{"id":437,"date":"2010-10-09T19:43:02","date_gmt":"2010-10-09T10:43:02","guid":{"rendered":"http:\/\/helloidea.org\/?p=437"},"modified":"2014-02-22T22:18:12","modified_gmt":"2014-02-22T13:18:12","slug":"rsa-%e5%85%ac%e9%96%8b%e9%8d%b5%e3%81%a8%e7%a7%98%e5%af%86%e9%8d%b5%e3%81%ae%e4%bb%95%e7%b5%84%e3%81%bf","status":"publish","type":"post","link":"https:\/\/helloidea.org\/index.php\/archives\/437.html","title":{"rendered":"RSA \u516c\u958b\u9375\u3068\u79d8\u5bc6\u9375\u306e\u4ed5\u7d44\u307f"},"content":{"rendered":"

RSA\u6697\u53f7\u5316\u306b\u3064\u3044\u3066\u30e1\u30e2<\/p>\n

\u65e5\u672c\u8a9e\u3088\u308a\u5f0f\u306e\u65b9\u304c\u308f\u304b\u308a\u3084\u3059\u3044\u3068\u601d\u3046\u306e\u3067\u5f0f\u3067
\nx , y<\/strong>\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000 ( x\u3068y\u306f\u4efb\u610f\u306e\u7d20\u6570)
\n n * ( x – 1 ) * ( y – 1 ) + 1 = p*q<\/strong> \u3000( n\u306f\u4efb\u610f\u306e\u81ea\u7136\u6570)
\n x * y<\/strong>
\n(p , x * y)\u3000\u3068 (q, x* y) \u306e\u30bb\u30c3\u30c8\u304c\u9375
\n\u3069\u3061\u3089\u304c\u79d8\u5bc6\u9375\u3067\u3082\u516c\u958b\u9375\u3067\u3082\u304a\uff4b\u3067\u3059\u3002<\/p>\n

\u3048\u3089\u304f\u8907\u96d1\u306a\u3053\u3068\u3057\u3066\u308b\u306e\u304b\u3068\u601d\u3044\u304d\u3084\u3001
\n\u6570\u5b57\u3092(p * q)\u4e57\u3057\u3066\u3001mod (x * y)\u3059\u308b\u3068\u5143\u306e\u6570\u5b57\u306b\u623b\u308b\u3068\u3044\u3046\u3001\u6570\u5b57\u306e\u4e0d\u601d\u8b70\u3092\u5229\u7528\u3057\u305f\u6697\u53f7\u5316\u3067\u3057\u305f\u3002<\/p>\n

\u8a66\u3057\u306bx = 3, y = 11 \u3068\u3059\u308b\u3068\u3001p * q = 21\u3068\u306a\u308a p = 3, q = 7\u3068\u306a\u308a\u307e\u3059\u3002
\n\u9069\u5f53\u306b 5 \u3092 21 \u4e57\u3057\u3066\u3001mod (x * y)\u3059\u308b\u3068 (476837158203125 mod 33) = 5 \u3068\u306a\u308a\u5fa9\u53f7\u3067\u304d\u307e\u3059\u3002\u4e0d\u601d\u8b70\u3060\uff01<\/p>\n

\u4e00\u6c17\u306b21\u4e57\u3059\u308b\u3068\u3001\u3044\u304d\u306a\u308a\u5143\u306e\u5024\u306b\u623b\u3063\u3066\u3044\u307e\u3046\u306e\u3067\u3001\uff12\uff11\u3092\uff13\u3068\uff17\u306b\u5206\u5272\u3057\u307e\u3059\u3002
\n\u3064\u307e\u308a\u3001\u4eca\u56de\u306e\uff15\u3092\u6697\u53f7\u5316\u3057\u305f\u7d50\u679c\u306f\u3001 5^3 mod (x * y) = 26\u3068\u306a\u308a\u307e\u3059\u3002
\n\u5fa9\u53f7\u3059\u308b\u306b\u306f\u300126 ^ 7 mode (x * y) = 5\u3068\u306a\u308a\u5fa9\u53f7\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n

\u3053\u306e\u6027\u8cea\u3092\u5229\u7528\u3057\u3066\u3001
\n \u9375A\u3067\u6697\u53f7\u5316\u3057\u305f\u3051\u3069\u9375A\u3067\u306f\u5fa9\u53f7\u3067\u304d\u306a\u3044\u3001\u9375B\u3067\u306f\u8907\u5408\u3067\u304d\u308b
\n\u9375B\u3067\u6697\u53f7\u5316\u3057\u305f\u3051\u3069\u9375B\u3067\u306f\u5fa9\u53f7\u3067\u304d\u306a\u3044\u3001\u9375A\u3067\u306f\u8907\u5408\u3067\u304d\u308b<\/span>
\n\u3063\u3066\u3044\u3046\u5947\u5999\u306a\u4ed5\u7d44\u307f\u304c\u5b9f\u73fe\u3057\u3066\u308b\u307f\u305f\u3044\u3002(\u516c\u958b\u9375\u3001\u79d8\u5bc6\u9375)<\/p>\n

\u4eca\u56de\u3001\u7d20\u6570 3 \u3068 11 \u3092\u4f7f\u3063\u3066\u5207\u308a\u306e\u826f\u3044\u3001\u9375 3 \u3068 7 \u304c\u51fa\u6765\u305f\u3051\u3069\u3001
\n\u7d20\u6570\u304c 5 \u3068 11\u3068\u304b\u3060\u3068\u3001 p * q = 41 \u3068\u306a\u308a\u4e8c\u3064\u306b\u5206\u5272\u3067\u304d\u307e\u305b\u3093\u3002\u3002 41\u304c\u7d20\u6570\u306a\u306e\u3067\u7121\u7406\u3067\u3059\u3002\uff08\u6574\u6570\u3058\u3083\u306a\u3044\u306e\u3082\u304a\uff4b\u306a\u306e\u304b\u306a\uff1f
\n\u3055\u3089\u306b\u3001p * q = 29962177 \u3060\u3068 p \u3068 q \u304c\u60f3\u50cf\u3067\u304d\u306a\u3044\uff01 \uff08 x = 8287 y = 3617
\n\u3053\u308c\u306f\u4e0a\u624b\u3044\u3053\u3068\u8003\u3048\u306a\u3044\u3068\u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u51fa\u6765\u306a\u3044\uff01\u5b9f\u969b\u3069\u3046\u3084\u3063\u3066\u4f5c\u3063\u3066\u308b\u3093\u3060\u308d\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

RSA\u6697\u53f7\u5316\u306b\u3064\u3044\u3066\u30e1\u30e2 \u65e5\u672c\u8a9e\u3088\u308a\u5f0f\u306e\u65b9\u304c\u308f\u304b\u308a\u3084\u3059\u3044\u3068\u601d\u3046\u306e\u3067\u5f0f\u3067 x , y\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000 ( x\u3068y\u306f\u4efb\u610f\u306e\u7d20\u6570) n * ( x – 1 ) * ( y &#8 \u2026<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[49],"tags":[102,104,106,107,103,105],"class_list":["post-437","post","type-post","status-publish","format-standard","hentry","category-memo","tag-rsa","tag-public-key","tag-decoding","tag-code","tag-encryption","tag-private-key"],"_links":{"self":[{"href":"https:\/\/helloidea.org\/index.php\/wp-json\/wp\/v2\/posts\/437","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/helloidea.org\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/helloidea.org\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/helloidea.org\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/helloidea.org\/index.php\/wp-json\/wp\/v2\/comments?post=437"}],"version-history":[{"count":9,"href":"https:\/\/helloidea.org\/index.php\/wp-json\/wp\/v2\/posts\/437\/revisions"}],"predecessor-version":[{"id":468,"href":"https:\/\/helloidea.org\/index.php\/wp-json\/wp\/v2\/posts\/437\/revisions\/468"}],"wp:attachment":[{"href":"https:\/\/helloidea.org\/index.php\/wp-json\/wp\/v2\/media?parent=437"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/helloidea.org\/index.php\/wp-json\/wp\/v2\/categories?post=437"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/helloidea.org\/index.php\/wp-json\/wp\/v2\/tags?post=437"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}