faktorizacio/" rel="bookmark"> <h5 class="entry-title yp-postbox-second-line"> 23. rész: Alice és Bob prímszámok után nyomoz </h5> </a> </header> <div class="postbox-entry-meta"><span class="screen-reader-text">Posted on</span> <time class="entry-date published" datetime="2020-06-09T09:04:38+02:00">2020.06.09.</time><time class="updated" datetime="2020-12-18T14:17:22+01:00">2020.12.18.</time><p>Hogyan képes Alice és Bob az RSA-kulcsgeneráláshoz szükséges többszázjegyű prímszámokat találni? Hogyan tudják ezt megtenni anélkül, hogy az idők végezetéig osztáspróbákat kellene végezniük? Mik azok a prímtesztek, és pontosan hogyan működnek? Mely számokat nevezzük univerzális álprímeknek, és hogyan tudunk megszabadulni tőlük?</p> </div> </div> </a> </article> <article id="post-5582" class="row postbox postboxloop post-5582 post type-post status-publish format-standard has-post-thumbnail hentry category-elemi-szamelmelet tag-adi-shamir tag-alice tag-aszimmetrikus-kulcsu-titkositas tag-bezout-lemma tag-bob tag-digitalis-alairas tag-euklideszi-algoritmus tag-euler-fuggveny tag-eve tag-kituntetett-kozos-oszto tag-kongruencia tag-len-adleman tag-linearis-kongruencia tag-modularis-aritmetika tag-prim tag-ron-rivest tag-rsa-algoritmus yp_series-kriptografia" > <div class="medium-4 columns"> <div class="postlistthumb"> <div class="postlistthumbwrap"> <a href="https://youproof.hu/kriptografia/21-rsa-algoritmus-kibovitett-euklideszi-algoritmus-euler-fuggveny-kulcsgeneralas-ismetelt-negyzetreemeles-modszere/" rel="bookmark"> <img loading="lazy" width="1142" height="630" src="https://youproof.hu/wp-content/uploads/kriptografia_21_thumbnail_orig-1142x630.jpg" class="attachment-post-thumbnail size-post-thumbnail wp-post-image" alt="" decoding="async" /> </a> </div> </div> </div> <div class=" medium-8 columns"> <header class="entry-header"> <h5 class="yp-series-title yp-postbox-first-line">Episode I: Alice és Bob</h5> <a href="https://youproof.hu/kriptografia/21-rsa-algoritmus-kibovitett-euklideszi-algoritmus-euler-fuggveny-kulcsgeneralas-ismetelt-negyzetreemeles-modszere/" rel="bookmark"> <h5 class="entry-title yp-postbox-second-line"> 21. rész: Alice és Bob titkosít </h5> </a> </header> <div class="postbox-entry-meta"><span class="screen-reader-text">Posted on</span> <time class="entry-date published" datetime="2020-04-21T21:51:50+02:00">2020.04.21.</time><time class="updated" datetime="2020-10-27T12:18:18+01:00">2020.10.27.</time><p>Hogyan működik az Internet biztonságát adó RSA nevű aszimmetrikus kulcsú rejtjelező eljárás? Hogyan kell előállítani a publikus és titkos kulcsokat? Hogyan lehet az euklidészi algoritmust lineáris kongruenciák megoldásához is használni? Hogyan kell kiszámítani az Euler-függvény értékét egy adott számra, és milyen információra van ehhez szükség?</p> </div> </div> </a> </article> <article id="post-4876" class="row postbox postboxloop post-4876 post type-post status-publish format-standard has-post-thumbnail hentry category-algebrai-szamelmelet category-halmazelmelet-logika tag-euklideszi-gyuru tag-felbonthatatlan tag-foideal tag-foidealgyuru tag-generalt-ideal tag-halmaz tag-halmazmuvelet tag-halmazrendszer tag-ideal tag-kituntetett-kozos-oszto tag-oszthatosag tag-prim tag-rendezett-halmaz tag-reszgyuru tag-reszhalmaz tag-szamelmelet-alaptetele yp_series-kriptografia" > <div class="medium-4 columns"> <div class="postlistthumb"> <div class="postlistthumbwrap"> <a href="https://youproof.hu/kriptografia/19-foidealgyuruk-generalt-ideal-foideal-szamelmelet-alaptetele-halmaz-halmazrendszer-metszet-unio/" rel="bookmark"> <img loading="lazy" width="1142" height="630" src="https://youproof.hu/wp-content/uploads/kriptografia_18_thumbnail_orig-1142x630.jpg" class="attachment-post-thumbnail size-post-thumbnail wp-post-image" alt="" decoding="async" /> </a> </div> </div> </div> <div class=" medium-8 columns"> <header class="entry-header"> <h5 class="yp-series-title yp-postbox-first-line">Episode I: Alice és Bob</h5> <a href="https://youproof.hu/kriptografia/19-foidealgyuruk-generalt-ideal-foideal-szamelmelet-alaptetele-halmaz-halmazrendszer-metszet-unio/" rel="bookmark"> <h5 class="entry-title yp-postbox-second-line"> 19. rész: Alice és Bob ideáljai </h5> </a> </header> <div class="postbox-entry-meta"><span class="screen-reader-text">Posted on</span> <time class="entry-date published" datetime="2020-03-05T00:27:12+01:00">2020.03.05.</time><time class="updated" datetime="2021-01-20T12:06:41+01:00">2021.01.20.</time><p>Hogyan néznek ki az egész számok gyűrűjének ideáljai? Mi a kapcsolat az ideálok és az oszthatósági alapfogalmak között? Mik azok a főideálgyűrűk, és ezeknek milyen jó tulajdonságaik vannak? Mi közük az euklidészi gyűrűkhöz? Hogyan zárható le a számelmélet alaptételének kérdése végérvényesen az ideálok segítségével?</p> </div> </div> </a> </article> <article id="post-4115" class="row postbox postboxloop post-4115 post type-post status-publish format-standard has-post-thumbnail hentry category-algebrai-szamelmelet tag-abszolutertek tag-euklidesz tag-euklideszi-algoritmus tag-euklideszi-gyuru tag-euklideszi-norma tag-felbonthatatlan tag-gyuru tag-integritastartomany tag-kituntetett-kozos-oszto tag-legnagyobb-kozos-oszto tag-maradekos-osztas tag-prim tag-relativ-prim tag-szamelmelet-alaptetele tag-teljes-indukcio tag-vegtelen-leszallas yp_series-kriptografia" > <div class="medium-4 columns"> <div class="postlistthumb"> <div class="postlistthumbwrap"> <a href="https://youproof.hu/kriptografia/17-euklideszi-algoritmus-maradekos-osztas-legnagyobb-kozos-oszto-euklideszi-gyuru/" rel="bookmark"> <img loading="lazy" width="1142" height="630" src="https://youproof.hu/wp-content/uploads/kriptografia_17_thumbnail_orig-1142x630.jpg" class="attachment-post-thumbnail size-post-thumbnail wp-post-image" alt="" decoding="async" /> </a> </div> </div> </div> <div class=" medium-8 columns"> <header class="entry-header"> <h5 class="yp-series-title yp-postbox-first-line">Episode I: Alice és Bob</h5> <a href="https://youproof.hu/kriptografia/17-euklideszi-algoritmus-maradekos-osztas-legnagyobb-kozos-oszto-euklideszi-gyuru/" rel="bookmark"> <h5 class="entry-title yp-postbox-second-line"> 17. rész: Alice és Bob ókori haverja </h5> </a> </header> <div class="postbox-entry-meta"><span class="screen-reader-text">Posted on</span> <time class="entry-date published" datetime="2020-01-20T07:49:42+01:00">2020.01.20.</time><time class="updated" datetime="2020-11-21T07:09:34+01:00">2020.11.21.</time><p>Mi az oka annak, hogy minden egész szám egyértelműen felbontható prímszámok szorzatára? Mit jelent a „legnagyobb közös osztó”, és hogyan lehet az iskolában tanult módszernél sokkal gyorsabban kiszámolni az euklidészi algoritmus segítségével? Mik azok az euklidészi gyűrűk és mi közük a számelmélet alaptételéhez?</p> </div> </div> </a> </article> <article id="post-3770" class="row postbox postboxloop post-3770 post type-post status-publish format-standard has-post-thumbnail hentry category-algebrai-szamelmelet tag-asszocialt tag-egesz-szam tag-egyseg tag-felbonthatatlan tag-gyuru tag-integritastartomany tag-nullosztomentes tag-oszthatosag tag-prim tag-szamelmelet-alaptetele tag-test yp_series-kriptografia" > <div class="medium-4 columns"> <div class="postlistthumb"> <div class="postlistthumbwrap"> <a href="https://youproof.hu/kriptografia/16-oszhatosag-egyseg-asszocialt-felbonthatatlan-prim-szamelmelet-alaptetele/" rel="bookmark"> <img loading="lazy" width="1142" height="630" src="https://youproof.hu/wp-content/uploads/kriptografia_16_thumbnail_orig-1142x630.jpg" class="attachment-post-thumbnail size-post-thumbnail wp-post-image" alt="" decoding="async" /> </a> </div> </div> </div> <div class=" medium-8 columns"> <header class="entry-header"> <h5 class="yp-series-title yp-postbox-first-line">Episode I: Alice és Bob</h5> <a href="https://youproof.hu/kriptografia/16-oszhatosag-egyseg-asszocialt-felbonthatatlan-prim-szamelmelet-alaptetele/" rel="bookmark"> <h5 class="entry-title yp-postbox-second-line"> 16. rész: Alice és Bob alaptétele </h5> </a> </header> <div class="postbox-entry-meta"><span class="screen-reader-text">Posted on</span> <time class="entry-date published" datetime="2019-12-29T13:42:01+01:00">2019.12.29.</time><time class="updated" datetime="2020-10-27T12:16:05+01:00">2020.10.27.</time><p>Mit kezdjünk azzal, hogy az „osztás” művelete általában nem végezhető el gyűrűkben? Mit jelent az „oszthatóság”? Mikor mondjuk egy gyűrű valamely elemére, hogy „felbonthatatlan” és mely elemeket nevezzük „prímeknek”? Miért van ezeknek kitüntetett szerepük bizonyos gyűrűkben? Mi a helyzet az egész számok gyűrűjében?</p> </div> </div> </a> </article> </div> </div>  <footer id="site-footer" > <div id="footermenu" class="row"> <div class="columns"> <div class="menu footernav"><ul id="footer-navigation" class="menu"><li id="menu-item-36" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-36"><a href="https://youproof.hu/impresszum/">Impresszum</a></li> <li id="menu-item-40" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-40"><a href="https://youproof.hu/suti-cookie-kezelese/">Süti-Cookie</a></li> <li id="menu-item-58" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-privacy-policy menu-item-58"><a rel="privacy-policy" href="https://youproof.hu/adatkezeles/">Adatkezelés</a></li> <li id="menu-item-65" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-65"><a href="https://youproof.hu/jogi-nyilatkozat/">Jogi nyilatkozat</a></li> </ul></div> </div> </div> <div id="copyright" class="row"> <div class="columns"> © 2024 YOUPROOF - Minden jog fenntartva </div> <div class="columns">v1.2.2</div> </div> <script type="text/javascript" id="cookie-notice-front-js-before"> /* <![CDATA[ */ var cnArgs = {"ajaxUrl":"https:\/\/youproof.hu\/wp-admin\/admin-ajax.php","nonce":"824f069ba8","hideEffect":"fade","position":"bottom","onScroll":false,"onScrollOffset":100,"onClick":false,"cookieName":"cookie_notice_accepted","cookieTime":2592000,"cookieTimeRejected":2592000,"globalCookie":false,"redirection":false,"cache":false,"revokeCookies":false,"revokeCookiesOpt":"automatic"}; /* ]]> */ </script> <script type="text/javascript" src="https://youproof.hu/wp-content/plugins/cookie-notice/js/front.min.js?ver=2.4.16" id="cookie-notice-front-js"></script> <script type="text/javascript" src="https://youproof.hu/wp-content/themes/minimum-minimal/assets/js/app.js?ver=1.0" id="minimumminimal-main-js"></script> <script type="text/javascript" src="https://youproof.hu/wp-content/themes/minimum-minimal/foundation.js?ver=1" id="minimumminimal-foundation-init-js-js"></script>  <div id="cookie-notice" role="dialog" class="cookie-notice-hidden cookie-revoke-hidden cn-position-bottom" aria-label="Cookie Notice" style="background-color: rgba(0,0,0,1);"><div class="cookie-notice-container" style="color: #fff"><span id="cn-notice-text" class="cn-text-container">Kedves Látogató! 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