{"id":2490,"date":"2025-11-13T13:26:50","date_gmt":"2025-11-13T05:26:50","guid":{"rendered":"https:\/\/pjq.me\/?p=2490"},"modified":"2025-11-13T19:02:06","modified_gmt":"2025-11-13T11:02:06","slug":"%e5%af%86%e7%a0%81%e5%ad%a6cryptography%e7%ae%80%e5%8f%b2-%e9%9d%9e%e5%af%b9%e7%a7%b0%e5%8a%a0%e7%a7%98asymmetric-encryption","status":"publish","type":"post","link":"https:\/\/pjq.me\/?p=2490","title":{"rendered":"\u5bc6\u7801\u5b66(Cryptography)\u7b80\u53f2-\u975e\u5bf9\u79f0\u52a0\u79d8(Asymmetric Encryption)"},"content":{"rendered":"\n<p>\u4e4b\u524d\u8bb2\u8fc7\u5bf9\u79f0\u52a0\u5bc6\uff0c\u6bd4\u5982DES, AES, \u8fd8\u6709AES\u5bf9\u5e94\u5230\u7684\u5404\u79cd\u6a21\u5f0f\uff0c\u6bd4\u5982ECB, CBC, CTR, GCM.<\/p>\n\n\n\n<p>\u5bf9\u79f0\u52a0\u5bc6\u552f\u4e00\u4fdd\u5bc6\u7684\u5c31\u662f\u5bc6\u94a5(Key), \u6709\u4e86\u8fd9\u4e2a\u5bc6\u7801\u4f60\u5c31\u80fd\u89e3\u5bc6\u5176\u4e2d\u7684\u5185\u5bb9\u3002<\/p>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_81 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/pjq.me\/?p=2490\/#%E5%85%AC%E5%BC%80%E9%80%9A%E4%BF%A1%E4%BF%A1%E9%81%93Channel\" >\u516c\u5f00\u901a\u4fe1\u4fe1\u9053(Channel)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/pjq.me\/?p=2490\/#%E5%8A%A8%E6%9C%BAMotivation\" >\u52a8\u673a(Motivation)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/pjq.me\/?p=2490\/#RSARivest_Shamir_Adleman\" >RSA(Rivest, Shamir, Adleman)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/pjq.me\/?p=2490\/#OAEP_%E2%80%93_Optimal_Asymmetric_Encryption_Padding\" >OAEP &#8211; Optimal Asymmetric Encryption Padding<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/pjq.me\/?p=2490\/#%E5%88%9D%E6%AC%A1%E5%AE%9E%E7%8E%B0%E4%BA%86%E9%9D%9E%E5%AE%89%E5%85%A8%E4%BF%A1%E9%81%93%E6%B6%88%E6%81%AF%E4%BC%A0%E9%80%92\" >\u521d\u6b21\u5b9e\u73b0\u4e86\u975e\u5b89\u5168\u4fe1\u9053\u6d88\u606f\u4f20\u9012<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/pjq.me\/?p=2490\/#%E6%95%B0%E5%AD%97%E7%AD%BE%E5%90%8DDigital_Signatures\" >\u6570\u5b57\u7b7e\u540d(Digital Signatures)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/pjq.me\/?p=2490\/#DH%E5%92%8CFPSPerfect_Forward_Secrecy\" >DH\u548cFPS(Perfect Forward Secrecy)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/pjq.me\/?p=2490\/#ECCElliptic_Curves_%E6%A4%AD%E5%9C%86%E6%9B%B2%E7%BA%BF\" >ECC(Elliptic Curves, \u692d\u5706\u66f2\u7ebf)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/pjq.me\/?p=2490\/#%E6%B7%B7%E5%90%88%E5%8A%A0%E5%AF%86%E6%A8%A1%E5%BC%8F\" >\u6df7\u5408\u52a0\u5bc6\u6a21\u5f0f<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%85%AC%E5%BC%80%E9%80%9A%E4%BF%A1%E4%BF%A1%E9%81%93Channel\"><\/span>\u516c\u5f00\u901a\u4fe1\u4fe1\u9053(Channel)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u6570\u5b57\u4e16\u754c\u4e2d\u7684\u901a\u4fe1\u4fe1\u9053\u5176\u5b9e\u53ef\u4ee5\u7c7b\u6bd4\u771f\u5b9e\u7269\u7406\u4e16\u754c\uff0c \u6211\u4eec\u8981\u4ece\u4e0a\u6d77\u5230\u5317\u4eac\u5c31\u8981\u7ecf\u5e38\u5404\u79cd\u5404\u6837\u7684\u9053\u8def\uff0c\u6bd4\u5982\u8d70\u9ad8\u901f\u516c\u8def\uff0c\u5c31\u53ef\u80fd\u8981\u7ecf\u5e38\u5404\u79cd\u68c0\u67e5\u7ad9\uff0c\u6536\u8d39\u7ad9\uff0c\u7406\u8bba\u4e0a\u8fd9\u4e9b\u7ad9\u70b9\u90fd\u53ef\u4ee5\u5bf9\u4f60\u7684\u8f66\u8fdb\u884c\u5168\u65b9\u4f4d\u7684\u641c\u7d22\u68c0\u67e5\uff0c\u770b\u6709\u6ca1\u6709\u643a\u5e26\u8fdd\u7981\u54c1\u3002\u4e92\u8054\u7f51\u4e16\u754c\u4e00\u6837\uff0c\u4f60\u7684\u6570\u636e\u8981\u7ecf\u5e38\u4e2d\u95f4\u7684\u5404\u79cdWifi, \u8def\u7531\uff0c\u7f51\u5173\uff0c\u5149\u7ea4\uff0c\u6bcf\u4e2a\u8def\u7531\u7f51\u5173\u7406\u8bba\u4e0a\u90fd\u53ef\u4ee5\u628a\u4f60\u7684\u4f20\u8f93\u6570\u636e\u62e6\u622a\u4e0b\u6765\uff0c\u751a\u81f3\u7be1\u6539\uff0c\u6240\u4ee5\u6211\u4eec\u8981\u77e5\u9053\u516c\u5f00\u7684\u8fd9\u4e9b\u901a\u4fe1\u4fe1\u9053\u662f\u4e0d\u5b89\u5168\u4e0d\u53ef\u4fe1\u4efb\u7684\u3002<\/p>\n\n\n\n<p>\u6240\u4ee5\u60f3\u60f3\u6211\u4eec\u7684\u6570\u636e\u5728\u8fd9\u4e9b\u4e0d\u53ef\u4fe1\u4efb\u7684\u8def\u9014\u4e2d\u7a7f\u68ad\u8fd8\u662f\u633a\u53ef\u6015\u7684\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%8A%A8%E6%9C%BAMotivation\"><\/span>\u52a8\u673a(Motivation)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u53ef\u4ee5\u901a\u8fc7AES\u52a0\u5bc6\u6570\u636e\u4e86\uff0c\u628a\u52a0\u5bc6\u7684\u5185\u5bb9\u4f20\u8f93\u51fa\u53bb\u3002\u4f46\u662f\u5bc6\u7801\u8981\u600e\u4e48\u4f20\u8f93\u51fa\u53bb\u4e86\uff0c\u56e0\u4e3a\u5bc6\u7801\u662f\u660e\u6587\u7684\uff0c\u5b83\u5728\u8fd9\u4e9b\u516c\u5f00\u901a\u4fe1\u4fe1\u606f\u91cc\u9762\u4f20\u8f93\u5c31\u4e00\u5b9a\u4f1a\u53ef\u80fd\u88ab\u9ed1\u5ba2\u62e6\u622a\u5230\uff0c\u8fd8\u6709\u4e00\u4e2a\u95ee\u9898\uff0c\u5982\u679c\u4f60\u4e00\u76f4\u7528\u540c\u4e00\u4e2a\u5bc6\u7801\uff0c\u90a3\u4e48\u9ed1\u5ba2\u5c31\u53ef\u4ee5\u4e00\u76f4\u62e6\u622a\u4f60\u7684\u4fe1\u606f\uff0c\u751a\u81f3\u5728\u5f97\u5230\u5bc6\u7801\u4e4b\u524d\u5c31\u4e00\u76f4\u5728\u62e6\u622a\uff0c\u76f4\u5230\u67d0\u4e00\u5929\u5f97\u5230\u5bc6\u7801\u4e86\uff0c\u90a3\u4e48\u9ed1\u5ba2\u5c31\u53ef\u4ee5\u540c\u65f6\u89e3\u5bc6\u4e4b\u524d\u5df2\u7ecf\u5b58\u5728\u5f88\u7684\u52a0\u5bc6\u4fe1\u606f\u4e86\uff0c\u5982\u679c\u5bc6\u7801\u4e0d\u6539\uff0c\u90a3\u5c06\u6765\u7684\u52a0\u5bc6\u4fe1\u606f\u4e5f\u4e00\u6837\u4f1a\u88ab\u9ed1\u5ba2\u89e3\u5bc6\u3002<\/p>\n\n\n\n<p>\u6240\u4ee5\u5bc6\u7801\u5b66\u79d1\u5b66\u5bb6\u4eec\u7ede\u5c3d\u8111\u6c41\u60f3\u8bbe\u8ba1\u51fa\u6765\u4e00\u79cd\u65b9\u6cd5\uff0c\u53ef\u4ee5\u89e3\u51b3\u5728\u4e0d\u5b89\u5168\u4fe1\u9053\u4e2d\u4ea4\u4e92\u5bc6\u94a5\u7684\u95ee\u9898<\/p>\n\n\n\n<p>\u4e8e\u662f\u5c31\u8bbe\u8ba1\u51fa\u4e86\u4e00\u79cd\u901a\u8fc7\u5bc6\u94a5\u5bf9\u7684\u52a0\u89e3\u5bc6\u65b9\u5f0f\uff0c\u540c\u65f6\u751f\u6210\u4e00\u5bf9\u5bc6\u94a5<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u79c1\u94a5(Private Key) &#8212; \u81ea\u5df1\u4fdd\u7559\uff0c\u7edd\u5bf9\u4fdd\u5bc6<\/li>\n\n\n\n<li>\u516c\u94a5(Public Key) &#8212; \u516c\u5f00\u53d1\u5e03\uff0c\u5206\u4eab\u7ed9\u5176\u5b83\u4eba<\/li>\n<\/ul>\n\n\n\n<p>\u516c\u94a5\u52a0\u5bc6\uff0c\u79c1\u94a5\u89e3\u5bc6\u3002\u8fd9\u6837\u522b\u4eba\u5c31\u53ef\u4ee5\u62ff\u5230\u4f60\u7684\u516c\u94a5\u628a\u9700\u8981\u4fdd\u5bc6\u7684\u4fe1\u606f\u8fdb\u884c\u52a0\u5bc6\u53d1\u7ed9\u4f60\uff0c\u4f60\u6536\u5230\u540e\u901a\u8fc7\u79c1\u94a5\u8fdb\u884c\u89e3\u5bc6\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u60f3\u6cd5\u5f88\u5947\u5999\uff0c\u7136\u540e\u771f\u7684\u5c31\u505a\u51fa\u6765\u4e86\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"RSARivest_Shamir_Adleman\"><\/span>RSA(Rivest, Shamir, Adleman)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>RSA\u5c31\u662f\u5176\u4e2d\u4e00\u79cd\u975e\u5bf9\u79f0\u52a0\u5bc6\u7b97\u6cd5\uff0c\u5b83\u5c31\u662f\u53ef\u4ee5\u751f\u6210\u4e00\u5bf9\u516c\u94a5\uff0c\u79c1\u94a5\u3002\u53ef\u80fd\u5927\u5bb6\u4ee5\u4e3a\u8fd9\u4e2a\u662f\u6700\u8fd1\u624d\u53d1\u660e\u7684\uff0c\u4f46\u5176\u5b9e\u8fd9\u4e2a\u662f\u5f88\u65e9\uff0c\u57281977\u5e74\uff0cRSA\u5c31\u53d1\u660e\u4e86\uff0c\u4e00\u76f4\u7528\u5230\u73b0\u5728\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"319\" height=\"223\" src=\"https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-18.png\" alt=\"\" class=\"wp-image-2491\" srcset=\"https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-18.png 319w, https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-18-300x210.png 300w\" sizes=\"auto, (max-width: 319px) 100vw, 319px\" \/><\/figure>\n\n\n\n<p>\u5b83\u57fa\u4e8e\u7684\u6570\u5b66\u539f\u7406\u5176\u5b9e\u5f88\u7b80\u5355\uff0c\u7b80\u5355\u5230\u4e00\u4e2a\u5c0f\u5b66\u751f\u90fd\u5bb9\u6613\u7406\u89e3<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5927\u6574\u6570\u7684\u56e0\u5f0f\u5206\u89e3<\/li>\n<\/ul>\n\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e24\u4e2a\u8d28\u6570p, q, N=p*q, \u90a3\u5f53\u6211\u4eec\u53ea\u77e5\u9053N\u7684\u65f6\u5019\u662f\u6ca1\u529e\u6cd5\u7b97\u51fap\u548cq\u7684\uff0c\u8fd9\u4e2a\u57fa\u672c\u539f\u7406\u5c31\u662fRSA\u7684\u672c\u8d28\u3002<\/p>\n\n\n\n<p>\u5176\u5b9e\u60f3\u60f3\u5f88\u7b80\u5355\uff0c\u4f46\u603b\u4f1a\u89c9\u5f97\u6709\u70b9\u4e0d\u53ef\u601d\u8bae\u5bf9\u5427\uff0c\u4f46\u73b0\u5b9e\u5c31\u662f\u8fd9\u6837\uff0c\u5982\u679c\u6709\u8c01\u80fd\u8fc7\u591f\u5728\u53ea\u77e5\u9053N\u7684\u60c5\u51b5\u4e0b\u7b97\u51fap\u548cq,\u90a3\u4e48RSA\u5c31\u5b8c\u86cb\u4e86\u3002<\/p>\n\n\n\n<p>RSA\u7684\u8ba1\u7b97\u8fc7\u7a0b\u5f88\u7b80\u5355<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u9009\u62e9\u4e24\u4e2a\u8d28\u6570 p, q\nN= p * q\nPhi(N) = (p-1) * (q-1)\n\u518d\u9009\u53d6\u4e00\u4e2ae, 1&lt;e&lt;Phi(N)\uff0c\u901a\u5e38\u6211\u4eec\u4f1a\u9009\u62e9e=65537\n\u901a\u8fc7\u516c\u5f0f\u7b97\u51fad\uff0c \u6ee1\u8db3\u6761\u4ef6 e * d mod Phi(N) = 1\n\u8fd9\u6837\u5c31\u5f97\u5230\u516c\u94a5Public Key(e, N), \u79c1\u94a5Private Key(d, N)<\/code><\/pre>\n\n\n\n<p>\u5f53\u7136\u5b9e\u9645\u7684\u8fc7\u7a0b\u4e2d\u8fd9\u4e9b\u6570\u6570\u4f1a\u957f\uff0c\u6bd4\u5982&gt;1024\uff0c\u5982\u4e0b\u9762\u8fd9\u4e2a\u662f\u6211\u4ece\u4e00\u4e2a\u8bc1\u4e66\u91cc\u9762\u6293\u53d6\u5230\u7684\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>p: 132069789892654411168004522386293936563648260984708049888769058861400033840104922637240827355145535778467721990046061228393420363010924409941513508800258809981119101399937003195217979917259199066675447728576676098948661691324234988484581514373041670098119069924124636404134462689209640493314790132976282083611\u000b\nq: 137105056982080406391028823084893501194543535606308088202698272087931645688882684542797221955650442538986772234601648478841035329665841202081550877179575957078786677686845060335508172755008305533505548942627696405948787947081088462002379085459968945063951380151782547161878405562777603813013479678683689059989\u000b\ne: 65537\nd: 756214848412734766389636904239299485009061447036919688389891952047609574545734290864923373793452280368637781527992131423339716753716888185459331923714856645280928404198259347205993579213846803666627529909232828722879650374490951581311985882248017934718743944682742282487622451272419143686155769738092352440521581984122740725976684511860250924537999931049740452351974285438729683375867711220177807812280621918795246117514339543091408571088210170010573980132856774272424920513332731618240977627013497573799860486533079269798618961305686700083116612832032852006212842303481886949894366447734991011109426370041918678153\u000b\nN: 18107436068843769961592120494384716970785115109411255249546345948609495318598388096607410722799226196024630722689083053376476074858729887106484558379430237472333286381418093839181293825698895861125235085005989001100242472266354948404984880805585806133599679175254980258454991811852588023295429551087087505259481055918651153874312403039948814343657680828818579172724766105080872512340183146177770234401565111928007670988819164086328954605138596051183819569014922240750776080760982732900349444868680946505230852975887754348080529969823222341004758720100799077687160346328480228883962117022614977552611965834106892740279\u000b\nphi_N: 18107436068843769961592120494384716970785115109411255249546345948609495318598388096607410722799226196024630722689083053376476074858729887106484558379430237472333286381418093839181293825698895861125235085005989001100242472266354948404984880805585806133599679175254980258454991811852588023295429551087087505259211881071776419056753369694477626905899489032227563034633298774131540832811195538997732185090769133610553176764171454379094498912461830439160755183035087473690870301674200669369623292196413441905049856304683381843183080331417898890517798120267788462525089896252573045317949248770627733246283696022446921596680\n<\/code><\/pre>\n\n\n\n<p>RSA \u52a0\u5bc6\u662f<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\ud835\udc40^\ud835\udc52  \ud835\udc5a\ud835\udc5c\ud835\udc51 \ud835\udc41=\ud835\udc36<\/code><\/pre>\n\n\n\n<p>\u89e3\u5bc6\u662f<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\ud835\udc36^\ud835\udc51  \ud835\udc5a\ud835\udc5c\ud835\udc51 \ud835\udc41=\ud835\udc40<\/code><\/pre>\n\n\n\n<p>\u5176\u4e2dM\u662f\u660e\u6587\uff0cC\u662f\u5bc6\u6587<\/p>\n\n\n\n<p>\u9488\u5bf9RSA\u4e5f\u6709\u5f88\u591a\u653b\u51fb\u65b9\u5f0f\uff0c\u6bd4\u5982<em>Timing-Attack against <a href=\"https:\/\/www.chegg.com\/homework-help\/questions-and-answers\/716-let-us-investigate-side-channel-attacks-rsa-simple-imple-mentation-rsa-without-counter-q74047610\">Square-&amp;-Multiply<\/a><\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"371\" height=\"298\" src=\"https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-19.png\" alt=\"\" class=\"wp-image-2494\" srcset=\"https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-19.png 371w, https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-19-300x241.png 300w\" sizes=\"auto, (max-width: 371px) 100vw, 371px\" \/><\/figure>\n\n\n\n<p>\u7531\u4e8eRSA\u7684\u8ba1\u7b97\u65b9\u5f0f\uff0c\u4f7f\u7528\u4e86\u4e00\u79cdSquare&amp;Multiply\u7684\u65b9\u5f0f\uff0c\u5728CPU\u8fd0\u7b97\u65f6\u4f1a\u6709\u4e0a\u56fe\u8fd9\u79cd\u5bf9\u5e94\u5173\u7cfb\u3002<\/p>\n\n\n\n<p>\u7136\u540e\u5bf9Phi(N)\u4e5f\u8fdb\u884c\u4fdd\u5bc6\uff0c\u4e0d\u8981\u590d\u7528N\uff0c\u6bcf\u6b21\u90fd\u91cd\u65b0\u751f\u6210p, q\u7b49\u7b49\u3002<\/p>\n\n\n\n<p>\u5982\u679c\u6d88\u606f\u957f\u5ea6\u8fc7\u77ed\u4e5f\u4f1a\u51fa\u73b0\u95ee\u9898<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>M=3,\u516c\u94a5(e=13, N=3000009)\n\u52a0\u5bc6=M^e mod 3000009 = 3^13 mod 3000009 = 1594323 mod 3000009 = 1594323 = 3^13 = M^e\n\u6240\u4ee5\u6700\u7ec8\u53ea\u9700\u8981\u5f00\u6839\u540e\u5c31\u53ef\u4ee5\u5f97\u5230\u660e\u6587\uff1a3<\/code><\/pre>\n\n\n\n<p>\u6240\u4ee5\u9488\u5bf9RSA\u52a0\u5bc6\u6709\u4e00\u6761\u94c1\u5f8b\uff0c\u4e00\u5b9a\u8981\u4f7f\u7528OAEP(Optimal Asymmetric Encryption Padding)\u8bd5\u5bf9\u539f\u660e\u6587\u8fdb\u884cpadding<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"OAEP_%E2%80%93_Optimal_Asymmetric_Encryption_Padding\"><\/span><strong>OAEP &#8211; Optimal Asymmetric Encryption Padding<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>OAEP\u672c\u8eab\u53ea\u662f\u52a0\u5165\u4e86\u4e00\u79cd\u989d\u5916\u7684Padding, \u52a0\u4e86\u4e00\u4e9b\u8f6c\u6362\u64cd\u4f5c\uff0c\u8fd9\u6837\u5728\u8fdb\u884cRSA\u52a0\u5bc6\u524d\uff0c\u5148\u628a\u660e\u6587M\u53d8\u6210X,Y\u7136\u540e\u518d\u52a0\u5bc6\uff0c\u89e3\u5bc6\u8fc7\u7a0b\u6b63\u597d\u76f8\u53cd,\u8fd9\u6837\u56e0\u4e3a\u6709r(\u968f\u673a\u6570)\u7684\u5b58\u5728\uff0c\u6bcf\u6b21\u52a0\u5bc6\u51fa\u7684\u5185\u5bb9\u90fd\u662f\u4e0d\u4e00\u6837\u7684\u3002<\/p>\n\n\n\n<p>\u5982\u4e0b\u56fe<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"136\" src=\"https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-21-1024x136.png\" alt=\"\" class=\"wp-image-2496\" srcset=\"https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-21-1024x136.png 1024w, https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-21-300x40.png 300w, https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-21-768x102.png 768w, https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-21.png 1186w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"452\" height=\"451\" src=\"https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-20.png\" alt=\"\" class=\"wp-image-2495\" srcset=\"https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-20.png 452w, https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-20-300x300.png 300w, https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-20-150x150.png 150w, https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-20-270x270.png 270w, https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-20-230x230.png 230w\" sizes=\"auto, (max-width: 452px) 100vw, 452px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%88%9D%E6%AC%A1%E5%AE%9E%E7%8E%B0%E4%BA%86%E9%9D%9E%E5%AE%89%E5%85%A8%E4%BF%A1%E9%81%93%E6%B6%88%E6%81%AF%E4%BC%A0%E9%80%92\"><\/span>\u521d\u6b21\u5b9e\u73b0\u4e86\u975e\u5b89\u5168\u4fe1\u9053\u6d88\u606f\u4f20\u9012<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u518d\u56de\u5230\u6211\u4eec\u4e4b\u524d\u60f3\u4f20\u9012\u4e00\u4e2a\u901a\u8fc7AES\u5bc6\u7801\u52a0\u5bc6\u7684\u6587\u4ef6\uff0c\u73b0\u5728\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7RSA\u628a\u5bc6\u94a5\u4f20\u9001\u8fc7\u6765\u4e86\u3002<\/p>\n\n\n\n<p>\u6709\u4e86RSA\u518d\u52a0\u4e0a\u5bf9\u79f0\u52a0\u5bc6AES\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u7b2c\u4e00\u6b21\u5b9e\u73b0\u5728\u975e\u5b89\u5168\u4fe1\u9053\u4e0a\u7684\u6d88\u606f\u4f20\u9012\uff0c\u6211\u4eec\u628aRSA\u516c\u94a5\u5206\u53d1\u7ed9\u5bf9\u65b9\uff0c\u5bf9\u65b9\u7528RSA\u516c\u94a5\u628a\u4ed6\u7684AES\u5bc6\u7801\u8fdb\u884c\u52a0\u5bc6\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u7528\u6211\u4eec\u7684\u79c1\u94a5\u89e3\u5bc6\u5f97\u5230\u8fd9\u4e2a\u6587\u4ef6\u7684AES\u5bc6\u7801\uff0c\u7136\u540e\u5c31\u53ef\u4ee5\u89e3\u5bc6\u5bf9\u5e94\u7684\u6587\u4ef6\u4e86\u3002<\/p>\n\n\n\n<p>\u592a\u4e0d\u5bb9\u6613\u4e86\uff0c\u7ec8\u4e8e\u5b9e\u73b0\u4e86\u7b2c\u4e00\u6b21\u5728\u975e\u5b89\u5168\u4fe1\u606f\u4e0a\u7684\u6587\u4ef6+\u5bc6\u7801\u4f20\u9012\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%95%B0%E5%AD%97%E7%AD%BE%E5%90%8DDigital_Signatures\"><\/span>\u6570\u5b57\u7b7e\u540d(Digital Signatures)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u5176\u5b9e\u6211\u4eec\u770b\u5230RSA\u516c\u94a5\u53ef\u4ee5\u5206\u53d1\u51fa\u53bb\uff0c\u8fd9\u6837\u522b\u4eba\u5c31\u53ef\u4ee5\u7528\u516c\u94a5\u52a0\u5bc6\u53d1\u7ed9\u4f60\u4e86\uff0c\u4f46\u6709\u4e00\u4e2a\u95ee\u9898\uff0c\u6bcf\u4e2a\u4eba\u90fd\u53ef\u4ee5\u901a\u8fc7\u8fd9\u4e2a\u516c\u94a5\u52a0\u5bc6\u4fe1\u606f\u53d1\u7ed9\u4f60\uff0c\u4f46\u4f60\u6ca1\u529e\u6cd5\u533a\u5206\u5230\u5e95\u662f\u8c01\u53d1\u7684\u3002<\/p>\n\n\n\n<p>\u8fd9\u6837\u6211\u4eec\u5c31\u8981\u5f15\u5165\u6570\u5b57\u7b7e\u540d\u6280\u672f\u4e86<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u53d1\u9001\u65b9\u5148\u8ba1\u7b97\u51fa\u6587\u4ef6\u7684hash, \u6bd4\u5982SHA256, \u7136\u540e\u518d\u7528\u79c1\u94a5\u8fdb\u884c\u7b7e\u540dhash^d mod N<\/code><\/pre>\n\n\n\n<p>\u8fd9\u91cc\u7684\u7b7e\u540d\u8981\u6ce8\u610f\u662f\u7528\u7684\u7528\u7684\u5bf9\u65b9\u81ea\u5df1\u7684\u79c1\u94a5\uff0c\u53ea\u6709\u6587\u4ef6\u6301\u6709\u8005\u624d\u62e5\u6709\u7684\u79c1\u7528\uff0c\u522b\u4eba\u53ea\u80fd\u6709\u4ed6\u7684\u516c\u94a5\u3002<\/p>\n\n\n\n<p>\u8fd9\u6837\u5bf9\u522b\u4e0a\u6536\u5230\u6587\u4ef6\u540e\uff0c\u5c31\u53ef\u4ee5\u7528\u5b83\u7684\u516c\u94a5\u8fdb\u884c\u9a8c\u8bc1<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>signature^e mod N = hash<\/code><\/pre>\n\n\n\n<p>\u8fd9\u6837\u6536\u4ef6\u65b9\u901a\u8fc7\u8ba1\u7b97\u6587\u4ef6\u7684hash\u503c\uff0c\u7136\u540e\u518d\u901a\u8fc7\u6bd4\u5bf9\u8fd9\u4e24\u4e2ahash\u662f\u5426\u4e00\u6837\u7528\u6765\u89c9\u5f97\u8fd9\u4e2a\u5185\u5bb9\u662f\u5426\u88ab\u7be1\u6539\u8fc7\uff0c\u8fd8\u6709\u662f\u5426\u662f\u5bf9\u65b9\u672c\u4eba\u53d1\u7684\uff0c\u56e0\u4e3a\u79c1\u94a5\u522b\u4eba\u662f\u6ca1\u6709\u7684\u3002<\/p>\n\n\n\n<p>\u6240\u4ee5\u8bb0\u4f4f\u6570\u5b57\u7b7e\u540d\u662f\uff0c\u79c1\u94a5\u7b7e\u540d\uff0c\u516c\u94a5\u9a8c\u7b7e\uff0c\u9a8c\u8bc1\u7684\u662fhash\u503c\u3002<\/p>\n\n\n\n<p>\u5f88\u5de7\u5999\u5bf9\u5427\uff0c\u8fd9\u4e9b\u4e5f\u4e0d\u77e5\u9053\u6700\u65e9\u662f\u8c01\u60f3\u51fa\u6765\u7684\uff0c\u7b80\u76f4\u5929\u624d\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"DH%E5%92%8CFPSPerfect_Forward_Secrecy\"><\/span>DH\u548cFPS(Perfect Forward Secrecy)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u867d\u7136\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7RSA\u751f\u6210\u5bc6\u94a5\u5bf9\uff0c\u4f46\u6211\u4eec\u4e0d\u80fd\u6bcf\u6b21\u90fd\u751f\u6210\u4e00\u4e2a\uff0c\u56e0\u4e3a\u516c\u94a5\u5206\u53d1\u662f\u6709\u6210\u529f\u548c\u65f6\u95f4\u7684\u3002\u5982\u679c\u6211\u4eec\u4e00\u76f4\u7528\u540c\u4e00\u4e2aRSA\u516c\u79df\u94a5\u5bf9\uff0c\u9ed1\u5ba2\u53ef\u4ee5\u4e00\u76f4\u6293\u53d6\u6211\u4eec\u7684\u5bc6\u6587\uff0c\u76f4\u5230\u6709\u4e00\u5929\uff0c\u4ed6\u5f97\u5230\u4e86\u79c1\u79df\uff0c\u90a3\u4e48\u6211\u4eec\u4e4b\u524d\u6240\u6709\u7684\u5185\u5bb9\u90fd\u4f1a\u88ab\u89e3\u5bc6\uff0c\u8fd9\u662f\u6211\u4eec\u4e0d\u5e0c\u671b\u770b\u5230\u7684\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u95ee\u9898\u5c31\u53ef\u4ee5\u53eb\u505aFPS(\u5b8c\u7f8e\u524d\u5411\u4fdd\u5bc6)\u3002<\/p>\n\n\n\n<p>\u6240\u4ee5\u4e3a\u4e86\u89e3\u51b3\u8fd9\u8fd9\u4e2a\u95ee\u9898\uff0c\u79d1\u5b66\u5bb6\u53c8\u53d1\u660e\u4e86Diffie-Hellman(DH)\u5bc6\u94a5\u4ea4\u6362\u7b97\u6cd5\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u7b97\u6cd5\u662f\u57fa\u4e8e\u79bb\u6563\u5bf9\u6570\u96be\u89e3\u7684\u95ee\u9898<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>g^x mod p = a<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u79bb\u6563\u5bf9\u6570\u95ee\u9898\u662f\u5047\u8bbe\u522b\u4eba\u77e5\u9053\u4e86g, p, a\uff0c\u5b83\u662f\u5f88\u96be\u8ba1\u7b97\u51fax\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"957\" height=\"526\" src=\"https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-22.png\" alt=\"\" class=\"wp-image-2498\" srcset=\"https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-22.png 957w, https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-22-300x165.png 300w, https:\/\/pjq.me\/wp-content\/uploads\/2025\/11\/image-22-768x422.png 768w\" sizes=\"auto, (max-width: 957px) 100vw, 957px\" \/><\/figure>\n\n\n\n<p>\u901a\u8fc7\u5171\u4eabg, p, \u7136\u540e\u518d\u5206\u522b\u9009\u53d6\u79c1\u6709\u7684a, b, \u8ba1\u7b97\u51faA\uff0c B\u5206\u522b\u5171\u4eab\u7ed9\u5bf9\u65b9\uff0c\u5f97\u5230A, B\u4e4b\u540e\u4e24\u4e2a\u4eba\u518d\u5206\u522b\u8ba1\u7b97\u51fa\u5171\u4eab\u5bc6\u94a5S\uff0c \u4e0b\u9762\u8fd9\u4e2a\u516c\u5f0f\u63a8\u5bfc\u5c31\u8bc1\u660e\u4e86\u4e24\u4e2a\u4eba\u7684\u5bc6\u94a5\u4e00\u81f4\u3002<\/p>\n\n\n\n<p>DH\u540c\u6837\u6ca1\u6709\u89e3\u51b3\u4e2d\u95f4\u4eba\u653b\u51fb\u95ee\u9898\uff0c\u6240\u4ee5\u8fd8\u662f\u8981\u52a0\u4e0a\u7b7e\u540d\u624d\u80fd\u4fdd\u8bc1\u6570\u636e\u5b8c\u6574\u6027\uff0c\u8ba4\u8bc1\u6027\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ECCElliptic_Curves_%E6%A4%AD%E5%9C%86%E6%9B%B2%E7%BA%BF\"><\/span>ECC(Elliptic Curves, \u692d\u5706\u66f2\u7ebf)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u867d\u7136\u6211\u4eec\u5df2\u7ecf\u6709\u4e86RSA\uff0c\u4f46\u5b83\u7684\u8fd0\u7b97\u6548\u7387\u6ca1\u6709\u90a3\u4e48\u9ad8\uff0c\u6240\u4ee5\u53c8\u6709\u79d1\u5b66\u5bb6\u57fa\u4e8e\u692d\u5706\u66f2\u7ebf\u96be\u89e3\u7684\u95ee\u9898\uff0c\u53d1\u660e\u4e86\u53e6\u5916\u4e00\u4e2a\u516c\u94a5\u52a0\u5bc6\u7b97\u6cd5\uff0c\u6700\u5173\u952e\u7684\u662f\u5b83\u7684\u52a0\u5bc6\u6548\u7387\u5f88\u9ad8\uff0c\u8fd0\u7b97\u901f\u5ea6\u9ad8\uff0c\u53ea\u9700\u8981\u5f88\u77ed\u7684\u5bc6\u94a5\u5c31\u80fd\u8fbe\u5230RSA 1024\uff0c 2048\u7684\u4fdd\u5bc6\u6548\u679c\u3002<\/p>\n\n\n\n<p>\u6240\u4ee5ECC\u7edd\u5bf9\u662fRSA\u66ff\u6362\u9996\u9009\uff0c\u5728\u4e00\u4e9b\u5d4c\u5165\u5f0f\u8bbe\u5907\u6216\u8005\u786c\u4ef6\u6027\u80fd\u6ca1\u6709\u90a3\u4e48\u597d\u7684\u8bbe\u5907\u4e0a\u5c31\u53ef\u4ee5\u4f7f\u7528ECC\u4e86\uff0c\u5f53\u7136\u5176\u5b83\u5730\u65b9\u6211\u89c9\u5f97\u4e00\u6837\u662f\u63a8\u8350\u7528ECC\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%B7%B7%E5%90%88%E5%8A%A0%E5%AF%86%E6%A8%A1%E5%BC%8F\"><\/span>\u6df7\u5408\u52a0\u5bc6\u6a21\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u73b0\u5728\u6211\u4eec\u6709\u975e\u5bf9\u79f0\u52a0\u5bc6\u7b97\u6cd5\uff0c\u53ef\u4ee5\u5728\u4e0d\u5b89\u5168\u7684\u4fe1\u9053\u4e0a\u4ea4\u6362\u5bc6\u94a5\uff0c\u4e5f\u53ef\u4ee5\u901a\u8fc7DH\u65b9\u5f0f\u52a8\u6001\u5bc6\u94a5\u4e92\u6362(Key Exchange), \u6bcf\u6b21\u534f\u5546\u53c8\u89e3\u51b3\u4e86\u524d\u5411\u5b89\u5168\u95ee\u9898\u3002<\/p>\n\n\n\n<p>\u6709\u4e86\u5bc6\u94a5\u4e92\u6362\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u751f\u6210\u5171\u4eab\u5bc6\u94a5\uff0c\u518d\u7528AES\u5bf9\u79f0\u52a0\u5bc6\u5bf9\u6570\u636e\u8fdb\u884c\u52a0\u5bc6\u548c\u89e3\u5bc6\uff0c\u5b8c\u6210\u6574\u4e2a\u6570\u636e\u5728\u975e\u5b89\u5168\u4fe1\u9053\u4e0a\u7684\u4ea4\u4e92\u3002<\/p>\n\n\n\n<p>\u6240\u4ee5\u6574\u4e2a\u6570\u5b57\u4e16\u754c\uff0c\u4e92\u8054\u7f51\u5c31\u662f\u7531\u8fd9\u4e48\u591a\u4e0d\u4e00\u6837\u7684\u52a0\u5bc6\u7b97\u6cd5\u53e0\u52a0\u5728\u4e00\u8d77\uff0c\u4fdd\u8bc1\u6211\u4eec\u7684\u901a\u4fe1\u5b89\u5168\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1. AES\uff0c\u5bf9\u79f0\u52a0\u5bc6\u7b97\u6cd5\uff0c\u53ef\u4ee5\u5b9e\u73b0\u7528\u540c\u4e00\u4e2aKey\u7684\u5feb\u901f\u52a0\u89e3\u5bc6\uff0c\u4ece\u5b89\u5168\u89d2\u5ea6\u53c8\u884d\u751f\u51fa\u4e86\u4e0d\u540c\u7684\u6a21\u5f0f: ECB, CBC, CTR, GCM, CCM<\/li>\n\n\n\n<li>2. MAC\/HMAC\uff0c\u6d88\u606f\u8ba4\u8bc1\u7801\uff0c\u7528\u6765\u5b9e\u73b0\u6d88\u606f\u5b8c\u6574\u6027\u548c\u8ba4\u8bc1\u6027\u95ee\u9898<\/li>\n\n\n\n<li>3. RSA\uff0c\u57fa\u4e8e\u5927\u6574\u6570\u7684\u56e0\u5f0f\u5206\u89e3\u96be\u9898\uff0c\u521b\u5efa\u516c\u79c1\u94a5\u5bf9\uff0c\u5b9e\u73b0\u516c\u94a5\u52a0\u5bc6\uff0c\u79c1\u94a5\u89e3\u5bc6\uff0c\u4e3a\u4e86\u89e3\u51b3\u968f\u673a\u548c\u6d88\u606f\u957f\u5ea6\u95ee\u9898\uff0c\u4e00\u5b9a\u8981\u4f7f\u7528OAEP\u8fdb\u884cpadding\u8f6c\u6362\uff0c\u52a0\u5bc6\u5b89\u5168\u7b49\u7ea7\u518d\u4e0a\u4e00\u4e2a\u53f0\u9636\u3002<\/li>\n\n\n\n<li>4. DH\uff0c\u57fa\u4e8e\u79bb\u6563\u5bf9\u6570\u96be\u89e3\u95ee\u9898(DLP)\uff0c\u5b9e\u73b0\u5bc6\u94a5\u4ea4\u4e92\uff0c\u6bcf\u6b21\u90fd\u901a\u8fc7DH\u751f\u6210\u52a8\u6001\u5171\u4eab\u5bc6\u94a5\uff0c\u5b9e\u73b0\u524d\u7f6e\u5b89\u5168\uff0c\u5c31\u7b97\u5bc6\u94a5\u6cc4\u6f0f\uff0c\u5f71\u54cd\u8303\u56f4\u4e5f\u4ec5\u9650\u4e8e\u5f53\u524d\u5bf9\u8bdd\u3002<\/li>\n\n\n\n<li>5. ECC\uff0c\u57fa\u4e8e\u692d\u5706\u66f2\u7ebf\u96be\u89e3\u95ee\u9898\uff0c\u80fd\u591f\u5728\u5f88\u77ed\u7684\u5bc6\u94a5\u957f\u5ea6\u4e0a\u5b9e\u73b0\u9ad8\u7b49\u7ea7\u7684\u52a0\u5bc6\u6548\u679c\uff0c\u5f3a\u529b\u63a8\u8350\uff0c\u800c\u4e14\u8fd0\u7b97\u901f\u5ea6\u5feb\u3002<\/li>\n\n\n\n<li>6. \u6570\u5b57\u7b7e\u540d\uff0c\u7528\u79c1\u94a5\u7b7e\u540d\uff0c\u516c\u94a5\u9a8c\u7b7e\uff0c\u89e3\u51b3\u6d88\u606f\u5b8c\u6574\u6027\uff0c\u8ba4\u8bc1\u6027\u95ee\u9898\uff0cPKI\u8bc1\u4e66\u7cfb\u7edf\u7ecf\u5e38\u7528\u5230\uff0c\u6bd4\u5982CA\u7528\u79c1\u94a5\u5bf9\u7684\u516c\u94a5\u8bc1\u4e66\u8fdb\u884c\u7b7e\u540d\uff0c\u4f60\u7684\u516c\u94a5\u4f1a\u4e0b\u53d1\u5230\u6d4f\u89c8\u5668\uff0c\u6d4f\u89c8\u5668\u901a\u8fc7\u9884\u88c5\u7684CA\u516c\u94a5\u8bc1\u4e66\uff0c\u5bf9\u4f60\u8fd9\u4e2a\u516c\u94a5\u7b7e\u540d\u8fdb\u884c\u9a8c\u8bc1\u3002\u5f53\u7136\u4e5f\u4f1a\u7528\u5230\u901a\u4fe1\u8fc7\u7a0b\u4e2d\u9632\u6b62\u4e2d\u95f4\u4eba\u653b\u51fb\uff0c\u5bf9\u6570\u636e\u8fdb\u884c\u7b7e\u540d\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u5176\u4e2d\u6709\u4e24\u53e5\u8bdd\uff0c\u6211\u662f\u82b1\u4e86\u5f88\u957f\u65f6\u95f4\u624d\u7406\u89e3\u7684<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u516c\u94a5\u52a0\u5bc6\uff0c\u79c1\u94a5\u89e3\u5bc6<\/li>\n\n\n\n<li>\u79c1\u94a5\u7b7e\u540d\uff0c\u516c\u94a5\u9a8c\u7b7e<\/li>\n<\/ol>\n\n\n\n<p>\u5f53\u4f60\u7406\u89e3\u4e86\u8fd9\u4e9b\uff0c\u53ef\u80fd\u5c31\u4f1a\u5bf9\u5e26\u4e2a\u901a\u4fe1\u52a0\u5bc6\u94fe\u8def\u6709\u4e2a\u6bd4\u8f83\u6e05\u695a\u7684\u8ba4\u77e5\u3002<\/p>\n\n\n\n<p>\u6240\u4ee5\u6574\u4e2a\u6570\u5b57\u4e16\u754c\u5176\u5b9e\u662f\u4e00\u5957\u5f88\u7cbe\u5bc6\u7684\u52a0\u5bc6\u7cfb\u7edf\u5728\u540e\u9762\u9ed8\u9ed8\u8fd0\u884c\uff0c\u4f60\u6bcf\u4e00\u6b21\u4e0a\u7f51\uff0c\u6bcf\u4e00\u6b21\u53d1\u6d88\u606f\uff0c\u90fd\u7528\u5230\u4e86\u4e0a\u9762\u8fd9\u4e9b\u5bf9\u79f0\u52a0\u5bc6\u548c\u975e\u5bf9\u79f0\u52a0\u5bc6\u7b97\u6cd5\u3002<\/p>\n\n\n\n<p>\u611f\u8c22\u4e16\u754c\u4e0a\u8fd9\u4e48\u591a\u4f1f\u5927\u7684\u79d1\u5b66\u5bb6\uff0c\u6570\u5b66\u5bb6\uff0c\u5bc6\u7801\u5b66\u5bb6\u6784\u5efa\u4e86\u8fd9\u4e48\u5b8c\u6574\u7684\u52a0\u5bc6\u4f53\u7cfb\u3002<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e4b\u524d\u8bb2\u8fc7\u5bf9\u79f0\u52a0\u5bc6\uff0c\u6bd4\u5982DES, AES, \u8fd8\u6709AES\u5bf9\u5e94\u5230\u7684\u5404\u79cd\u6a21\u5f0f\uff0c\u6bd4\u5982ECB, CBC, CTR, GCM. \u5bf9\u79f0\u52a0\u5bc6\u552f\u4e00\u4fdd\u5bc6\u7684\u5c31\u662f\u5bc6\u94a5(Key), \u6709\u4e86\u8fd9\u4e2a\u5bc6\u7801\u4f60\u5c31\u80fd\u89e3\u5bc6\u5176\u4e2d\u7684\u5185\u5bb9\u3002 \u516c\u5f00\u901a\u4fe1\u4fe1\u9053(Channel) \u6570\u5b57\u4e16\u754c\u4e2d\u7684\u901a\u4fe1\u4fe1\u9053\u5176\u5b9e\u53ef\u4ee5\u7c7b\u6bd4\u771f\u5b9e\u7269\u7406\u4e16\u754c\uff0c \u6211\u4eec\u8981\u4ece\u4e0a\u6d77\u5230\u5317\u4eac\u5c31\u8981\u7ecf\u5e38\u5404\u79cd\u5404\u6837\u7684\u9053\u8def\uff0c\u6bd4\u5982\u8d70\u9ad8\u901f\u516c\u8def\uff0c\u5c31\u53ef\u80fd\u8981\u7ecf\u5e38\u5404\u79cd\u68c0\u67e5\u7ad9\uff0c\u6536\u8d39\u7ad9\uff0c\u7406\u8bba\u4e0a\u8fd9\u4e9b\u7ad9\u70b9\u90fd\u53ef\u4ee5\u5bf9\u4f60\u7684\u8f66\u8fdb\u884c\u5168\u65b9\u4f4d\u7684\u641c\u7d22\u68c0\u67e5\uff0c\u770b\u6709\u6ca1\u6709\u643a\u5e26\u8fdd\u7981\u54c1\u3002\u4e92\u8054\u7f51\u4e16\u754c\u4e00\u6837\uff0c\u4f60\u7684\u6570\u636e\u8981\u7ecf\u5e38\u4e2d\u95f4\u7684\u5404\u79cdWifi, \u8def\u7531\uff0c\u7f51\u5173\uff0c\u5149\u7ea4\uff0c\u6bcf\u4e2a\u8def\u7531\u7f51\u5173\u7406\u8bba\u4e0a\u90fd\u53ef\u4ee5\u628a\u4f60\u7684\u4f20\u8f93\u6570\u636e\u62e6\u622a\u4e0b\u6765\uff0c\u751a\u81f3\u7be1\u6539\uff0c\u6240\u4ee5\u6211\u4eec\u8981\u77e5\u9053\u516c\u5f00\u7684\u8fd9\u4e9b\u901a\u4fe1\u4fe1\u9053\u662f\u4e0d\u5b89\u5168\u4e0d\u53ef\u4fe1\u4efb\u7684\u3002 \u6240\u4ee5\u60f3\u60f3\u6211\u4eec\u7684\u6570\u636e\u5728\u8fd9\u4e9b\u4e0d\u53ef\u4fe1\u4efb\u7684\u8def\u9014\u4e2d\u7a7f\u68ad\u8fd8\u662f\u633a\u53ef\u6015\u7684\u3002 \u52a8\u673a(Motivation) \u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u53ef\u4ee5\u901a\u8fc7AES\u52a0\u5bc6\u6570\u636e\u4e86\uff0c\u628a\u52a0\u5bc6\u7684\u5185\u5bb9\u4f20\u8f93\u51fa\u53bb\u3002\u4f46\u662f\u5bc6\u7801\u8981\u600e\u4e48\u4f20\u8f93\u51fa\u53bb\u4e86\uff0c\u56e0\u4e3a\u5bc6\u7801\u662f\u660e\u6587\u7684\uff0c\u5b83\u5728\u8fd9\u4e9b\u516c\u5f00\u901a\u4fe1\u4fe1\u606f\u91cc\u9762\u4f20\u8f93\u5c31\u4e00\u5b9a\u4f1a\u53ef\u80fd\u88ab\u9ed1\u5ba2\u62e6\u622a\u5230\uff0c\u8fd8\u6709\u4e00\u4e2a\u95ee\u9898\uff0c\u5982\u679c\u4f60\u4e00\u76f4\u7528\u540c\u4e00\u4e2a\u5bc6\u7801\uff0c\u90a3\u4e48\u9ed1\u5ba2\u5c31\u53ef\u4ee5\u4e00\u76f4\u62e6\u622a\u4f60\u7684\u4fe1\u606f\uff0c\u751a\u81f3\u5728\u5f97\u5230\u5bc6\u7801\u4e4b\u524d\u5c31\u4e00\u76f4\u5728\u62e6\u622a\uff0c\u76f4\u5230\u67d0\u4e00\u5929\u5f97\u5230\u5bc6\u7801\u4e86\uff0c\u90a3\u4e48\u9ed1\u5ba2\u5c31\u53ef\u4ee5\u540c\u65f6\u89e3\u5bc6\u4e4b\u524d\u5df2\u7ecf\u5b58\u5728\u5f88\u7684\u52a0\u5bc6\u4fe1\u606f\u4e86\uff0c\u5982\u679c\u5bc6\u7801\u4e0d\u6539\uff0c\u90a3\u5c06\u6765\u7684\u52a0\u5bc6\u4fe1\u606f\u4e5f\u4e00\u6837\u4f1a\u88ab\u9ed1\u5ba2\u89e3\u5bc6\u3002 \u6240\u4ee5\u5bc6\u7801\u5b66\u79d1\u5b66\u5bb6\u4eec\u7ede\u5c3d\u8111\u6c41\u60f3\u8bbe\u8ba1\u51fa\u6765\u4e00\u79cd\u65b9\u6cd5\uff0c\u53ef\u4ee5\u89e3\u51b3\u5728\u4e0d\u5b89\u5168\u4fe1\u9053\u4e2d\u4ea4\u4e92\u5bc6\u94a5\u7684\u95ee\u9898 \u4e8e\u662f\u5c31\u8bbe\u8ba1\u51fa\u4e86\u4e00\u79cd\u901a\u8fc7\u5bc6\u94a5\u5bf9\u7684\u52a0\u89e3\u5bc6\u65b9\u5f0f\uff0c\u540c\u65f6\u751f\u6210\u4e00\u5bf9\u5bc6\u94a5 \u516c\u94a5\u52a0\u5bc6\uff0c\u79c1\u94a5\u89e3\u5bc6\u3002\u8fd9\u6837\u522b\u4eba\u5c31\u53ef\u4ee5\u62ff\u5230\u4f60\u7684\u516c\u94a5\u628a\u9700\u8981\u4fdd\u5bc6\u7684\u4fe1\u606f\u8fdb\u884c\u52a0\u5bc6\u53d1\u7ed9\u4f60\uff0c\u4f60\u6536\u5230\u540e\u901a\u8fc7\u79c1\u94a5\u8fdb\u884c\u89e3\u5bc6\u3002 \u8fd9\u4e2a\u60f3\u6cd5\u5f88\u5947\u5999\uff0c\u7136\u540e\u771f\u7684\u5c31\u505a\u51fa\u6765\u4e86\u3002 RSA(Rivest, Shamir, Adleman) RSA\u5c31\u662f\u5176\u4e2d\u4e00\u79cd\u975e\u5bf9\u79f0\u52a0\u5bc6\u7b97\u6cd5\uff0c\u5b83\u5c31\u662f\u53ef\u4ee5\u751f\u6210\u4e00\u5bf9\u516c\u94a5\uff0c\u79c1\u94a5\u3002\u53ef\u80fd\u5927\u5bb6\u4ee5\u4e3a\u8fd9\u4e2a\u662f\u6700\u8fd1\u624d\u53d1\u660e\u7684\uff0c\u4f46\u5176\u5b9e\u8fd9\u4e2a\u662f\u5f88\u65e9\uff0c\u57281977\u5e74\uff0cRSA\u5c31\u53d1\u660e\u4e86\uff0c\u4e00\u76f4\u7528\u5230\u73b0\u5728\u3002 \u5b83\u57fa\u4e8e\u7684\u6570\u5b66\u539f\u7406\u5176\u5b9e\u5f88\u7b80\u5355\uff0c\u7b80\u5355\u5230\u4e00\u4e2a\u5c0f\u5b66\u751f\u90fd\u5bb9\u6613\u7406\u89e3 \u5047\u8bbe\u6211\u4eec\u6709\u4e24\u4e2a\u8d28\u6570p, q, N=p*q, \u90a3\u5f53\u6211\u4eec\u53ea\u77e5\u9053N\u7684\u65f6\u5019\u662f\u6ca1\u529e\u6cd5\u7b97\u51fap\u548cq\u7684\uff0c\u8fd9\u4e2a\u57fa\u672c\u539f\u7406\u5c31\u662fRSA\u7684\u672c\u8d28\u3002 \u5176\u5b9e\u60f3\u60f3\u5f88\u7b80\u5355\uff0c\u4f46\u603b\u4f1a\u89c9\u5f97\u6709\u70b9\u4e0d\u53ef\u601d\u8bae\u5bf9\u5427\uff0c\u4f46\u73b0\u5b9e\u5c31\u662f\u8fd9\u6837\uff0c\u5982\u679c\u6709\u8c01\u80fd\u8fc7\u591f\u5728\u53ea\u77e5\u9053N\u7684\u60c5\u51b5\u4e0b\u7b97\u51fap\u548cq,\u90a3\u4e48RSA\u5c31\u5b8c\u86cb\u4e86\u3002 RSA\u7684\u8ba1\u7b97\u8fc7\u7a0b\u5f88\u7b80\u5355 \u5f53\u7136\u5b9e\u9645\u7684\u8fc7\u7a0b\u4e2d\u8fd9\u4e9b\u6570\u6570\u4f1a\u957f\uff0c\u6bd4\u5982&gt;1024\uff0c\u5982\u4e0b\u9762\u8fd9\u4e2a\u662f\u6211\u4ece\u4e00\u4e2a\u8bc1\u4e66\u91cc\u9762\u6293\u53d6\u5230\u7684\u3002 RSA \u52a0\u5bc6\u662f \u89e3\u5bc6\u662f \u5176\u4e2dM\u662f\u660e\u6587\uff0cC\u662f\u5bc6\u6587 \u9488\u5bf9RSA\u4e5f\u6709\u5f88\u591a\u653b\u51fb\u65b9\u5f0f\uff0c\u6bd4\u5982Timing-Attack against Square-&amp;-Multiply \u7531\u4e8eRSA\u7684\u8ba1\u7b97\u65b9\u5f0f\uff0c\u4f7f\u7528\u4e86\u4e00\u79cdSquare&amp;Multiply\u7684\u65b9\u5f0f\uff0c\u5728CPU\u8fd0\u7b97\u65f6\u4f1a\u6709\u4e0a\u56fe\u8fd9\u79cd\u5bf9\u5e94\u5173\u7cfb\u3002 \u7136\u540e\u5bf9Phi(N)\u4e5f\u8fdb\u884c\u4fdd\u5bc6\uff0c\u4e0d\u8981\u590d\u7528N\uff0c\u6bcf\u6b21\u90fd\u91cd\u65b0\u751f\u6210p,<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[270,169],"tags":[263,228,266,240,265,264,267],"class_list":["post-2490","post","type-post","status-publish","format-standard","hentry","category-cryptography","category-tech","tag-asymmetric","tag-cryptography","tag-dh","tag-ecc","tag-oaep","tag-rsa","tag-signature"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u5bc6\u7801\u5b66(Cryptography)\u7b80\u53f2-\u975e\u5bf9\u79f0\u52a0\u79d8(Asymmetric Encryption) - Jianqing&#039;s Blog<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/pjq.me\/?p=2490\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u5bc6\u7801\u5b66(Cryptography)\u7b80\u53f2-\u975e\u5bf9\u79f0\u52a0\u79d8(Asymmetric Encryption) - Jianqing&#039;s Blog\" \/>\n<meta property=\"og:description\" content=\"\u4e4b\u524d\u8bb2\u8fc7\u5bf9\u79f0\u52a0\u5bc6\uff0c\u6bd4\u5982DES, AES, \u8fd8\u6709AES\u5bf9\u5e94\u5230\u7684\u5404\u79cd\u6a21\u5f0f\uff0c\u6bd4\u5982ECB, CBC, CTR, GCM. \u5bf9\u79f0\u52a0\u5bc6\u552f\u4e00\u4fdd\u5bc6\u7684\u5c31\u662f\u5bc6\u94a5(Key), \u6709\u4e86\u8fd9\u4e2a\u5bc6\u7801\u4f60\u5c31\u80fd\u89e3\u5bc6\u5176\u4e2d\u7684\u5185\u5bb9\u3002 \u516c\u5f00\u901a\u4fe1\u4fe1\u9053(Channel) \u6570\u5b57\u4e16\u754c\u4e2d\u7684\u901a\u4fe1\u4fe1\u9053\u5176\u5b9e\u53ef\u4ee5\u7c7b\u6bd4\u771f\u5b9e\u7269\u7406\u4e16\u754c\uff0c \u6211\u4eec\u8981\u4ece\u4e0a\u6d77\u5230\u5317\u4eac\u5c31\u8981\u7ecf\u5e38\u5404\u79cd\u5404\u6837\u7684\u9053\u8def\uff0c\u6bd4\u5982\u8d70\u9ad8\u901f\u516c\u8def\uff0c\u5c31\u53ef\u80fd\u8981\u7ecf\u5e38\u5404\u79cd\u68c0\u67e5\u7ad9\uff0c\u6536\u8d39\u7ad9\uff0c\u7406\u8bba\u4e0a\u8fd9\u4e9b\u7ad9\u70b9\u90fd\u53ef\u4ee5\u5bf9\u4f60\u7684\u8f66\u8fdb\u884c\u5168\u65b9\u4f4d\u7684\u641c\u7d22\u68c0\u67e5\uff0c\u770b\u6709\u6ca1\u6709\u643a\u5e26\u8fdd\u7981\u54c1\u3002\u4e92\u8054\u7f51\u4e16\u754c\u4e00\u6837\uff0c\u4f60\u7684\u6570\u636e\u8981\u7ecf\u5e38\u4e2d\u95f4\u7684\u5404\u79cdWifi, \u8def\u7531\uff0c\u7f51\u5173\uff0c\u5149\u7ea4\uff0c\u6bcf\u4e2a\u8def\u7531\u7f51\u5173\u7406\u8bba\u4e0a\u90fd\u53ef\u4ee5\u628a\u4f60\u7684\u4f20\u8f93\u6570\u636e\u62e6\u622a\u4e0b\u6765\uff0c\u751a\u81f3\u7be1\u6539\uff0c\u6240\u4ee5\u6211\u4eec\u8981\u77e5\u9053\u516c\u5f00\u7684\u8fd9\u4e9b\u901a\u4fe1\u4fe1\u9053\u662f\u4e0d\u5b89\u5168\u4e0d\u53ef\u4fe1\u4efb\u7684\u3002 \u6240\u4ee5\u60f3\u60f3\u6211\u4eec\u7684\u6570\u636e\u5728\u8fd9\u4e9b\u4e0d\u53ef\u4fe1\u4efb\u7684\u8def\u9014\u4e2d\u7a7f\u68ad\u8fd8\u662f\u633a\u53ef\u6015\u7684\u3002 \u52a8\u673a(Motivation) \u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u53ef\u4ee5\u901a\u8fc7AES\u52a0\u5bc6\u6570\u636e\u4e86\uff0c\u628a\u52a0\u5bc6\u7684\u5185\u5bb9\u4f20\u8f93\u51fa\u53bb\u3002\u4f46\u662f\u5bc6\u7801\u8981\u600e\u4e48\u4f20\u8f93\u51fa\u53bb\u4e86\uff0c\u56e0\u4e3a\u5bc6\u7801\u662f\u660e\u6587\u7684\uff0c\u5b83\u5728\u8fd9\u4e9b\u516c\u5f00\u901a\u4fe1\u4fe1\u606f\u91cc\u9762\u4f20\u8f93\u5c31\u4e00\u5b9a\u4f1a\u53ef\u80fd\u88ab\u9ed1\u5ba2\u62e6\u622a\u5230\uff0c\u8fd8\u6709\u4e00\u4e2a\u95ee\u9898\uff0c\u5982\u679c\u4f60\u4e00\u76f4\u7528\u540c\u4e00\u4e2a\u5bc6\u7801\uff0c\u90a3\u4e48\u9ed1\u5ba2\u5c31\u53ef\u4ee5\u4e00\u76f4\u62e6\u622a\u4f60\u7684\u4fe1\u606f\uff0c\u751a\u81f3\u5728\u5f97\u5230\u5bc6\u7801\u4e4b\u524d\u5c31\u4e00\u76f4\u5728\u62e6\u622a\uff0c\u76f4\u5230\u67d0\u4e00\u5929\u5f97\u5230\u5bc6\u7801\u4e86\uff0c\u90a3\u4e48\u9ed1\u5ba2\u5c31\u53ef\u4ee5\u540c\u65f6\u89e3\u5bc6\u4e4b\u524d\u5df2\u7ecf\u5b58\u5728\u5f88\u7684\u52a0\u5bc6\u4fe1\u606f\u4e86\uff0c\u5982\u679c\u5bc6\u7801\u4e0d\u6539\uff0c\u90a3\u5c06\u6765\u7684\u52a0\u5bc6\u4fe1\u606f\u4e5f\u4e00\u6837\u4f1a\u88ab\u9ed1\u5ba2\u89e3\u5bc6\u3002 \u6240\u4ee5\u5bc6\u7801\u5b66\u79d1\u5b66\u5bb6\u4eec\u7ede\u5c3d\u8111\u6c41\u60f3\u8bbe\u8ba1\u51fa\u6765\u4e00\u79cd\u65b9\u6cd5\uff0c\u53ef\u4ee5\u89e3\u51b3\u5728\u4e0d\u5b89\u5168\u4fe1\u9053\u4e2d\u4ea4\u4e92\u5bc6\u94a5\u7684\u95ee\u9898 \u4e8e\u662f\u5c31\u8bbe\u8ba1\u51fa\u4e86\u4e00\u79cd\u901a\u8fc7\u5bc6\u94a5\u5bf9\u7684\u52a0\u89e3\u5bc6\u65b9\u5f0f\uff0c\u540c\u65f6\u751f\u6210\u4e00\u5bf9\u5bc6\u94a5 \u516c\u94a5\u52a0\u5bc6\uff0c\u79c1\u94a5\u89e3\u5bc6\u3002\u8fd9\u6837\u522b\u4eba\u5c31\u53ef\u4ee5\u62ff\u5230\u4f60\u7684\u516c\u94a5\u628a\u9700\u8981\u4fdd\u5bc6\u7684\u4fe1\u606f\u8fdb\u884c\u52a0\u5bc6\u53d1\u7ed9\u4f60\uff0c\u4f60\u6536\u5230\u540e\u901a\u8fc7\u79c1\u94a5\u8fdb\u884c\u89e3\u5bc6\u3002 \u8fd9\u4e2a\u60f3\u6cd5\u5f88\u5947\u5999\uff0c\u7136\u540e\u771f\u7684\u5c31\u505a\u51fa\u6765\u4e86\u3002 RSA(Rivest, Shamir, Adleman) RSA\u5c31\u662f\u5176\u4e2d\u4e00\u79cd\u975e\u5bf9\u79f0\u52a0\u5bc6\u7b97\u6cd5\uff0c\u5b83\u5c31\u662f\u53ef\u4ee5\u751f\u6210\u4e00\u5bf9\u516c\u94a5\uff0c\u79c1\u94a5\u3002\u53ef\u80fd\u5927\u5bb6\u4ee5\u4e3a\u8fd9\u4e2a\u662f\u6700\u8fd1\u624d\u53d1\u660e\u7684\uff0c\u4f46\u5176\u5b9e\u8fd9\u4e2a\u662f\u5f88\u65e9\uff0c\u57281977\u5e74\uff0cRSA\u5c31\u53d1\u660e\u4e86\uff0c\u4e00\u76f4\u7528\u5230\u73b0\u5728\u3002 \u5b83\u57fa\u4e8e\u7684\u6570\u5b66\u539f\u7406\u5176\u5b9e\u5f88\u7b80\u5355\uff0c\u7b80\u5355\u5230\u4e00\u4e2a\u5c0f\u5b66\u751f\u90fd\u5bb9\u6613\u7406\u89e3 \u5047\u8bbe\u6211\u4eec\u6709\u4e24\u4e2a\u8d28\u6570p, q, N=p*q, \u90a3\u5f53\u6211\u4eec\u53ea\u77e5\u9053N\u7684\u65f6\u5019\u662f\u6ca1\u529e\u6cd5\u7b97\u51fap\u548cq\u7684\uff0c\u8fd9\u4e2a\u57fa\u672c\u539f\u7406\u5c31\u662fRSA\u7684\u672c\u8d28\u3002 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