锘??xml version="1.0" encoding="utf-8" standalone="yes"?>人人狠狠综合久久88成人,色综合久久夜色精品国产,麻豆久久http://www.shnenglu.com/qinqing1984/zh-cnTue, 06 May 2025 09:45:57 GMTTue, 06 May 2025 09:45:57 GMT60浜屽厓浜屾鍨嬬殑鐩鎬技鍙樻崲涓庢瀹氭?/title><link>http://www.shnenglu.com/qinqing1984/archive/2025/04/25/230436.html</link><dc:creator>鏄ョ鍗佷簩鏈?/dc:creator><author>鏄ョ鍗佷簩鏈?/author><pubDate>Fri, 25 Apr 2025 11:05:00 GMT</pubDate><guid>http://www.shnenglu.com/qinqing1984/archive/2025/04/25/230436.html</guid><wfw:comment>http://www.shnenglu.com/qinqing1984/comments/230436.html</wfw:comment><comments>http://www.shnenglu.com/qinqing1984/archive/2025/04/25/230436.html#Feedback</comments><slash:comments>0</slash:comments><wfw:commentRss>http://www.shnenglu.com/qinqing1984/comments/commentRss/230436.html</wfw:commentRss><trackback:ping>http://www.shnenglu.com/qinqing1984/services/trackbacks/230436.html</trackback:ping><description><![CDATA[<div>   鏈枃涓昏闃愯堪鐢ㄤ袱縐嶆柟娉曞垽鏂粰瀹氫袱涓簩鍏冧簩嬈″瀷鏄惁鐩鎬技錛岀浉浼兼儏鍐典笅鐨勫叿浣撳彉鎹€?br /> 鐩鎬技鍙樻崲濡傛灉紜畾浜嗭紝涔熷埄浜庡垽鏂瀹氭э紝鍥犱負鐩鎬技浜屾鍨嬬殑姝ｅ畾鎬х浉鍚?br /> <br /> <div><span style="font-size: 12pt;"><strong>鍩烘湰瀹氫箟</strong></span></div> <div>  涓嬭堪瀹氫箟鏉ヨ嚜鏂囩尞[1] 12.1鑺傦紝鏈夋墍鎵╁睍 <br />   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/binary-quadric-form-basic-definition.png" alt="" /><br /> <strong><br /> <span style="font-size: 12pt;">鍙樻崲姹傝В</span></strong></div> <div>  鍏堟潵鐪嬭繍鐢ㄨВ鏂圭▼鐨勬柟娉?nbsp;<br />   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/binary-quadric-form-similar-transform-solve-equation.jpg" width="555" height="919" alt="" /><br /> <br /> <div> <br />  鍐嶆潵鐪嬬敤鐭╅樀鐨勮鐐規柟娉曪紝姹傝В鍙樻崲銆傝繖縐嶆柟娉曟洿閫傚悎姹傝В鍒板瑙掑瀷鐨勫彉鎹?br />  <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/binary-quadric-form-similar-transform-matrix-method.jpg" alt="" /><br />  <br />  <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/binary-quadric-form-similar-transform-matrix-method-example.jpg" alt="" /><br /> <br /> <div><span style="font-size: 11pt;"><strong><br /> 鍙傝冩枃鐚?/strong></span> </div> <div>   [1] 鍗庣綏搴氭枃闆嗘暟璁哄嵎2</div> <div>   [2] 楂樼瓑浠ｆ暟                 涓樼淮澹?/div> </div> </div> </div><img src ="http://www.shnenglu.com/qinqing1984/aggbug/230436.html" width = "1" height = "1" /><br><br><div align=right><a style="text-decoration:none;" href="http://www.shnenglu.com/qinqing1984/" target="_blank">鏄ョ鍗佷簩鏈?/a> 2025-04-25 19:05 <a href="http://www.shnenglu.com/qinqing1984/archive/2025/04/25/230436.html#Feedback" target="_blank" style="text-decoration:none;">鍙戣〃璇勮</a></div>]]></description></item><item><title>鍏充簬緹ょ殑涓浜涚粨璁哄強搴旂敤http://www.shnenglu.com/qinqing1984/archive/2025/04/22/230435.html鏄ョ鍗佷簩鏈?/dc:creator>鏄ョ鍗佷簩鏈?/author>Tue, 22 Apr 2025 13:18:00 GMThttp://www.shnenglu.com/qinqing1984/archive/2025/04/22/230435.htmlhttp://www.shnenglu.com/qinqing1984/comments/230435.htmlhttp://www.shnenglu.com/qinqing1984/archive/2025/04/22/230435.html#Feedback0http://www.shnenglu.com/qinqing1984/comments/commentRss/230435.htmlhttp://www.shnenglu.com/qinqing1984/services/trackbacks/230435.html銆?strong>鍛介1銆?鎵鏈夌兢鍚屾佺殑鍘熷儚涓暟鐩稿悓錛屽嵆涓烘牳鐨勫ぇ灝?/span> 
    

  涓嬮潰鐪嬩笅榪欎釜緇撹鍦ㄦ枃鐚甗1]涓?.2鑺傜殑搴旂敤 
     

銆?strong>鍛介2銆戞墍鏈夊厓绱犻樁灝忎簬絳変簬2 鐨勭兢涓轟氦鎹㈢兢錛屼笖鍏墮樁涓?鐨勬暣鏁板箓 
  
 璇ョ粨璁哄湪https://zhuanlan.zhihu.com/p/644888274涓殑鎺ㄨ2.2璇佹槑涓敤鍒?br />
銆?strong>鍛介3銆戠兢涓換涓鍏冪殑鐩稿浜庢瑙勫瓙緹ょ殑鎸囨暟嬈″箓灞炰簬姝ｈ瀛愮兢錛?闃舵瑙勫瓙緹ゅ繀
灞炰簬緹ょ殑涓績
 

銆愬畾鐞嗐?/strong>妯″鍚堟暟鐨勬棦綰︿箻娉曠兢錛屽叾涓泤鍙瘮絎﹀彿涓?鐨勫厓绱犳瀯鎴愬畠鐨勫瓙緹わ紝鍏墮樁涓?/span>
鏃㈢害涔樻硶緹ょ兢闃剁殑涓鍗?br />     


鍙傝冩枃鐚?/strong>
  [1] 妞渾鏇茬嚎鍙婂叾鍦ㄥ瘑鐮佸涓殑搴旂敤—瀵煎紩  Andreas Enge
  [2] 鎶借薄浠ｆ暟I                                      璧墊槬鏉?寰愭槑鏇?br />   [3] 鍗庣綏搴氭枃闆嗘暟璁哄嵎2
  [4] 緇勫悎鏁板                                       鍐崳鏉?瀹嬫槬浼?/div>


]]>涓嶅畾鏂圭▼鐨勪唬鏁版暟璁鴻В娉?/title><link>http://www.shnenglu.com/qinqing1984/archive/2024/12/23/230411.html</link><dc:creator>鏄ョ鍗佷簩鏈?/dc:creator><author>鏄ョ鍗佷簩鏈?/author><pubDate>Mon, 23 Dec 2024 03:33:00 GMT</pubDate><guid>http://www.shnenglu.com/qinqing1984/archive/2024/12/23/230411.html</guid><wfw:comment>http://www.shnenglu.com/qinqing1984/comments/230411.html</wfw:comment><comments>http://www.shnenglu.com/qinqing1984/archive/2024/12/23/230411.html#Feedback</comments><slash:comments>0</slash:comments><wfw:commentRss>http://www.shnenglu.com/qinqing1984/comments/commentRss/230411.html</wfw:commentRss><trackback:ping>http://www.shnenglu.com/qinqing1984/services/trackbacks/230411.html</trackback:ping><description><![CDATA[<div><strong style="font-size: 12pt;">絎﹀彿鍚箟涓庨傜敤鍓嶆彁</strong><br /> <p>  <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/diophantine-equation-term-premise.png" width="591" height="246" alt="" /><br /> <br /> <span style="font-size: 12pt;"><strong><br /> 浜屾鍩熺殑鍩烘湰緇撹</strong></span> </p> <p>   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/diophantine-equation-quadratic-field-conclusion.png" width="600" height="551" alt="" /><br />   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/diophantine-equation-quadratic-field-conclusion2.png" width="599" height="272" alt="" /><br /> <br /> </p> <div><strong style="font-size: 12pt;">x<sup>2</sup>-dy<sup>2</sup>=</strong><strong style="font-size: 12pt;">±1</strong>   </div> <div>  <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/diophantine-equation-pell-solve.jpg" alt="" /><br /> <br />   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/diophantine-equation-pell-solve2.jpg" width="635" height="955" alt="" /><br />   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/diophantine-equation-pell-solve3.jpg" width="623" height="1026" alt="" /><strong style="font-size: 12pt;"><br /> x<sup>2</sup> + d = y<sup>3</sup></strong>  </div> <div>  <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/diophantine-equation-x2-d-y3-solve.jpg" width="586" height="802" alt="" /><br />   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/diophantine-equation-x2-d-y3-solve2.jpg" width="574" height="1000" alt="" /><br />   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/diophantine-equation-x2-d-y3-solve3.jpg" alt="" /> <br /> <br /> <div><strong style="font-size: 12pt;"><br /> x<sup>2</sup> + y<sup>2</sup> = n</strong>   </div> <div>  <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/diophantine-equation-two-quadratic-sum-solve.jpg" alt="" /><br /> <br />   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/diophantine-equation-two-quadratic-sum-solve2.jpg" alt="" /><br /> <br /> <br /> <div><strong>鍙傝冩枃鐚?/strong> <strong><br /> </strong><strong>    </strong>[1] 浠ｆ暟涓庢暟璁?nbsp;          鏉庤秴  鍛ㄦ偊</div> </div> </div> </div><img src ="http://www.shnenglu.com/qinqing1984/aggbug/230411.html" width = "1" height = "1" /><br><br><div align=right><a style="text-decoration:none;" href="http://www.shnenglu.com/qinqing1984/" target="_blank">鏄ョ鍗佷簩鏈?/a> 2024-12-23 11:33 <a href="http://www.shnenglu.com/qinqing1984/archive/2024/12/23/230411.html#Feedback" target="_blank" style="text-decoration:none;">鍙戣〃璇勮</a></div>]]></description></item><item><title>鍏充簬妞渾鏇茬嚎鐨勯獙璇佽綆?/title><link>http://www.shnenglu.com/qinqing1984/archive/2024/11/10/230402.html</link><dc:creator>鏄ョ鍗佷簩鏈?/dc:creator><author>鏄ョ鍗佷簩鏈?/author><pubDate>Sun, 10 Nov 2024 13:45:00 GMT</pubDate><guid>http://www.shnenglu.com/qinqing1984/archive/2024/11/10/230402.html</guid><wfw:comment>http://www.shnenglu.com/qinqing1984/comments/230402.html</wfw:comment><comments>http://www.shnenglu.com/qinqing1984/archive/2024/11/10/230402.html#Feedback</comments><slash:comments>0</slash:comments><wfw:commentRss>http://www.shnenglu.com/qinqing1984/comments/commentRss/230402.html</wfw:commentRss><trackback:ping>http://www.shnenglu.com/qinqing1984/services/trackbacks/230402.html</trackback:ping><description><![CDATA[<span style="font-size: 13pt;"><strong>絎﹀彿鍚箟</strong></span>  <div>    E            琛ㄧず婊¤凍妞渾鏇茬嚎Weierstrass鏂圭▼涓婄殑鐐圭兢</div> <div>    K            浠ｆ暟闂煙錛岀敤鏉ラ檺鍒禬eierstrass鏂圭▼鐨勭郴鏁頒笌E涓殑鐐?/div> <div>    E(K)        瀹氫箟鍦↘涓婄殑鐐圭兢E</div> <div>    E/K         瀹氫箟鍦↘涓婄殑妞渾鏇茬嚎E</div> <div>    End(E)    E涓婄殑鑷悓鎬佺幆<br /> <br /> <br /> <span style="font-size: 13pt;"><strong>鍩熸墿寮犲垎鏋?/strong></span><span style="background-color: #c0c0c0; font-size: 1px;"> </span><span style="font-size: 13pt;"><strong><br /></strong></span>   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-field-extention-analysis.png" alt="" /><br /> <br /> <div><span style="font-size: 13pt;"><strong>End(E)妯′笌Z浠ｆ暟</strong></span> <span style="font-size: 14pt;"><br /> </span><span>  <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-ende-module-z-algebra.png" width="550" height="760" alt="" /><br /> <br /> </span> <div><span style="font-size: 13pt;"><strong>鏋佺偣棣栭」緋繪暟</strong></span> <span style="font-size: 14pt;"><br /> </span><span style="font-size: 14pt;">  <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-acnode-leading-term-coefficient-theory.jpg" width="571" height="970" alt="" /><br />   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-acnode-leading-term-coefficient-example.png" width="562" height="831" alt="" /><br /> </span> <div><span style="font-size: 13pt;"><br /> <strong> 闄ゅ瓙鏄犲皠鍙婂悓鏋?/strong></span> <strong style="font-size: 1px;"> </strong></div> <div>   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-divisor-map-isomorphism.jpg" width="560" height="918" alt="" /><br /> <br /> <div><span style="font-size: 13pt;"><strong>鍚岀鏄犲皠鍚屾佹х殑瑙ｉ噴</strong></span> <span style="font-size: 14pt;"><br /> </span><span>  <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-isogeny-homomorphism-theorem.PNG" width="453" height="388" alt="" /><br />   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-principal-divisor-corollary.PNG" width="454" height="218" alt="" /><br />   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-isogeny-map-homomorphism-explain.png" width="531" height="238" alt="" /><br /> <br /> </span> <div><span style="font-size: 13pt;"><strong>Hasse瀹氱悊涔嬪紩鐞嗚瘉鏄庣殑琛ュ厖</strong></span>  </div> <div>  <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-hasse-lemma-proof-supplement.jpg" width="591" height="958" alt="" /><br /> <br /> <div><span style="font-size: 13pt;"><strong>鎸犳洸綰垮強鍏朵釜鏁?/strong></span>   </div>   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-torsional-curve-and-num.jpg" width="584" height="978" alt="" /><br /> <br /> <div><strong><span style="font-size: 13pt;">鏈夐檺鍩熶笂鐨勬き鍦嗘洸綰?/span> </strong>  <div><span style="font-size: 11pt;">  <strong>涓縐嶇‘瀹氬瀷緹ら樁璁＄畻娉?/strong></span> <span style="font-size: 12pt;"><br /> </span><span>    <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-odd-prime-field-calc-ecgrouporder-algo.png" width="563" height="507" alt="" /><br /> </span><span style="font-size: 12pt;"> <br /> </span><span style="font-size: 11pt;">  <strong>濂囩礌鍩熶笂鐨勭畻娉曞簲鐢?/strong></span><strong> </strong><span style="font-size: 12pt;"><br /> </span><span>    <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-odd-prime-field-calc-ecgrouporder-algo-apply.png" width="571" height="380" alt="" /><br />    <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-odd-prime-field-calc-ecgrouporder-algo-apply2.jpg" width="571" height="1019" alt="" /><br /> <br /> </span> <div><span style="font-size: 11pt;"> <strong>GF鍩熶笂鐨勭兢闃惰綆?/strong></span>  </div> <div><span>   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-gf-calc-grouporder-weil-example.jpg" width="543" height="995" alt="" /><br />    <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-gf-calc-grouporder-weil-example2.jpg" width="571" height="1019" alt="" /><br /> <br /> </span> <div><span style="font-size: 13pt;"><strong>Schoof綆楁硶姝ｇ‘鎬ф牴鏈?/strong></span>   </div> <div>    涓縐嶈綆楁き鍦嗘洸綰跨兢鐨勯樁鐨勭‘瀹氬瀷澶氶」寮忔椂闂寸畻娉曪紝紜畾鍨嬫槸鍥犱負綆楁硶鍐呴儴娌℃湁闅忔満閫夋嫨/姒傜巼鎶涘竵鎿嶄綔錛屽欏瑰紡鏃墮棿鏄洜涓哄煙<em>k</em>鐨勪箻娉曚笌姹傞嗘繪鏁版槸O((logq)^6)<br /> 錛?em>q</em>涓?em>k</em>鐨勫ぇ灝忥紝涔樻硶涓庢眰閫嗙浉瀵瑰姞鍑忚繍綆楁樉钁楄楁椂錛夈傚叿浣撳師鐞嗗強嫻佺▼璇﹁鍙傝冩枃鐚甗1]涓?.2鑺傘傝繖閲岀粰鍑虹瑪鑰呯殑涓浜涙濊? <div>​     1. Hasse瀹氱悊錛團robenius鑷悓鎬佹柟紼嬪紡錛夊湪鎵偣緹や笂鐨勯檺鍒朵害鎴愮珛錛岃繖鍐沖畾浜?em>t</em>妯?em>l</em>鐨勪竴涓悓浣欐柟紼嬫垚绔嬶紝涓斿湪妯鐨勬渶灝忛潪璐熷墿浣欑郴涓嬭В鏄敮涓鐨?/div> <div>​     2. 瀛欏瓙瀹氱悊淇濊瘉浜嗘煇鍙栧艱寖鍥村唴鐨勪竴涓?em>t</em>妯?em>L</em>錛?em>L</em>涓哄悇绱犲洜瀛恖鐨勪箻縐級鐨勫敮涓瑙ｏ紝鍗崇敱<em>t</em>妯?em>L</em>鍚勪釜绱犲洜瀛?em>l</em>鐨勫悓浣欐柟紼嬫瀯鎴愮殑鍚屼綑鏂圭▼緇勭殑瑙ｆ槸鍞竴鐨?/div> <div>​     3. <em>L</em>蹇呴』澶т簬<em>t</em>鍙栧間笂闄愮殑2鍊嶃傝繖鏄負浜嗙畻娉曟眰寰楃殑瑙ｆ弧瓚充笂榪?錛堝惁鍒欏湪鏇村皬鐨凩鍐呭緱鍒扮殑瑙ｄ笉鍞竴錛屽洜<em>L</em>涓?em>t</em>涓婇檺鎴栦笅闄愰棿鐨勬煇鏁板彲浠ヤ笌<em>t</em>妯?em>L</em>鍚屼綑錛?/div> <div>​     4. 绱犲洜瀛?em>l</em>鐨勯夋嫨鎺掗櫎2涓庢き鍦嗘洸綰跨壒寰?em>p</em>銆傝繖鏄洜涓虹畻娉曟瀯閫犳墍渚濊禆鐨勪竴涓紩鐞嗕箣鍓嶆彁鏉′歡錛氫負濂囩礌鏁頒繚璇?em>l</em>嬈￠櫎瀛愬欏瑰紡灞炰簬<em>k</em>[X]錛屽嵆寮曠悊璁烘柇鏈夋剰涔夛紱<br />        涓嶇瓑浜?em>p</em>淇濊瘉媯嫻嬩竴涓欏瑰紡f鏄惁闆跺欏瑰紡鐨勫厖瑕佹潯浠舵垚绔嬶紝鍗沖彲浠ョ敤<em>l</em>嬈￠櫎瀛愬欏瑰紡鍘繪暣闄?em>f</em>鏉ュ垽鏂傚彟l涓虹礌鏁頒繚璇佷簡涓庡叾瀹冮櫎瀛愬欏瑰紡錛堝強鍏跺箓嬈★級浜掔礌<br />      鍙﹀鍙戠幇浜嗙畻娉曠殑涓澶勭憰鐤碉紝鍗崇4姝ラ璁＄畻闄ゅ瓙澶氶」寮忎笌Frobenius鑷悓鎬佺殑澶嶅悎灝戜簡涓や釜鍊鹼紝榪欏鑷寸5姝ュ彲鑳藉穿婧冿紝褰撲緷璧栫殑鍚庣畫涓や釜澶嶅悎澶氶」寮忔病琚綆楁椂銆?br />   榪欎釜綰犳鍙氳繃淇敼絎?姝ユ墿澶?涓鹼紝鎴栫5姝ラ氳繃闄ゅ瓙澶氶」寮忕殑閫掓帹鍏紡鎸夐渶璁＄畻</div> <br /> <div><strong><span style="font-size: 13pt;">鎵偣鐨勯樁璁＄畻姝ｇ‘鎬ф牴鏈?/span></strong> <strong> </strong></div>     <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-calc-torsion-point-order-algo-correctness-analysis.png" width="599" height="374" alt="" /><br /> <br /> <div><span style="font-size: 13pt;"><strong>鍦ㄥ瘑鐮佸涓殑搴旂敤</strong></span><span style="background-color: #c0c0c0; font-size: 1px;"> </span> </div><div>    <span style="font-size: 11pt;"> <strong>閫夊彇鍘熷垯</strong></span>  </div> <div>        1. 鎺掗櫎瓚呭寮傛き鍦嗘洸綰褲傝繖鏄負閬垮厤<span style="color: #ff6600;">MOV</span>絳夌害鍖栨敾鍑伙紝綰﹀寲鏀誨嚮鏃墮棿澶嶆潅搴︽槸浜氭寚鏁?/div> <div>        2. 鏈夐檺鍩熺殑閫夋嫨瑕佷嬌<em>E</em>(<em>F</em><sub><em>q</em></sub>)鐨勭兢闃惰凍澶熷ぇ銆傝繖鏄負浜嗙紦瑙?span style="color: #ff00ff;">Shanks</span>鍙?span style="color: #ff00ff;">Pollard ρ</span>鏀誨嚮</div> <div>        3. <em>E</em>(<em>F</em><sub><em>q</em></sub>)瀛樺湪闃朵負澶х礌鏁扮殑瀛愮兢銆傝繖鏄負浜嗘姷鎶?span style="color: #ff00ff;">Pohlig-Hellman</span>鏀誨嚮</div> <div>      瀵逛簬絎?鐐癸紝灝辨帓闄や簡char(<em>K</em>)=2鎴?涓?em>j</em>(<em>E</em>)=0瀵瑰簲鐨勫涓嬫爣鍑嗗艦寮忔洸綰?/div> <div>           Y<sup>2</sup>+α<sub>3</sub>Y=X<sup>3</sup>+α<sub>4</sub>X+α<sub>6</sub>錛?#945;<sub>3</sub>≠0錛?涓?nbsp; Y<sup>2</sup>=X<sup>3</sup>+α<sub>4</sub>X+α<sub>6</sub> <br />      <br />     <span style="font-size: 11pt;"> <strong>涓縐嶅吀鍨嬫柟妗?/strong></span><span style="background-color: #c0c0c0; font-size: 1px;"><strong> </strong></span><span style="font-size: 12pt;"><br /> </span>           妞渾鏇茬嚎鍙婃湁闄愬煙鐨勯夋嫨浣垮緱|<em>E</em>(<em>F<sub>q</sub></em>)|=cm錛屼笖char(<em>F<sub>q</sub></em>) ∤ <em>q</em>+1-<em>cm</em>銆傚叾涓?em>m</em>鏄竴涓ぇ绱犳暟錛堥氬父涓嶄綆浜?56浣嶄簩榪涘埗闀垮害錛屾彁渚涗腑闀挎湡瀹夊叏鎬э級錛?em>c</em>灝忎簬<em>m</em>銆?br />          m闃跺瓙緹ょ殑鐢熸垚鍏冨彲閫氳繃浠ヤ笅鏂規硶紜畾錛氶殢鏈洪夋嫨<em>E</em>涓婄殑涓涓湁鐞嗙偣<em>P</em>錛屽鏋?em>Q</em>=<em>cP</em>涓洪浂鍏冿紙鍗蟲棤絀瘋繙鐐癸級錛屽垯閲嶅閫夋嫨錛岀洿鍒板叾涓嶇瓑浜庨浂鍏冦?br />          涓鏃︽壘鍒頒簡鐢熸垚鍏冿紝閭ｄ箞瀛愮兢灝卞彲浠ユ瀯閫犲嚭鏉ヤ簡銆備笅闈㈠垎鏋愭紜?nbsp; </div> <div>           <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/ec-cryptography-apply-typical-scheme.png" width="472" height="364" alt="" /><br /> <br /> <br /> <div><span style="font-size: 12pt;"><strong>鍙傝冩枃鐚?/strong></span></div> <div>  [1] 妞渾鏇茬嚎鍙婂叾鍦ㄥ瘑鐮佸涓殑搴旂敤—瀵煎紩      Andreas Enge</div> <div>  [2] 綆楁硶鏁拌                                           瑁村畾涓銆佺璺冮 </div> <div>  [3] The Arithmetic of Elliptic Curves        Joseph H. Silverman</div> <div>  [4] 鏍囪瘑瀵嗙爜瀛?nbsp;                                       紼嬫湞杈?/div> <div>  [5] 浠ｆ暟瀛﹀熀紜涓庢湁闄愬煙                             鏋椾笢宀?br /> <div>  [6] 鎶借薄浠ｆ暟I                                          璧墊槬鏉?寰愭槑鏇?/div> <div>  [7] 浠ｆ暟涓庢暟璁?nbsp;                                       鏉庤秴   鍛ㄦ偊</div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div><img src ="http://www.shnenglu.com/qinqing1984/aggbug/230402.html" width = "1" height = "1" /><br><br><div align=right><a style="text-decoration:none;" href="http://www.shnenglu.com/qinqing1984/" target="_blank">鏄ョ鍗佷簩鏈?/a> 2024-11-10 21:45 <a href="http://www.shnenglu.com/qinqing1984/archive/2024/11/10/230402.html#Feedback" target="_blank" style="text-decoration:none;">鍙戣〃璇勮</a></div>]]></description></item><item><title>涓嶅彲綰﹀欏瑰紡鍒ゅ埆綆楁硶鐨勬敼姝?/title><link>http://www.shnenglu.com/qinqing1984/archive/2024/09/07/230392.html</link><dc:creator>鏄ョ鍗佷簩鏈?/dc:creator><author>鏄ョ鍗佷簩鏈?/author><pubDate>Sat, 07 Sep 2024 15:07:00 GMT</pubDate><guid>http://www.shnenglu.com/qinqing1984/archive/2024/09/07/230392.html</guid><wfw:comment>http://www.shnenglu.com/qinqing1984/comments/230392.html</wfw:comment><comments>http://www.shnenglu.com/qinqing1984/archive/2024/09/07/230392.html#Feedback</comments><slash:comments>0</slash:comments><wfw:commentRss>http://www.shnenglu.com/qinqing1984/comments/commentRss/230392.html</wfw:commentRss><trackback:ping>http://www.shnenglu.com/qinqing1984/services/trackbacks/230392.html</trackback:ping><description><![CDATA[<div><strong style="font-size: 12pt;">鍘熸湰綆楁硶<br /> </strong> <div>    鎽樻妱<em>鍙傝冩枃鐚?</em>涓檮褰曠殑綆楁硶嫻佺▼濡備笅</div> <strong style="font-size: 12pt;">    <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/Irreducible-polynomial-decide-original-algo.PNG" width="547" height="298" alt="" /><br /> <br /> </strong> <div><strong style="font-size: 12pt;">渚嬪瓙嫻嬮獙</strong><br />    <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/Irreducible-polynomial-decide-example-test-prime-field.PNG" width="558" height="442" alt="" /><br />     <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/Irreducible-polynomial-decide-example-test-extend-field.PNG" width="556" height="367" alt="" /><br /> <div><br /> <strong style="font-size: 12pt;">鏀規鍚庣殑綆楁硶</strong></div> <div>       鏀規涔嬪墠錛屽厛鐞嗘竻鍘熸湰綆楁硶鍒ゅ埆涓嶅彲綰﹀欏瑰紡鎵鐢ㄧ殑鍘熺悊銆傚叾鍘熺悊鏄嫢f(x)鍙害錛屽綋涓斾粎褰撳瓨鍦ㄦ鏁癷<=d=[deg(f(x))/2]鐨勪笉鍙害鍥犲瓙g(x)錛岃屾鏃秅cd(x<sup>q^i</sup>-x, f(x))≠1銆?br />    鏍規嵁<em>鍙傝冩枃鐚?</em>錛堣瑙佸涓嬪畾鐞嗭級錛寈<sup>q^i</sup>-x鏄墍鏈塱嬈′笉鍙害澶氶」寮忕殑涔樼Н錛屽洜姝ゅ畠蹇呭畾鍖呭惈g(x)鑰屼笌f(x)瀛樺湪鍏洜瀛愩備笉鍙害鍒ゅ埆綆楁硶鐨勬濇兂搴旇鏄亶鍘嗘鏁?鍒癲鐨勬墍鏈変笉鍙害澶氶」寮?br />  錛堟病蹇呰媯嫻嬪ぇ浜巇鐨勪笉鍙害澶氶」寮忥紝鍥犱負鑻(x)鍙害鍒欏叾鍒嗚В鍥犲瓙涓繀瀹氬瓨鍦ㄤ笉澶т簬d鐨勪笉鍙害澶氶」寮忥級錛屾嫻嬭緭鍏ュ欏瑰紡涓庡畠浠槸鍚﹀瓨鍦ㄥ叕鍥犲瓙銆傛墍浠ヨ繖涓師鐞嗘槸姝ｇ‘鐨勶紝鍙槸瀹炵幇涓嶅錛?br />    鐣ヤ綔鏀規濡備笅錛堢被c璇█鎻忚堪錛?br />    <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/Irreducible-polynomial-decide-correct-algo.PNG" width="602" height="420" alt="" /><br /> <div><br /> <strong style="font-size: 12pt;">閲嶆柊嫻嬮獙</strong><br />    <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/Irreducible-polynomial-decide-example-retest-prime-field.PNG" alt="" /><br /><br />    <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/Irreducible-polynomial-decide-example-retest-extend-field.PNG" width="452" height="838" alt="" /><br /> <br /> <br /> <div><strong style="font-size: 11pt;">鍙傝冩枃鐚?/strong></div> <div>   [1] 綆楁硶鏁拌                 瑁村畾涓銆佺璺冮</div> <div>   [2] 浠ｆ暟瀛﹀熀紜涓庢湁闄愬煙   鏋椾笢宀?/div> </div> </div> </div> </div><img src ="http://www.shnenglu.com/qinqing1984/aggbug/230392.html" width = "1" height = "1" /><br><br><div align=right><a style="text-decoration:none;" href="http://www.shnenglu.com/qinqing1984/" target="_blank">鏄ョ鍗佷簩鏈?/a> 2024-09-07 23:07 <a href="http://www.shnenglu.com/qinqing1984/archive/2024/09/07/230392.html#Feedback" target="_blank" style="text-decoration:none;">鍙戣〃璇勮</a></div>]]></description></item><item><title>璁鴻瘉鏈夐檺鍩熶笂騫蟲柟鏍圭殑姹傝Вhttp://www.shnenglu.com/qinqing1984/archive/2024/08/30/230390.html鏄ョ鍗佷簩鏈?/dc:creator>鏄ョ鍗佷簩鏈?/author>Fri, 30 Aug 2024 14:22:00 GMThttp://www.shnenglu.com/qinqing1984/archive/2024/08/30/230390.htmlhttp://www.shnenglu.com/qinqing1984/comments/230390.htmlhttp://www.shnenglu.com/qinqing1984/archive/2024/08/30/230390.html#Feedback0http://www.shnenglu.com/qinqing1984/comments/commentRss/230390.htmlhttp://www.shnenglu.com/qinqing1984/services/trackbacks/230390.html閫氱敤綆楁硶
   鍏堟憳鎶勫弬鑰冩枃鐚甗1]涓殑綆楁硶嫻佺▼濡備笅
   

   姝ｇ‘鎬у垎鏋?br />       涓嬮潰璇佹槑浠ヤ笂綆楁硶鐢ㄥ埌鐨勪簨瀹炵粨璁猴紝鎻愮偧涓哄涓嬪嚑涓紩鐞?br />       
     

   綆楁硶鏋勯犳濇兂
         鐢ㄥ埌浜屾鍓╀綑鐭ヨ瘑錛屽嵆涓涓緟姹傚鉤鏂瑰厓蓱鍙互涓斿彧鑳借〃紺轟負涓や釜騫蟲柟鍥犲瓙鐨勪箻縐紝鍏朵腑涓鍥犲瓙涓轟換鎰忛殢鏈洪夊彇鐨勯潪騫蟲柟鍥犲瓙β鐨勫伓鏁板箓錛?br />       鍙︿竴鍥犲瓙涓哄彾瀛愮兢H鐨勪竴鍏冪礌r錛孒浣滀負闄泦鍒掑垎鏍圭兢錛堟湁闄愬煙涔樻硶緹わ級寰楀埌β鐢熸垚鐨勯泦鍚堝嵆鍟嗙兢G/H鐨勪竴涓唬琛ㄥ厓緋匯傝繖鏍蜂竴鏉ワ紝灝嗗紑鏂硅漿鍖栦負β涓巖鐨勪箻鏂硅繍綆楋紝
      榪唬鐨勮繃紼嬪氨鏄負姹傞偅涓叿浣撶殑浠ｈ〃鍏?#946;e涓殑鎸囨暟e錛堟敞鎰廵蹇呬負鍋舵暟錛夛紝浠嶨s-2鍒癎0=H錛岃凱浠ｇ粨鏉熷悗r琚敮涓紜畾錛宺鐨勫紑鏂圭瓑浜巖鐨?t+1)/2嬈℃柟錛堝洜涓簍鏄疕鐨勯樁涓斾負濂囨暟錛宺t+1=r錛夈?br />      瑙傚療綆楁硶嫻佺▼錛屽彲浠ュ彂鐜板鏋滃垎瑙-1鍚庡緱鍒皊=1錛岄偅涔堝氨娌″繀瑕侀夊彇闈炲鉤鏂瑰厓β浜嗭紙榪欐椂浠?#946;=1錛夛紝鐩存帴璺沖埌絎?姝ュ緱鍒扮粨鏋溿備粎褰搒≠1鎵嶉殢鏈洪夊彇β銆傝繖鏍鋒敼榪涘悗鍙姞蹇畻娉曡繍琛?br />
   渚嬪瓙嫻嬮獙
      
      
鐗規畩綆楁硶
   褰搎鏄礌鏁頒笖q≡3(mod 4)鏃訛紝瀛樺湪鏇村揩鐨勭畻娉曞強嫻嬮獙濡備笅 
   


鍙傝冩枃鐚?/strong>
   [1]  綆楁硶鏁拌   瑁村畾涓銆佺璺冮


]]>姹傝В紱繪暎瀵規暟闂鐨凾err綆楁硶http://www.shnenglu.com/qinqing1984/archive/2024/08/15/230388.html鏄ョ鍗佷簩鏈?/dc:creator>鏄ョ鍗佷簩鏈?/author>Thu, 15 Aug 2024 14:35:00 GMThttp://www.shnenglu.com/qinqing1984/archive/2024/08/15/230388.htmlhttp://www.shnenglu.com/qinqing1984/comments/230388.htmlhttp://www.shnenglu.com/qinqing1984/archive/2024/08/15/230388.html#Feedback0http://www.shnenglu.com/qinqing1984/comments/commentRss/230388.htmlhttp://www.shnenglu.com/qinqing1984/services/trackbacks/230388.html鍩烘湰鍘熺悊  
   
   鍐嶆潵鐪婽err綆楁硶鐢ㄥ埌鐨勫涓嬪畾鐞?br />      瀹氱悊 錛堝熀浜?em>鍙傝冩枃鐚?鏀規鍚庣殑鎻忚堪錛?span style="color: #ff6600;">瀵規瘡涓姝ｆ暣鏁皌錛屽瓨鍦ㄥ敮涓紜畾鐨勪竴緇勬暣鏁発鍜宩錛?<=k<j錛屼嬌寰梩=Tj+1-k錛屽叾涓璗0=0錛孴n=Tn-1+n-1錛宯>=1
    
     濡傛灉t=0錛岄偅涔坖鍦ㄥ尯闂碵0,1)錛屾晠鍙兘鍙?錛屾鏃秌=0涓庢潯浠秌<j鐭涚浘錛岃嫢鍏佽k=j錛屽垯涓嶄繚璇佸敮涓錛屾瘮濡倀=1 => j=1, k=0 鎴?j=2, k=2銆?/span>
     鎵浠?em>鍙傝冩枃鐚?涓師鏉ュ畾鐞嗙殑鎻忚堪“瀵規瘡涓闈炶礋鏁存暟t”鏄敊璇殑銆備笅闈㈠垪涓句竴浜涘疄渚嬮獙璇乯涓巏鐨勫敮涓瑙?/div>
               t=1  =>  j=1, k=0
               t=2  =>  j=2, k=1
               t=3  =>  j=2, k=0
               t=4  =>  j=3, k=2
               t=5  =>  j=3, k=1
               t=6  =>  j=3, k=0
   

綆楁硶浼唬鐮?/strong>
      


渚嬪瓙嫻嬮獙
     


鍙傝冩枃鐚?/strong>
   [1] 浠ｆ暟瀛﹀熀紜涓庢湁闄愬煙   鏋椾笢宀?/div>


]]>綆鍗曠閽ュ姞瀵嗘瀯閫犵殑楠岃瘉鍙婂畨鍏ㄦу垎鏋?/title><link>http://www.shnenglu.com/qinqing1984/archive/2024/06/29/230365.html</link><dc:creator>鏄ョ鍗佷簩鏈?/dc:creator><author>鏄ョ鍗佷簩鏈?/author><pubDate>Sat, 29 Jun 2024 09:00:00 GMT</pubDate><guid>http://www.shnenglu.com/qinqing1984/archive/2024/06/29/230365.html</guid><wfw:comment>http://www.shnenglu.com/qinqing1984/comments/230365.html</wfw:comment><comments>http://www.shnenglu.com/qinqing1984/archive/2024/06/29/230365.html#Feedback</comments><slash:comments>0</slash:comments><wfw:commentRss>http://www.shnenglu.com/qinqing1984/comments/commentRss/230365.html</wfw:commentRss><trackback:ping>http://www.shnenglu.com/qinqing1984/services/trackbacks/230365.html</trackback:ping><description><![CDATA[<strong style="font-size: 12pt;">縐侀挜鍒嗙粍鍔犲瘑</strong>  <br /> <dt></dt><dt><strong style="font-size: 12pt;">   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/privkey-block-cipher-base-prf.PNG" width="492" height="592" alt="" /></strong></dt><strong style="font-size: 12pt;">   <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/privkey-block-cipher-base-prf_proof-semantic-security.PNG" width="488" height="367" alt="" /><br />    </strong>涓婂浘鐨勮瘉鏄庝腑錛宺<sup>(j)</sup>涓や袱涓嶅悓鐨勬鐜囪綆楁槸鍏抽敭錛屼笅闈㈢粰鍑鴻緇嗚繃紼?br /> <strong style="font-size: 12pt;">       <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/privkey-block-cipher-base-prf_proof-probability-calc.PNG" width="434" height="251" alt="" /><br /> </strong> <div>    鍙﹀涓や釜鍒嗗竷緇熻鐨勪笉鍚屾剰鍛崇潃璁＄畻鍙垎杈紙鍙嶄箣鍒欒綆椾笉鍙垎杈級錛屼害鍗硆<sup>(j)</sup>鑷沖皯涓や釜鐩稿悓鐨勬鐜囥?/div> <strong style="font-size: 12pt;">  </strong><span style="color: #f37d31;">Construction 5.3.9</span>涓嬈″彧鑳藉姞瀵嗕笌瀵嗛挜絳夐暱鐨勬槑鏂囷紝濡傛灉瑕佸姞瀵嗘洿闀跨殑鏄庢枃錛屾庝箞鍔烇紵涓涓畝鍗曠洿鎺?br />   鐨勬柟娉曟槸灝嗘槑鏂囧垎鎴愬涓ぇ灝忎負n鐨勫潡錛屽姣忎釜鍧楄皟鐢ㄤ笂榪板姞瀵嗘楠わ紝閭ｄ箞灝卞緱鍒板艦濡備笅鐨勫瘑鏂囧潡搴忓垪<strong style="font-size: 12pt;"><br /> </strong><strong style="font-size: 12pt;">       <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/privkey-block-cipher-base-prf_ciphertext-sequence.PNG" width="356" height="79" alt="" /><br />   </strong>瀵嗘枃鍧楀簭鍒椾粠<span style="color: #c00000;">Proposition 5.3.10</span>鐨勮瘉鏄庝腑鍙煡鏄綆椾笉鍙垎杈ㄧ殑錛屾弧瓚?span style="font-family: 瀹嬩綋;">銆?/span>澶氱粍娑堟伅瀹夊叏鎬?span style="font-family: 瀹嬩綋; font-size: 10.5pt;">銆?/span>銆備絾瀵逛簬瑙ｅ瘑<br />   闇瑕佸瓨鍌ㄦ瘡涓鍧楃殑闅忔満鏁幫紝鍥犳姣旇緝鍗犵┖闂達紝鎵浠ヨ鐢熷嚭涓嬮潰鏇撮珮鏁堢殑鏂規<span style="color: #f37d31;">Construction 5.3.12</span><strong style="font-size: 12pt;"><br /> </strong><strong style="font-size: 12pt;"><br /> </strong> <div><strong style="font-size: 12pt;">縐佸瘑閫氱敤鍔犲瘑</strong><strong style="font-size: 12pt;"><br /> </strong>    <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/privkey-encryption-scheme-base-prf.PNG" width="490" height="422" alt="" /><br />   <strong style="font-size: 11pt;">   <br />      璇箟瀹夊叏鎬у垎鏋?/strong>    </div> <div>          <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/privkey-encryption-scheme-base-prf_security-analysis.PNG" alt="" /><br />           <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/privkey-encryption-scheme-base-prf_security-analysis-2.PNG" alt="" /><br /> <div><strong style="font-size: 12pt;"><br /> 鎶椾富鍔ㄦ敾鍑誨畨鍏ㄦ?/strong></div> <div>       浠ヤ笂涓ょ鏋勯犲洜婊¤凍<span style="font-family: 瀹嬩綋; font-size: 10.5pt;">銆?/span>澶氱粍娑堟伅瀹夊叏鎬?span style="font-family: 瀹嬩綋; font-size: 10.5pt;">銆?/span>錛屾晠婊¤凍<span style="color: #ff0000;">CPA</span>涓?span style="color: #ff0000;">CCA1</span>錛屽叿浣撶殑璇佹槑鍙弬鑰僌ded Goldreich銆婂瘑鐮佸鍩虹銆嬬殑<span style="color: #f37d31;">Proposition 5.4.12</span>銆?span style="color: #f37d31;">Proposition 5.4.18</span>銆?br />    浣嗕笉婊¤凍<span style="color: #ff0000;">CCA2錛?/span>鍥犱負鏀誨嚮鑰呮嬁鍒版寫鎴樺瘑鏂囧悗錛屽彲浠ヤ慨鏀瑰畠鍐嶅彂鍑鴻В瀵嗚川鐤戯紝寰楀埌鍥炵瓟鐨勬槑鏂囦粠鑰屽紓鎴栨眰瑙?em>f<sub>k</sub></em>(<em>r<sub>i</sub></em>)錛屾渶鍚庝笌鎸戞垬瀵嗘枃寮傛垨姹傝В鎸戞垬鏄庢枃<br />   瀵逛簬閫氱敤鍔犲瘑鏋勯犵殑CCA2鏀誨嚮緇嗚妭濡備笅<br />           <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/privkey-encryption-scheme-base-prf-cca2-detail.PNG" width="312" height="288" alt="" /></div> </div><img src ="http://www.shnenglu.com/qinqing1984/aggbug/230365.html" width = "1" height = "1" /><br><br><div align=right><a style="text-decoration:none;" href="http://www.shnenglu.com/qinqing1984/" target="_blank">鏄ョ鍗佷簩鏈?/a> 2024-06-29 17:00 <a href="http://www.shnenglu.com/qinqing1984/archive/2024/06/29/230365.html#Feedback" target="_blank" style="text-decoration:none;">鍙戣〃璇勮</a></div>]]></description></item><item><title>浜屽厓鏈夐檺鍩熷強鍏舵墿鍩熶笂鐨勮綆?/title><link>http://www.shnenglu.com/qinqing1984/archive/2024/05/16/230353.html</link><dc:creator>鏄ョ鍗佷簩鏈?/dc:creator><author>鏄ョ鍗佷簩鏈?/author><pubDate>Thu, 16 May 2024 05:41:00 GMT</pubDate><guid>http://www.shnenglu.com/qinqing1984/archive/2024/05/16/230353.html</guid><wfw:comment>http://www.shnenglu.com/qinqing1984/comments/230353.html</wfw:comment><comments>http://www.shnenglu.com/qinqing1984/archive/2024/05/16/230353.html#Feedback</comments><slash:comments>0</slash:comments><wfw:commentRss>http://www.shnenglu.com/qinqing1984/comments/commentRss/230353.html</wfw:commentRss><trackback:ping>http://www.shnenglu.com/qinqing1984/services/trackbacks/230353.html</trackback:ping><description><![CDATA[<span style="font-size: 12pt;"><strong>瀹氫箟<br />     <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/finite-field-extend-compute_define.png" width="351" height="51" alt="" /><br /> <br /> </strong></span><strong> </strong><strong style="font-size: 12pt;">Berlekamp鍒嗚В綆楁硶<br />     <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/finite-field-extend-compute_berlekamp.png" alt="" /><br /> </strong><br /> <strong> </strong><strong style="font-size: 12pt;">AES鏈夐檺鍩?br />    <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/finite-field-extend-compute_aes-element-denote.png" width="536" height="88" alt="" /><br /> <br /> </strong> <strong style="font-size: 11pt;">  涓嶅彲綰︽ц瘉鏄?br /> </strong>       <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/finite-field-extend-compute_aes-polynomial-irreducible-proof.png" width="498" height="824" alt="" /><br /> <br /> <strong></strong><strong style="font-size: 11pt;">  闈炴湰鍘熸ч獙璇?br />       <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/finite-field-extend-compute_aes-polynomial-noprimitive-verify.png" alt="" /><br /> <br />   </strong><strong style="font-size: 11pt;">鎵懼嚭鏈師鍏?br />       <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/finite-field-extend-compute_aes-find-primitive-element.png" alt="" /><br /> <br /> </strong>   <strong style="font-size: 11pt;">涓嶅彲綰﹀欏瑰紡涓暟<br />        <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/finite-field-extend-compute_aes-irreducible-polynomial-count.png" alt="" /><br /> <br /> </strong><strong style="font-size: 12pt;">綰挎хЩ浣嶅瘎瀛樺櫒m搴忓垪<br />      </strong>鏍規嵁鍙傝冩枃鐚?鐭ョ嚎鐢熺Щ浣嶅瘎瀛樺櫒浜х敓m搴忓垪鐨勫厖瑕佹潯浠舵槸鐗瑰緛澶氶」寮廸(x)涓烘湰鍘熷欏瑰紡銆傝岀‘绔嬫湁闄愬煙涓婄殑鏈師澶氶」寮忥紝涓昏鏈変袱縐嶆柟娉曪細<br />       涓縐嶆柟娉曟槸鏍規嵁<strong>F</strong><sub>q</sub>涓婃墍鏈夋鏁頒負n鐨勬湰鍘熷欏瑰紡鐨勪箻縐濂界瓑浜庡壊鍦嗗欏瑰紡Q<sub>e</sub>錛屽叾涓璭=q<sup>n</sup>-1錛屼粠鑰屾墍鏈夋鏁頒負n鐨勬湰鍘熷欏瑰紡鍙互閫氳繃鍒嗚ВQ<sub>e</sub>寰楀埌銆?br />       鍙︿竴縐嶆柟娉曟槸閫氳繃鏋勯犳湰鍘熷厓鍐嶆眰鏈師鍏冪殑鏋佸皬澶氶」寮忥紝鍏堢礌鍥犲瓙鍒嗚Вq<sup>n</sup>-1=p<sub>1</sub>p<sub>2</sub>...p<sub>k</sub>錛屽鏋滃姣忎竴p<sub>i</sub>閮芥湁ord(<span style="color: #4b4b4b; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span><sub>i</sub>)=p<sub>i</sub>錛岄偅涔?span style="color: #4b4b4b; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span>=<span style="color: #4b4b4b; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span><sub>1</sub><span style="color: #4b4b4b; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span><sub>2</sub>...<span style="color: #4b4b4b; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span><sub>k</sub>鐨勯樁灝辨槸q<sup>n</sup>-1錛?br />       鍥犳鏄?strong>F</strong><sub>q</sub>涓婄殑鏈師鍏冿紝鍒檉(x)=(x-<span style="color: #4b4b4b; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span>)(x-<span style="color: #4b4b4b; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span><sup>2</sup>)...(x-<span style="color: #4b4b4b; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span><sup>r</sup>)錛宺=q<sup>n</sup>-1錛堝洜涓?span style="color: #4b4b4b; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span>鏄湰鍘熷厓錛屾墍浠鏄嬌<span style="color: #4b4b4b; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span><sup>q^n</sup>=<span style="color: #4b4b4b; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span>鎴愮珛鐨勬渶灝忔鏁存暟錛夈?br />     <br />     <strong style="font-size: 11pt;">姹傝В鏈師澶氶」寮?/strong><br />        鍋囪綰挎хЩ浣嶅瘎瀛樺櫒鐨勭駭鏁頒負4錛岃繖閲屼嬌鐢ㄤ笂榪頒簩縐嶆柟娉曟眰<strong>F</strong><sub>16</sub>涓婄殑鏈師澶氶」寮忥紝榪囩▼濡備笅<br />       <strong>鍒嗚В鍓插渾澶氶」寮忔硶</strong><br />          <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/finite-field-extend-compute_lfsr-solve-primitive-polynomial-algo1.png" alt="" /><br /> <br /><div>       <strong>鏋勯犳瀬灝忓欏瑰紡娉?/strong><br />          <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/finite-field-extend-compute_lfsr-solve-primitive-polynomial-algo2.png" alt="" /></div>        <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/finite-field-extend-compute_lfsr-solve-primitive-polynomial-algo2_1.png" alt="" /><br />         <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/finite-field-extend-compute_lfsr-solve-primitive-polynomial-algo2_2.png" alt="" /><br /><strong style="font-size: 11pt;">   <br />  鏈師澶氶」寮忎釜鏁?br />        <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/finite-field-extend-compute_lfsr-primitive-polynomial-count.png" width="554" height="191" alt="" /><br /> <br />    </strong><strong style="font-size: 11pt;">m搴忓垪紺轟緥<br />        <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/finite-field-extend-compute_lfsr-mseq-example.png" width="522" height="358" alt="" /><br /> <br /> <br /> </strong> <div><strong style="font-size: 12pt;">鍙傝冩枃鐚?br />     </strong>[1] 浠ｆ暟瀛﹀熀紜涓庢湁闄愬煙    鏋椾笢宀?/div><img src ="http://www.shnenglu.com/qinqing1984/aggbug/230353.html" width = "1" height = "1" /><br><br><div align=right><a style="text-decoration:none;" href="http://www.shnenglu.com/qinqing1984/" target="_blank">鏄ョ鍗佷簩鏈?/a> 2024-05-16 13:41 <a href="http://www.shnenglu.com/qinqing1984/archive/2024/05/16/230353.html#Feedback" target="_blank" style="text-decoration:none;">鍙戣〃璇勮</a></div>]]></description></item><item><title>綆鍗曡繛鍒嗘暟鏀誨嚮RSA鐨勮凱浠ｆ鏁板垎鏋?/title><link>http://www.shnenglu.com/qinqing1984/archive/2024/04/04/230326.html</link><dc:creator>鏄ョ鍗佷簩鏈?/dc:creator><author>鏄ョ鍗佷簩鏈?/author><pubDate>Thu, 04 Apr 2024 10:19:00 GMT</pubDate><guid>http://www.shnenglu.com/qinqing1984/archive/2024/04/04/230326.html</guid><wfw:comment>http://www.shnenglu.com/qinqing1984/comments/230326.html</wfw:comment><comments>http://www.shnenglu.com/qinqing1984/archive/2024/04/04/230326.html#Feedback</comments><slash:comments>0</slash:comments><wfw:commentRss>http://www.shnenglu.com/qinqing1984/comments/commentRss/230326.html</wfw:commentRss><trackback:ping>http://www.shnenglu.com/qinqing1984/services/trackbacks/230326.html</trackback:ping><description><![CDATA[<strong style="font-size: 12pt;">銆愰傜敤鍓嶆彁銆?/strong>澶ф暣鏁癗=pq鐨勭礌鍥犲瓙p<q<2p錛岃В瀵嗘寚鏁癲<(1/3)N<sup>1/4<br /> <br /> </sup> <strong style="font-size: 12pt;">銆愭敾鍑繪柟娉曘?/strong>  <br />     1錛夌敤嬈у嚑閲屽緱綆楁硶璁＄畻e/N鐨勫悇涓笎榪戝垎鏁発<sub>i</sub>/d<sub>i</sub>錛宨>=1錛岀洿鑷砫<sub>i>=</sub>(1/3)N<sup>1/4</sup>錛岃褰曟鏃剁殑i涓簃銆備護i=1   <br />     2錛夎綆桾=(e*d<sub>i</sub>-1)/k<sub>i</sub>錛岃嫢T涓嶄負鏁存暟鍒欒漿鍒?錛夛紝鍚﹀垯杞埌3錛?nbsp; <br />     3錛夎В鏂圭▼f(x)=x<sup>2</sup>-(N-T+1)x+N=0鐨勬牴錛屽鏋滄湁姝ｆ暣鏁版牴涓斾袱涓牴鐨嗗皬浜嶯錛屽垯杈撳嚭p銆乹錛屽茍榪斿洖鎴愬姛銆傚惁鍒欒漿鍒?錛?nbsp; <br />     4錛夐掑i錛岃嫢i<m鍒欒漿鍥?錛夛紝鍚﹀垯榪斿洖澶辮觸<br />    璇ユ柟娉曞嵆<strong>Wiener綆楁硶</strong>鐢ㄥ埌浜嗗叧浜庤繛鍒嗘暟鐨勪竴涓?strong>瀹氱悊錛?/strong><span style="color: #ff6600;">鑻?/span><span style="color: #ff6600; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span><span style="color: #ff6600;">涓轟換涓瀹炴暟錛屾湁鐞嗘暟p/q閫傚悎|</span><span style="color: #ff6600; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span><span style="color: #ff6600;">-(p/q)|<1/(2q</span><sup style="color: #ff6600;">2</sup><span style="color: #ff6600;">)錛屽垯p/q蹇呬負</span><span style="color: #ff6600; font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px; background-color: #ffffff;">α</span><span style="color: #ff6600;">鐨勬煇涓娓愯繎鍒嗘暟</span>銆傝瘉鏄庤瑙佸弬鑰冩枃鐚甗2]銆?br />    鐢卞畾鐞嗗彲鐭ユ敾鍑繪柟娉曟槸鍙鐨勶紝蹇呰兘鎵懼埌浣縡(x)=0鏈夊悎鐞嗚В鐨勬煇娓愯繎鍒嗘暟銆備笅闈㈣瘉鏄庯細鏀誨嚮榪唬嬈℃暟鐨勪笂鐣屼負<img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/continuedfraction-attack-rsa-iteration-upperbound.png" width="72" height="43" alt="" /><br /> <br /> <strong style="font-size: 12pt;">銆愯瘉鏄庛?br />     <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/continuedfraction-attack-rsa-iteration-proof.png" width="466" height="508" alt="" /><br /> <br /> <br /> </strong> <strong style="font-size: 12pt;">銆愪緥瀛愩?/strong>N = 9449868410449錛宔 = 6792605526025錛宒<(1/3)N<sup>1/4</sup>≈584錛岃瘯鍒嗚ВN<br />     <img src="http://www.shnenglu.com/images/cppblog_com/qinqing1984/continuedfraction-attack-rsa-example.png" alt="" /><br /> <br /> <strong style="font-size: 12pt;">鍙傝冩枃鐚?/strong> <br />     [1] 鍏挜瀵嗙爜瀛︾殑鏁板鍩虹  鐜嬪皬浜戙佺帇鏄庡己銆佸瓱瀹悓<br />     [2] 綆楁硶鏁拌                   瑁村畾涓銆佺璺冮<img src ="http://www.shnenglu.com/qinqing1984/aggbug/230326.html" width = "1" height = "1" /><br><br><div align=right><a style="text-decoration:none;" href="http://www.shnenglu.com/qinqing1984/" target="_blank">鏄ョ鍗佷簩鏈?/a> 2024-04-04 18:19 <a href="http://www.shnenglu.com/qinqing1984/archive/2024/04/04/230326.html#Feedback" target="_blank" style="text-decoration:none;">鍙戣〃璇勮</a></div>]]></description></item></channel></rss> <footer> <div class="friendship-link"> <p>感谢您访问我们的网站，您可能还对以下资源感兴趣：</p> <a href="http://www.shnenglu.com/" title="精品视频久久久久">精品视频久久久久</a> <div class="friend-links"> </div> </div> </footer> <a href="http://www.vtsg.cn" target="_blank">国产色综合久久无码有码</a>| <a href="http://www.bjhaoruida.com.cn" target="_blank">嫩草影院久久99</a>| <a href="http://www.fanerge.cn" target="_blank">色偷偷久久一区二区三区</a>| <a href="http://www.arqing.cn" target="_blank">AAA级久久久精品无码片</a>| <a href="http://www.beauty-queen.cn" target="_blank">青青青青久久精品国产h</a>| <a href="http://www.woaisheying.cn" target="_blank">久久中文字幕无码专区</a>| <a href="http://www.itshirts.cn" target="_blank">精品国产乱码久久久久久人妻</a>| <a href="http://www.nsom.org.cn" target="_blank">精品久久久久久国产</a>| <a href="http://www.jxscool.cn" target="_blank">国产精品久久久久蜜芽</a>| <a href="http://www.1rizu.cn" target="_blank">久久久久夜夜夜精品国产</a>| <a href="http://www.yaott2.cn" target="_blank">国内精品久久久久影院薰衣草</a>| <a href="http://www.shoucunshiyuan.cn" target="_blank">久久精品国产影库免费看</a>| <a href="http://www.u33w.cn" target="_blank">无码人妻久久一区二区三区免费丨</a>| <a href="http://www.cq81.cn" target="_blank">久久综合中文字幕</a>| <a href="http://www.silverprice.net.cn" target="_blank">一本色道久久99一综合</a>| <a href="http://www.ljvs.cn" target="_blank">人人狠狠综合88综合久久</a>| <a href="http://www.alibabataba.cn" target="_blank">久久久精品免费国产四虎</a>| <a href="http://www.zusang.cn" target="_blank">亚洲中文字幕无码久久精品1</a>| <a href="http://www.foxconm.cn" target="_blank">久久久国产精品</a>| <a href="http://www.yc-shop.cn" target="_blank">狠狠色丁香婷综合久久</a>| <a href="http://www.ts71.cn" target="_blank">麻豆一区二区99久久久久</a>| <a href="http://www.gfwi.cn" target="_blank">日韩人妻无码一区二区三区久久99</a>| <a href="http://www.jjj41.cn" target="_blank">9999国产精品欧美久久久久久</a>| <a href="http://www.txslcc.cn" target="_blank">久久久久免费看成人影片</a>| <a href="http://www.lwtjf.cn" target="_blank">久久久久久免费视频</a>| <a href="http://www.fangongdi.cn" target="_blank">99久久国产亚洲高清观看2024 </a>| <a href="http://www.51uhq.cn" target="_blank">亚洲综合久久夜AV </a>| <a href="http://www.yuleluntan.cn" target="_blank">国产精品免费久久</a>| <a href="http://www.s9990.cn" target="_blank">国产69精品久久久久99</a>| <a href="http://www.xeqw.cn" target="_blank">中文字幕成人精品久久不卡</a>| <a href="http://www.llqu.cn" target="_blank">久久精品国产91久久综合麻豆自制</a>| <a href="http://www.aurp.cn" target="_blank">久久久久亚洲AV无码永不</a>| <a href="http://www.otraveler.cn" target="_blank">亚洲伊人久久精品影院</a>| <a href="http://www.shufa520.cn" target="_blank">亚洲级αV无码毛片久久精品</a>| <a href="http://www.aimingshi.cn" target="_blank">中文国产成人精品久久亚洲精品AⅤ无码精品</a>| <a href="http://www.gdhaojulai.cn" target="_blank">久久亚洲国产精品一区二区</a>| <a href="http://www.qingjian8.cn" target="_blank">丰满少妇人妻久久久久久</a>| <a href="http://www.voos.org.cn" target="_blank">波多野结衣中文字幕久久</a>| <a href="http://www.car321.cn" target="_blank">国产精品久久久久影院嫩草</a>| <a href="http://www.cjubbs.cn" target="_blank">亚洲狠狠久久综合一区77777</a>| <a href="http://www.touzhi8.cn" target="_blank">亚洲综合精品香蕉久久网97</a>| <script> (function(){ var bp = document.createElement('script'); 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