{"id":477059,"date":"2023-08-09T09:06:59","date_gmt":"2023-08-09T09:06:59","guid":{"rendered":""},"modified":"2023-09-05T11:13:56","modified_gmt":"2023-09-05T11:13:56","slug":"elliptic-curve-cryptography","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/cn\/wiki\/elliptic-curve-cryptography\/","title":{"rendered":"\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66"},"content":{"rendered":"<p>\u692d\u5706\u66f2\u7ebf\u52a0\u5bc6 (ECC) \u662f\u4e00\u79cd\u73b0\u4ee3\u4e14\u9ad8\u6548\u7684\u516c\u94a5\u52a0\u5bc6\u65b9\u6cd5\uff0c\u7528\u4e8e\u4fdd\u62a4\u6570\u636e\u4f20\u8f93\u3001\u8eab\u4efd\u9a8c\u8bc1\u548c\u6570\u5b57\u7b7e\u540d\u3002\u5b83\u4f9d\u9760\u692d\u5706\u66f2\u7ebf\u7684\u6570\u5b66\u7279\u6027\u6765\u6267\u884c\u52a0\u5bc6\u64cd\u4f5c\uff0c\u4e3a RSA \u548c DSA \u7b49\u4f20\u7edf\u52a0\u5bc6\u7b97\u6cd5\u63d0\u4f9b\u4e86\u5f3a\u5927\u4e14\u9ad8\u6548\u7684\u66ff\u4ee3\u65b9\u6848\u3002 ECC \u56e0\u5176\u5f3a\u5927\u7684\u5b89\u5168\u529f\u80fd\u4ee5\u53ca\u80fd\u591f\u4ee5\u66f4\u77ed\u7684\u5bc6\u94a5\u957f\u5ea6\u63d0\u4f9b\u76f8\u540c\u7ea7\u522b\u7684\u5b89\u5168\u6027\u800c\u83b7\u5f97\u5e7f\u6cdb\u91c7\u7528\uff0c\u4f7f\u5176\u7279\u522b\u9002\u5408\u8d44\u6e90\u53d7\u9650\u7684\u73af\u5883\uff0c\u4f8b\u5982\u79fb\u52a8\u8bbe\u5907\u548c\u7269\u8054\u7f51 (IoT) \u3002<\/p>\n<h2>\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66\u7684\u8d77\u6e90\u5386\u53f2\u53ca\u5176\u9996\u6b21\u63d0\u53ca<\/h2>\n<p>\u692d\u5706\u66f2\u7ebf\u7684\u5386\u53f2\u53ef\u4ee5\u8ffd\u6eaf\u5230 19 \u4e16\u7eaa\u521d\uff0c\u5f53\u65f6\u6570\u5b66\u5bb6\u4eec\u63a2\u7d22\u4e86\u8fd9\u4e9b\u8ff7\u4eba\u66f2\u7ebf\u7684\u6709\u8da3\u7279\u6027\u3002\u7136\u800c\uff0c\u76f4\u5230 20 \u4e16\u7eaa 80 \u5e74\u4ee3\uff0cNeal Koblitz \u548c Victor Miller \u624d\u72ec\u7acb\u63d0\u51fa\u4e86\u4f7f\u7528\u692d\u5706\u66f2\u7ebf\u8fdb\u884c\u5bc6\u7801\u5b66\u7684\u6982\u5ff5\u3002\u4ed6\u4eec\u8ba4\u8bc6\u5230\u692d\u5706\u66f2\u7ebf\u4e0a\u7684\u79bb\u6563\u5bf9\u6570\u95ee\u9898\u53ef\u80fd\u662f\u5f3a\u5927\u7684\u516c\u94a5\u5bc6\u7801\u7cfb\u7edf\u7684\u57fa\u7840\u3002<\/p>\n<p>\u4e0d\u4e45\u4e4b\u540e\uff0c1985 \u5e74\uff0cNeal Koblitz \u548c Alfred Menezes \u4ee5\u53ca Scott Vanstone \u63a8\u51fa\u4e86\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66\u4f5c\u4e3a\u4e00\u79cd\u53ef\u884c\u7684\u5bc6\u7801\u65b9\u6848\u3002\u4ed6\u4eec\u7684\u5f00\u521b\u6027\u7814\u7a76\u4e3a ECC \u7684\u53d1\u5c55\u548c\u6700\u7ec8\u5e7f\u6cdb\u91c7\u7528\u5960\u5b9a\u4e86\u57fa\u7840\u3002<\/p>\n<h2>\u6709\u5173\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66\u7684\u8be6\u7ec6\u4fe1\u606f<\/h2>\n<p>\u4e0e\u5176\u4ed6\u516c\u94a5\u5bc6\u7801\u7cfb\u7edf\u4e00\u6837\uff0c\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u672f\u4f7f\u7528\u4e24\u4e2a\u6570\u5b66\u4e0a\u76f8\u5173\u7684\u5bc6\u94a5\uff1a\u6bcf\u4e2a\u4eba\u90fd\u77e5\u9053\u7684\u516c\u94a5\u548c\u7531\u4e2a\u4eba\u7528\u6237\u4fdd\u5bc6\u7684\u79c1\u94a5\u3002\u8be5\u8fc7\u7a0b\u6d89\u53ca\u5bc6\u94a5\u751f\u6210\u3001\u52a0\u5bc6\u548c\u89e3\u5bc6\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u5bc6\u94a5\u751f\u6210<\/strong>\uff1a\u6bcf\u4e2a\u7528\u6237\u751f\u6210\u4e00\u5bf9\u5bc6\u94a5\u2014\u2014\u79c1\u94a5\u548c\u76f8\u5e94\u7684\u516c\u94a5\u3002\u516c\u94a5\u7531\u79c1\u94a5\u884d\u751f\u800c\u6765\uff0c\u53ef\u4ee5\u516c\u5f00\u5171\u4eab\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u52a0\u5bc6<\/strong>\uff1a\u8981\u4e3a\u6536\u4ef6\u4eba\u52a0\u5bc6\u6d88\u606f\uff0c\u53d1\u4ef6\u4eba\u4f7f\u7528\u6536\u4ef6\u4eba\u7684\u516c\u94a5\u5c06\u660e\u6587\u8f6c\u6362\u4e3a\u5bc6\u6587\u3002\u53ea\u6709\u62e5\u6709\u76f8\u5e94\u79c1\u94a5\u7684\u63a5\u6536\u8005\u624d\u80fd\u89e3\u5bc6\u5bc6\u6587\u5e76\u6062\u590d\u539f\u59cb\u6d88\u606f\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u89e3\u5bc6<\/strong>\uff1a\u6536\u4ef6\u4eba\u4f7f\u7528\u5176\u79c1\u94a5\u89e3\u5bc6\u5bc6\u6587\u5e76\u8bbf\u95ee\u539f\u59cb\u6d88\u606f\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66\u7684\u5185\u90e8\u7ed3\u6784\u2014\u2014\u5b83\u662f\u5982\u4f55\u5de5\u4f5c\u7684<\/h2>\n<p>ECC\u7684\u6839\u672c\u57fa\u7840\u662f\u692d\u5706\u66f2\u7ebf\u7684\u6570\u5b66\u7ed3\u6784\u3002\u692d\u5706\u66f2\u7ebf\u7531\u4ee5\u4e0b\u5f62\u5f0f\u7684\u65b9\u7a0b\u5b9a\u4e49\uff1a<\/p>\n<pre><div class=\"bg-black rounded-md mb-4\"><div class=\"flex items-center relative text-gray-200 bg-gray-800 px-4 py-2 text-xs font-sans justify-between rounded-t-md\"><span>CSS<\/span><button class=\"flex ml-auto gap-2\"><svg stroke=\"currentColor\" fill=\"none\" stroke-width=\"2\" viewbox=\"0 0 24 24\" stroke-linecap=\"round\" stroke-linejoin=\"round\" class=\"h-4 w-4\" height=\"1em\" width=\"1em\" ><path d=\"M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2\"><\/path><rect x=\"8\" y=\"2\" width=\"8\" height=\"4\" rx=\"1\" ry=\"1\"><\/rect><\/svg>\u590d\u5236\u4ee3\u7801<\/button><\/div><div class=\"p-4 overflow-y-auto\"><code class=\"!whitespace-pre hljs language-css\" data-no-translation=\"\">y^<span class=\"hljs-number\">2<\/span> = x^<span class=\"hljs-number\">3<\/span> + ax + <span class=\"hljs-selector-tag\">b<\/span>\n<\/code><\/div><\/div><\/pre>\n<p>\u5728\u54ea\u91cc <code data-no-translation=\"\">a<\/code> \u548c <code data-no-translation=\"\">b<\/code> \u662f\u5e38\u6570\u3002\u8be5\u66f2\u7ebf\u5177\u6709\u4f7f\u5176\u9002\u5408\u52a0\u5bc6\u64cd\u4f5c\u7684\u9644\u52a0\u5c5e\u6027\u3002<\/p>\n<p>ECC\u4f9d\u8d56\u4e8e\u692d\u5706\u66f2\u7ebf\u79bb\u6563\u5bf9\u6570\u95ee\u9898\u7684\u96be\u5ea6\u3002\u7ed9\u5b9a\u4e00\u4e2a\u70b9 <code data-no-translation=\"\">P<\/code> \u5728\u66f2\u7ebf\u548c\u6807\u91cf\u4e0a <code data-no-translation=\"\">n<\/code>, \u8ba1\u7b97 <code data-no-translation=\"\">nP<\/code> \u76f8\u5bf9\u7b80\u5355\u3002\u7136\u800c\uff0c\u9274\u4e8e <code data-no-translation=\"\">P<\/code> \u548c <code data-no-translation=\"\">nP<\/code>\uff0c\u6c42\u6807\u91cf <code data-no-translation=\"\">n<\/code> \u8ba1\u7b97\u4e0a\u662f\u4e0d\u53ef\u884c\u7684\u3002\u6b64\u5c5e\u6027\u6784\u6210\u4e86 ECC \u5b89\u5168\u6027\u7684\u57fa\u7840\u3002<\/p>\n<p>ECC\u7684\u5b89\u5168\u6027\u5728\u4e8e\u89e3\u51b3\u692d\u5706\u66f2\u7ebf\u79bb\u6563\u5bf9\u6570\u95ee\u9898\u7684\u96be\u5ea6\u3002\u4e0e\u4f9d\u8d56\u4e8e\u6574\u6570\u5206\u89e3\u95ee\u9898\u7684 RSA \u4e0d\u540c\uff0cECC \u7684\u5b89\u5168\u6027\u6e90\u4e8e\u8fd9\u4e2a\u7279\u5b9a\u6570\u5b66\u95ee\u9898\u7684\u96be\u5ea6\u3002<\/p>\n<h2>\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66\u7684\u5173\u952e\u7279\u5f81\u5206\u6790<\/h2>\n<p>\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66\u63d0\u4f9b\u4e86\u51e0\u4e2a\u6709\u52a9\u4e8e\u5176\u6d41\u884c\u548c\u91c7\u7528\u7684\u5173\u952e\u529f\u80fd\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u5b89\u5168\u6027\u5f3a<\/strong>\uff1a\u4e0e\u5176\u4ed6\u516c\u94a5\u52a0\u5bc6\u7b97\u6cd5\u76f8\u6bd4\uff0cECC \u63d0\u4f9b\u4e86\u66f4\u9ad8\u7ea7\u522b\u7684\u5b89\u5168\u6027\u548c\u66f4\u77ed\u7684\u5bc6\u94a5\u957f\u5ea6\u3002\u8fd9\u4f1a\u964d\u4f4e\u8ba1\u7b97\u8981\u6c42\u5e76\u63d0\u9ad8\u6027\u80fd\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u6548\u7387<\/strong>\uff1aECC \u975e\u5e38\u9ad8\u6548\uff0c\u9002\u5408\u667a\u80fd\u624b\u673a\u548c\u7269\u8054\u7f51\u8bbe\u5907\u7b49\u8d44\u6e90\u53d7\u9650\u7684\u8bbe\u5907\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u8f83\u5c0f\u7684\u94a5\u5319\u5c3a\u5bf8<\/strong>\uff1a\u8f83\u5c0f\u7684\u5bc6\u94a5\u5927\u5c0f\u610f\u5473\u7740\u66f4\u5c11\u7684\u5b58\u50a8\u7a7a\u95f4\u548c\u66f4\u5feb\u7684\u6570\u636e\u4f20\u8f93\uff0c\u8fd9\u5728\u73b0\u4ee3\u5e94\u7528\u7a0b\u5e8f\u4e2d\u81f3\u5173\u91cd\u8981\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u524d\u5411\u4fdd\u5bc6<\/strong>\uff1aECC \u63d0\u4f9b\u524d\u5411\u4fdd\u5bc6\uff0c\u786e\u4fdd\u5373\u4f7f\u4e00\u4e2a\u4f1a\u8bdd\u7684\u79c1\u94a5\u88ab\u6cc4\u9732\uff0c\u8fc7\u53bb\u548c\u672a\u6765\u7684\u901a\u4fe1\u4ecd\u7136\u5b89\u5168\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u517c\u5bb9\u6027<\/strong>\uff1aECC \u53ef\u4ee5\u8f7b\u677e\u96c6\u6210\u5230\u73b0\u6709\u7684\u52a0\u5bc6\u7cfb\u7edf\u548c\u534f\u8bae\u4e2d\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66\u7684\u7c7b\u578b<\/h2>\n<p>\u6839\u636e\u692d\u5706\u66f2\u7ebf\u53ca\u5176\u57fa\u7840\u573a\u7684\u9009\u62e9\uff0cECC \u6709\u4e0d\u540c\u7684\u53d8\u5316\u548c\u53c2\u6570\u3002\u5e38\u7528\u7684\u53d8\u4f53\u5305\u62ec\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u692d\u5706\u66f2\u7ebf Diffie-Hellman (ECDH)<\/strong>\uff1a\u7528\u4e8e\u5efa\u7acb\u5b89\u5168\u901a\u4fe1\u901a\u9053\u7684\u5bc6\u94a5\u4ea4\u6362\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u692d\u5706\u66f2\u7ebf\u6570\u5b57\u7b7e\u540d\u7b97\u6cd5\uff08ECDSA\uff09<\/strong>\uff1a\u7528\u4e8e\u751f\u6210\u548c\u9a8c\u8bc1\u6570\u5b57\u7b7e\u540d\u4ee5\u9a8c\u8bc1\u6570\u636e\u548c\u6d88\u606f\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u692d\u5706\u66f2\u7ebf\u96c6\u6210\u52a0\u5bc6\u65b9\u6848 (ECIES)<\/strong>\uff1a\u7ed3\u5408ECC\u548c\u5bf9\u79f0\u52a0\u5bc6\u7684\u6df7\u5408\u52a0\u5bc6\u65b9\u6848\uff0c\u7528\u4e8e\u5b89\u5168\u6570\u636e\u4f20\u8f93\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7231\u5fb7\u534e\u5179\u66f2\u7ebf\u548c\u626d\u66f2\u7231\u5fb7\u534e\u5179\u66f2\u7ebf<\/strong>\uff1a\u63d0\u4f9b\u4e0d\u540c\u6570\u5b66\u5c5e\u6027\u7684\u692d\u5706\u66f2\u7ebf\u7684\u66ff\u4ee3\u5f62\u5f0f\u3002<\/p>\n<\/li>\n<\/ol>\n<p>\u4e0b\u9762\u7684\u6bd4\u8f83\u8868\u663e\u793a\u4e86\u4e00\u4e9b ECC \u53d8\u4f53\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th>ECC \u53d8\u4f53<\/th>\n<th>\u4f7f\u7528\u6848\u4f8b<\/th>\n<th>\u5bc6\u94a5\u957f\u5ea6<\/th>\n<th>\u663e\u7740\u7279\u70b9<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>ECDH<\/td>\n<td>\u5bc6\u94a5\u4ea4\u6362<\/td>\n<td>\u8f83\u77ed<\/td>\n<td>\u542f\u7528\u5b89\u5168\u7684\u901a\u4fe1\u901a\u9053<\/td>\n<\/tr>\n<tr>\n<td>\u7535\u5b50CDSA<\/td>\n<td>\u6570\u5b57\u7b7e\u540d<\/td>\n<td>\u8f83\u77ed<\/td>\n<td>\u63d0\u4f9b\u6570\u636e\u548c\u6d88\u606f\u8ba4\u8bc1<\/td>\n<\/tr>\n<tr>\n<td>\u6b27\u6d32\u7ecf\u6d4e\u5b66\u9662<\/td>\n<td>\u6df7\u5408\u52a0\u5bc6<\/td>\n<td>\u8f83\u77ed<\/td>\n<td>\u5c06 ECC \u4e0e\u5bf9\u79f0\u52a0\u5bc6\u76f8\u7ed3\u5408<\/td>\n<\/tr>\n<tr>\n<td>\u7231\u5fb7\u534e\u5179\u66f2\u7ebf<\/td>\n<td>\u4e00\u822c\u7528\u9014<\/td>\n<td>\u8f83\u77ed<\/td>\n<td>\u63d0\u4f9b\u4e0d\u540c\u7684\u6570\u5b66\u5c5e\u6027<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66\u7684\u4f7f\u7528\u65b9\u6cd5\u3001\u95ee\u9898\u548c\u89e3\u51b3\u65b9\u6848<\/h2>\n<p>ECC \u5728\u5404\u4e2a\u9886\u57df\u90fd\u6709\u5e94\u7528\uff0c\u5305\u62ec\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u5b89\u5168\u901a\u8baf<\/strong>\uff1aECC \u5728 SSL\/TLS \u534f\u8bae\u4e2d\u4f7f\u7528\uff0c\u4ee5\u4fdd\u62a4\u670d\u52a1\u5668\u548c\u5ba2\u6237\u7aef\u4e4b\u95f4\u7684\u4e92\u8054\u7f51\u901a\u4fe1\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u6570\u5b57\u7b7e\u540d<\/strong>\uff1a\u91c7\u7528ECC\u6765\u751f\u6210\u548c\u9a8c\u8bc1\u6570\u5b57\u7b7e\u540d\uff0c\u4fdd\u8bc1\u6570\u636e\u7684\u771f\u5b9e\u6027\u548c\u5b8c\u6574\u6027\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u79fb\u52a8\u8bbe\u5907\u548c\u7269\u8054\u7f51<\/strong>\uff1a\u7531\u4e8e\u5176\u6548\u7387\u9ad8\u4e14\u5bc6\u94a5\u5c3a\u5bf8\u5c0f\uff0cECC \u5e7f\u6cdb\u5e94\u7528\u4e8e\u79fb\u52a8\u5e94\u7528\u548c\u7269\u8054\u7f51\u8bbe\u5907\u3002<\/p>\n<\/li>\n<\/ol>\n<p>\u5c3d\u7ba1\u5177\u6709\u4f18\u52bf\uff0cECC \u4e5f\u9762\u4e34\u7740\u6311\u6218\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u4e13\u5229\u548c\u8bb8\u53ef\u95ee\u9898<\/strong>\uff1a\u4e00\u4e9b ECC \u7b97\u6cd5\u6700\u521d\u83b7\u5f97\u4e86\u4e13\u5229\uff0c\u5f15\u53d1\u4e86\u5bf9\u77e5\u8bc6\u4ea7\u6743\u548c\u8bb8\u53ef\u7684\u62c5\u5fe7\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u91cf\u5b50\u8ba1\u7b97\u5a01\u80c1<\/strong>\uff1a\u4e0e\u5176\u4ed6\u975e\u5bf9\u79f0\u52a0\u5bc6\u65b9\u6848\u4e00\u6837\uff0cECC \u5f88\u5bb9\u6613\u53d7\u5230\u91cf\u5b50\u8ba1\u7b97\u653b\u51fb\u3002\u6297\u91cf\u5b50 ECC \u53d8\u4f53\u6b63\u5728\u5f00\u53d1\u4e2d\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u4e3b\u8981\u7279\u70b9\u53ca\u4e0e\u540c\u7c7b\u672f\u8bed\u7684\u6bd4\u8f83<\/h2>\n<p>\u8ba9\u6211\u4eec\u5c06 ECC \u4e0e RSA\uff08\u6700\u5e7f\u6cdb\u4f7f\u7528\u7684\u975e\u5bf9\u79f0\u52a0\u5bc6\u65b9\u6848\u4e4b\u4e00\uff09\u8fdb\u884c\u6bd4\u8f83\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th>\u7279\u5f81<\/th>\n<th>\u692d\u5706\u66f2\u7ebf\u52a0\u5bc6 (ECC)<\/th>\n<th>RSA<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u7b49\u6548\u5b89\u5168\u6027\u7684\u5bc6\u94a5\u957f\u5ea6<\/td>\n<td>\u8f83\u77ed\u7684\u5bc6\u94a5\u957f\u5ea6\uff08\u4f8b\u5982\uff0c256 \u4f4d\uff09<\/td>\n<td>\u66f4\u957f\u7684\u5bc6\u94a5\u957f\u5ea6\uff08\u4f8b\u5982\uff0c2048 \u4f4d\uff09<\/td>\n<\/tr>\n<tr>\n<td>\u8ba1\u7b97\u6548\u7387<\/td>\n<td>\u66f4\u9ad8\u6548\uff0c\u5c24\u5176\u662f\u5bf9\u4e8e\u8f83\u5c0f\u7684\u6309\u952e<\/td>\n<td>\u5bf9\u4e8e\u8f83\u5927\u7684\u952e\u6548\u7387\u8f83\u4f4e<\/td>\n<\/tr>\n<tr>\n<td>\u5b89\u5168<\/td>\n<td>\u57fa\u4e8e\u692d\u5706\u66f2\u7ebf\u7684\u5f3a\u5b89\u5168\u6027<\/td>\n<td>\u57fa\u4e8e\u7d20\u6570\u7684\u5f3a\u5927\u5b89\u5168\u6027<\/td>\n<\/tr>\n<tr>\n<td>\u5bc6\u94a5\u751f\u6210\u901f\u5ea6<\/td>\n<td>\u66f4\u5feb\u7684\u5bc6\u94a5\u751f\u6210<\/td>\n<td>\u5bc6\u94a5\u751f\u6210\u901f\u5ea6\u8f83\u6162<\/td>\n<\/tr>\n<tr>\n<td>\u7b7e\u540d\u751f\u6210\/\u9a8c\u8bc1<\/td>\n<td>\u603b\u4f53\u4e0a\u66f4\u5feb<\/td>\n<td>\u901f\u5ea6\u8f83\u6162\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u9a8c\u8bc1\u800c\u8a00<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u4e0e\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66\u76f8\u5173\u7684\u672a\u6765\u524d\u666f\u548c\u6280\u672f<\/h2>\n<p>ECC \u7684\u672a\u6765\u770b\u8d77\u6765\u5145\u6ee1\u5e0c\u671b\u3002\u968f\u7740\u5bf9\u5b89\u5168\u901a\u4fe1\u7684\u9700\u6c42\u4e0d\u65ad\u589e\u957f\uff0cECC \u5c06\u53d1\u6325\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528\uff0c\u5c24\u5176\u662f\u5728\u8d44\u6e90\u6709\u9650\u7684\u73af\u5883\u4e2d\u3002\u76ee\u524d\u6b63\u5728\u52aa\u529b\u5f00\u53d1\u6297\u91cf\u5b50 ECC \u53d8\u4f53\uff0c\u4ee5\u786e\u4fdd\u5176\u5728\u540e\u91cf\u5b50\u8ba1\u7b97\u4e16\u754c\u4e2d\u7684\u957f\u671f\u751f\u5b58\u80fd\u529b\u3002<\/p>\n<h2>\u5982\u4f55\u4f7f\u7528\u4ee3\u7406\u670d\u52a1\u5668\u6216\u5982\u4f55\u5c06\u4ee3\u7406\u670d\u52a1\u5668\u4e0e\u692d\u5706\u66f2\u7ebf\u52a0\u5bc6\u76f8\u5173\u8054<\/h2>\n<p>\u4ee3\u7406\u670d\u52a1\u5668\u5145\u5f53\u5ba2\u6237\u7aef\u548c\u670d\u52a1\u5668\u4e4b\u95f4\u7684\u4e2d\u4ecb\uff0c\u8f6c\u53d1\u5ba2\u6237\u7aef\u8bf7\u6c42\u5e76\u63a5\u6536\u670d\u52a1\u5668\u54cd\u5e94\u3002\u867d\u7136 ECC \u4e3b\u8981\u7528\u4e8e\u6700\u7ec8\u7528\u6237\u548c\u670d\u52a1\u5668\u4e4b\u95f4\u7684\u5b89\u5168\u901a\u4fe1\uff0c\u4f46\u4ee3\u7406\u670d\u52a1\u5668\u53ef\u4ee5\u901a\u8fc7\u5728\u4e0e\u5ba2\u6237\u7aef\u548c\u670d\u52a1\u5668\u7684\u901a\u4fe1\u4e2d\u5b9e\u65bd\u57fa\u4e8e ECC \u7684\u52a0\u5bc6\u548c\u8eab\u4efd\u9a8c\u8bc1\u534f\u8bae\u6765\u589e\u5f3a\u5b89\u5168\u6027\u3002<\/p>\n<p>\u901a\u8fc7\u5728\u4ee3\u7406\u670d\u52a1\u5668\u4e2d\u5229\u7528 ECC\uff0c\u53ef\u4ee5\u4f7f\u7528\u8f83\u77ed\u7684\u5bc6\u94a5\u957f\u5ea6\u6765\u4fdd\u62a4\u5ba2\u6237\u7aef\u4e0e\u4ee3\u7406\u670d\u52a1\u5668\u4e4b\u95f4\u4ee5\u53ca\u4ee3\u7406\u670d\u52a1\u5668\u4e0e\u76ee\u6807\u670d\u52a1\u5668\u4e4b\u95f4\u7684\u6570\u636e\u4f20\u8f93\uff0c\u4ece\u800c\u51cf\u5c11\u8ba1\u7b97\u5f00\u9500\u5e76\u63d0\u9ad8\u6574\u4f53\u6027\u80fd\u3002<\/p>\n<h2>\u76f8\u5173\u94fe\u63a5<\/h2>\n<p>\u6709\u5173\u692d\u5706\u66f2\u7ebf\u52a0\u5bc6\u7684\u66f4\u591a\u4fe1\u606f\uff0c\u60a8\u53ef\u4ee5\u6d4f\u89c8\u4ee5\u4e0b\u8d44\u6e90\uff1a<\/p>\n<ol>\n<li><a href=\"https:\/\/csrc.nist.gov\/projects\/elliptic-curve-cryptography\" target=\"_new\" rel=\"noopener nofollow\">\u7f8e\u56fd\u56fd\u5bb6\u6807\u51c6\u4e0e\u6280\u672f\u7814\u7a76\u9662 (NIST) \u2013 \u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Elliptic-curve_cryptography\" target=\"_new\" rel=\"noopener nofollow\">\u7ef4\u57fa\u767e\u79d1\u4e0a\u7684\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66<\/a><\/li>\n<li><a href=\"https:\/\/www.khanacademy.org\/computing\/computer-science\/cryptography\/modern-crypt\/v\/elliptic-curve-cryptography-part-1\" target=\"_new\" rel=\"noopener nofollow\">\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66\u7b80\u4ecb \u2013 \u53ef\u6c57\u5b66\u9662<\/a><\/li>\n<\/ol>\n<p>\u603b\u4e4b\uff0c\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66\u5df2\u6210\u4e3a\u4e00\u79cd\u5f3a\u5927\u800c\u9ad8\u6548\u7684\u52a0\u5bc6\u6280\u672f\uff0c\u53ef\u89e3\u51b3\u73b0\u4ee3\u6570\u5b57\u901a\u4fe1\u7684\u5b89\u5168\u6311\u6218\u3002\u51ed\u501f\u5176\u5f3a\u5927\u7684\u5b89\u5168\u529f\u80fd\u3001\u8f83\u5c0f\u7684\u5bc6\u94a5\u5927\u5c0f\u4ee5\u53ca\u4e0e\u5404\u79cd\u5e94\u7528\u7a0b\u5e8f\u7684\u517c\u5bb9\u6027\uff0cECC \u6709\u671b\u7ee7\u7eed\u6210\u4e3a\u786e\u4fdd\u6570\u5b57\u4e16\u754c\u4e2d\u6570\u636e\u9690\u79c1\u548c\u5b8c\u6574\u6027\u7684\u57fa\u672c\u5de5\u5177\u3002\u901a\u8fc7\u5229\u7528ECC\u7684\u4f18\u52bf\uff0c\u4ee3\u7406\u670d\u52a1\u5668\u63d0\u4f9b\u5546\uff08\u4f8b\u5982OneProxy\uff09\u53ef\u4ee5\u8fdb\u4e00\u6b65\u589e\u5f3a\u5176\u670d\u52a1\u7684\u5b89\u5168\u6027\uff0c\u4e3a\u6784\u5efa\u66f4\u5b89\u5168\u7684\u5728\u7ebf\u73af\u5883\u505a\u51fa\u8d21\u732e\u3002<\/p>","protected":false},"featured_media":477060,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-477059","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Elliptic-curve cryptography: Securing the Digital World<\/mark>","faq_items":[{"question":"What is Elliptic-curve cryptography (ECC) and how does it work?","answer":"<p><strong>Elliptic-curve cryptography (ECC)<\/strong> is a modern cryptographic method that uses mathematical properties of elliptic curves to secure data transmission, authentication, and digital signatures. It involves two mathematically related keys - a public key and a private key. The public key is openly shared and used for encryption, while the private key, kept secret, is used for decryption.<\/p>"},{"question":"What makes Elliptic-curve cryptography superior to traditional encryption algorithms?","answer":"<p>ECC offers several advantages over traditional encryption algorithms like RSA. It provides strong security with shorter key lengths, making it more efficient in terms of computation and faster in performance. Additionally, ECC's smaller key sizes enable better resource utilization, making it suitable for devices with limited computing power, such as mobile devices and IoT gadgets.<\/p>"},{"question":"How does Elliptic-curve cryptography ensure the security of data?","answer":"<p>The security of ECC is based on the difficulty of the elliptic curve discrete logarithm problem. While it is relatively easy to compute <code>nP<\/code> given a point <code>P<\/code> on the curve and a scalar <code>n<\/code>, calculating the scalar <code>n<\/code> given <code>P<\/code> and <code>nP<\/code> is computationally infeasible. This property forms the foundation of ECC's security, making it highly resistant to attacks.<\/p>"},{"question":"What are the different types of Elliptic-curve cryptography?","answer":"<p>There are various variations of ECC, each serving specific cryptographic purposes. Some common types include:<\/p><ul><li><strong>Elliptic Curve Diffie-Hellman (ECDH)<\/strong>: Used for key exchange in secure communication channels.<\/li><li><strong>Elliptic Curve Digital Signature Algorithm (ECDSA)<\/strong>: Employed for generating and verifying digital signatures.<\/li><li><strong>Elliptic Curve Integrated Encryption Scheme (ECIES)<\/strong>: A hybrid encryption scheme combining ECC and symmetric encryption.<\/li><\/ul>"},{"question":"Can Elliptic-curve cryptography be used with proxy servers?","answer":"<p>Yes, absolutely! Elliptic-curve cryptography can be implemented in proxy servers to enhance the security of data transmission between clients and servers. By using ECC, proxy servers can establish secure channels and authenticate data, contributing to a safer online environment.<\/p>"},{"question":"Is Elliptic-curve cryptography immune to all threats?","answer":"<p>While Elliptic-curve cryptography provides robust security, it is not entirely invulnerable. Like any cryptographic system, ECC is subject to potential threats. However, its strong security features and ongoing research for quantum-resistant variants make it a reliable and future-proof option in today's digital landscape.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki\/477059","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki\/477059\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/media\/477060"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/media?parent=477059"}],"curies":[{"name":"\u53ef\u6e7f\u6027\u7c89\u5242","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}