{"id":477241,"date":"2023-08-09T09:09:43","date_gmt":"2023-08-09T09:09:43","guid":{"rendered":""},"modified":"2024-07-01T04:50:32","modified_gmt":"2024-07-01T04:50:32","slug":"finite-field","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/jp\/wiki\/finite-field\/","title":{"rendered":"\u6709\u9650\u4f53"},"content":{"rendered":"

\u6709\u9650\u4f53\u3001\u307e\u305f\u306f\u30ac\u30ed\u30a2\u4f53\u306f\u3001\u591a\u304f\u306e\u6570\u5b66\u7684\u304a\u3088\u3073\u8a08\u7b97\u7684\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u3067\u6975\u3081\u3066\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3059\u62bd\u8c61\u4ee3\u6570\u306e\u4e0d\u53ef\u6b20\u306a\u90e8\u5206\u3067\u3059\u3002\u6709\u9650\u500b\u306e\u8981\u7d20\u3092\u6301\u3064\u4f53\u3067\u3042\u308a\u3001\u6697\u53f7\u5316\u3001\u7b26\u53f7\u7406\u8ad6\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc \u30b5\u30a4\u30a8\u30f3\u30b9\u3001\u304a\u3088\u3073\u305d\u306e\u4ed6\u306e\u591a\u304f\u306e\u5206\u91ce\u3067\u91cd\u8981\u306a\u7528\u9014\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n

\u904e\u53bb\u3078\u306e\u65c5: \u6709\u9650\u4f53\u306e\u8d77\u6e90\u3068\u521d\u671f\u306e\u8a00\u53ca<\/h2>\n

\u6709\u9650\u4f53\u306f\u3001\u591a\u9805\u5f0f\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3068\u3044\u3046\u53e4\u4ee3\u306b\u9061\u308b\u7814\u7a76\u306e\u6587\u8108\u3067\u521d\u3081\u3066\u8aac\u660e\u3055\u308c\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u6982\u5ff5\u304c\u521d\u3081\u3066\u5f62\u5f0f\u5316\u3055\u308c\u305f\u306e\u306f 19 \u4e16\u7d00\u306b\u306a\u3063\u3066\u304b\u3089\u3067\u3057\u305f\u3002\u30d5\u30e9\u30f3\u30b9\u306e\u6570\u5b66\u8005\u30a8\u30f4\u30a1\u30ea\u30b9\u30c8\u30fb\u30ac\u30ed\u30a2\u306f\u6709\u9650\u4f53\u306e\u767a\u5c55\u306b\u591a\u5927\u306a\u8ca2\u732e\u3092\u3057\u305f\u305f\u3081\u3001\u5f7c\u306b\u656c\u610f\u3092\u8868\u3057\u3066\u6709\u9650\u4f53\u306f\u3057\u3070\u3057\u3070\u300c\u30ac\u30ed\u30a2\u4f53\u300d\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>\n

\u30ac\u30ed\u30a2\u306e\u7814\u7a76\u306f\u3001\u73fe\u4ee3\u306e\u7fa4\u8ad6\u3068\u6709\u9650\u4f53\u306e\u4e00\u822c\u7406\u8ad6\u306e\u57fa\u790e\u3092\u7bc9\u304d\u307e\u3057\u305f\u3002\u6709\u9650\u4f53\u306e\u4f53\u7cfb\u7684\u306a\u7814\u7a76\u306f\u3001\u30ea\u30d2\u30e3\u30eb\u30c8\u30fb\u30c7\u30c7\u30ad\u30f3\u30c8\u3084\u30a8\u30df\u30fc\u30fb\u30cd\u30fc\u30bf\u30fc\u306a\u3069\u306e\u6570\u5b66\u8005\u306e\u591a\u5927\u306a\u8ca2\u732e\u306b\u3088\u308a\u300120 \u4e16\u7d00\u306b\u3055\u3089\u306b\u9032\u6b69\u3057\u307e\u3057\u305f\u3002<\/p>\n

\u3088\u308a\u6df1\u304f\u6398\u308a\u4e0b\u3052\u308b: \u6709\u9650\u4f53\u3092\u7406\u89e3\u3059\u308b<\/h2>\n

\u6709\u9650\u4f53\u3068\u306f\u3001\u672c\u8cea\u7684\u306b\u306f\u3001\u3059\u3079\u3066\u306e\u57fa\u672c\u6f14\u7b97 (\u52a0\u7b97\u3001\u6e1b\u7b97\u3001\u4e57\u7b97\u3001\u9664\u7b97\u3001\u30bc\u30ed\u9664\u7b97\u3092\u9664\u304f) \u304c\u5b9a\u7fa9\u3055\u308c\u3001\u6709\u7406\u6570\u3001\u5b9f\u6570\u3001\u8907\u7d20\u6570\u306b\u671f\u5f85\u3055\u308c\u308b\u7279\u6027\u3092\u6301\u3064\u6570\u5024\u306e\u96c6\u5408\u3067\u3059\u3002<\/p>\n

\u6709\u9650\u4f53\u306b\u306f\u3001\u9806\u5e8f\u3068\u7279\u6027\u3068\u3044\u3046 2 \u3064\u306e\u91cd\u8981\u306a\u5c5e\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u9806\u5e8f\u306f\u4f53\u306b\u542b\u307e\u308c\u308b\u8981\u7d20\u306e\u7dcf\u6570\u3092\u6307\u3057\u3001\u7279\u6027\u306f\u4f53\u306e\u7b97\u8853\u6f14\u7b97\u3092\u6307\u793a\u3059\u308b\u7279\u6027\u3067\u3059\u3002\u7279\u306b\u3001\u6709\u9650\u4f53\u306e\u9806\u5e8f\u306f\u5e38\u306b\u7d20\u6570\u307e\u305f\u306f\u7d20\u6570\u306e\u7d2f\u4e57\u3067\u3059\u3002<\/p>\n

\u821e\u53f0\u88cf\uff1a\u6709\u9650\u4f53\u306e\u5185\u90e8\u69cb\u9020<\/h2>\n

\u6709\u9650\u4f53\u306e\u5185\u90e8\u69cb\u9020\u3067\u306f\u3001\u5404\u8981\u7d20\u3092\u5225\u306e\uff08\u30bc\u30ed\u3067\u306a\u3044\uff09\u8981\u7d20\u3067\u52a0\u7b97\u3001\u6e1b\u7b97\u3001\u4e57\u7b97\u3001\u307e\u305f\u306f\u9664\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u305d\u306e\u7d50\u679c\u3001\u540c\u3058\u304f\u4f53\u5185\u306b\u3042\u308b 3 \u756a\u76ee\u306e\u8981\u7d20\u304c\u751f\u6210\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u7279\u6027\u306f\u300c\u9589\u5305\u300d\u3068\u547c\u3070\u308c\u3001\u6709\u9650\u4f53\u306e\u6a5f\u80fd\u306b\u3068\u3063\u3066\u4e0d\u53ef\u6b20\u3067\u3059\u3002<\/p>\n

\u3055\u3089\u306b\u3001\u6709\u9650\u4f53\u306f\u7d50\u5408\u6cd5\u5247\u3001\u53ef\u63db\u6cd5\u5247\u3001\u5206\u914d\u6cd5\u5247\u3001\u5358\u4f4d\u5143\u306e\u5b58\u5728\u3001\u9006\u5143\u306e\u5b58\u5728\u3068\u3044\u3063\u305f\u6027\u8cea\u306b\u5f93\u3044\u307e\u3059\u3002\u672c\u8cea\u7684\u306b\u3001\u6709\u9650\u4f53\u306f\u6570\u5b66\u7684\u306b\u300c\u9069\u5207\u306b\u300d\u52d5\u4f5c\u3059\u308b\u305f\u3081\u3001\u3055\u307e\u3056\u307e\u306a\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u975e\u5e38\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n

\u6709\u9650\u4f53\u306e\u4e3b\u306a\u7279\u5fb4<\/h2>\n

\u6709\u9650\u4f53\u306e\u4e3b\u306a\u7279\u5fb4\u306b\u306f\u4ee5\u4e0b\u306e\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n

    \n
  1. \u72ec\u81ea\u6027<\/strong>: \u3059\u3079\u3066\u306e\u7d20\u6570\u7d2f\u4e57 q \u306b\u5bfe\u3057\u3066\u3001\u4f4d\u6570 q \u306e\u6709\u9650\u4f53\u306f\u672c\u8cea\u7684\u306b 1 \u3064\u3060\u3051\u5b58\u5728\u3057\u307e\u3059\u3002<\/li>\n
  2. \u52a0\u6cd5\u69cb\u9020\u3068\u4e57\u6cd5\u69cb\u9020<\/strong>: q = p^n \u3067\u3042\u308b q \u4f4d\u6570\u306e\u6709\u9650\u4f53\u306e\u52a0\u6cd5\u7fa4\u69cb\u9020\u306f\u3001p \u4f4d\u6570\u306e\u5de1\u56de\u7fa4\u306e n \u500b\u306e\u76f4\u548c\u306b\u540c\u578b\u3067\u3059\u3002\u975e\u30bc\u30ed\u5143\u306e\u4e57\u6cd5\u7fa4\u306f\u3001q-1 \u4f4d\u6570\u306e\u5de1\u56de\u7fa4\u3067\u3059\u3002<\/li>\n
  3. \u30b5\u30d6\u30d5\u30a3\u30fc\u30eb\u30c9\u306e\u5b58\u5728<\/strong>: q = p^n \u500b\u306e\u5143\u3092\u6301\u3064\u6709\u9650\u4f53\u306b\u306f\u3001n \u306e\u7d04\u6570 d \u3054\u3068\u306b\u30b5\u30d6\u30d5\u30a3\u30fc\u30eb\u30c9\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30b5\u30d6\u30d5\u30a3\u30fc\u30eb\u30c9\u306e\u305d\u308c\u305e\u308c\u306f\u3001\u591a\u9805\u5f0f x^(p^d) \u2013 x = 0 \u306e\u3059\u3079\u3066\u306e\u89e3\u306e\u96c6\u5408\u3067\u3059\u3002<\/li>\n<\/ol>\n

    \u7d71\u4e00\u306e\u4e2d\u306e\u591a\u69d8\u6027: \u6709\u9650\u4f53\u306e\u7a2e\u985e<\/h2>\n

    \u6709\u9650\u4f53\u306f\u4f4d\u6570\u306b\u57fa\u3065\u3044\u3066\u5206\u985e\u3055\u308c\u3001\u4f4d\u6570 q \u306e\u6709\u9650\u4f53\u306f\u901a\u5e38 GF(q) \u3068\u8868\u8a18\u3055\u308c\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u30012 \u3064\u306e\u5143\u3092\u6301\u3064\u6709\u9650\u4f53\u306f GF(2) \u3068\u8868\u8a18\u3055\u308c\u30013 \u3064\u306e\u5143\u3092\u6301\u3064\u6709\u9650\u4f53\u306f GF(3) \u3068\u8868\u8a18\u3055\u308c\u307e\u3059\u3002<\/p>\n

    \u6709\u9650\u4f53\u306e\u9806\u5e8f\u306f\u7d20\u6570\u306e\u7d2f\u4e57\u3067\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u305f\u3081\u3001\u6709\u9650\u4f53\u306e\u7a2e\u985e\u306f GF(p)\u3001GF(p^2)\u3001GF(p^3)\u3001GF(p^4) \u306a\u3069\u3068\u306a\u308a\u3001p \u306f\u7d20\u6570\u3067\u3059\u3002<\/p>\n\n\n\n\n\n\n\n\n\n\n
    \u30d5\u30a3\u30fc\u30eb\u30c9\u306e\u9806\u5e8f<\/th>\n\u6709\u9650\u4f53 (GF)<\/th>\n<\/tr>\n<\/thead>\n
    2<\/td>\nGF(2)<\/td>\n<\/tr>\n
    3<\/td>\nGF(3)<\/td>\n<\/tr>\n
    4<\/td>\nGF(4)<\/td>\n<\/tr>\n
    5<\/td>\nGF(5)<\/td>\n<\/tr>\n
    p<\/td>\nGF(p)<\/td>\n<\/tr>\n
    p^n<\/td>\nGF(p^n)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u6709\u9650\u4f53\u306e\u5fdc\u7528\u3068\u554f\u984c\u89e3\u6c7a<\/h2>\n

    \u6709\u9650\u4f53\u306f\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30b5\u30a4\u30a8\u30f3\u30b9\u3068\u30a8\u30f3\u30b8\u30cb\u30a2\u30ea\u30f3\u30b0\u3001\u7279\u306b\u30c7\u30fc\u30bf\u8ee2\u9001\u3068\u6697\u53f7\u5316\u30d7\u30ed\u30c8\u30b3\u30eb\u306b\u304a\u3044\u3066\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002\u6709\u9650\u4f53\u306f\u3001\u30c7\u30fc\u30bf\u8ee2\u9001\u306e\u30a8\u30e9\u30fc\u3092\u4fee\u6b63\u3059\u308b\u7b26\u53f7\u7406\u8ad6\u3084\u3001\u30a4\u30f3\u30bf\u30fc\u30cd\u30c3\u30c8\u4e0a\u3067\u306e\u5b89\u5168\u306a\u901a\u4fe1\u3092\u5b9f\u73fe\u3059\u308b\u6697\u53f7\u5316\u306b\u304a\u3044\u3066\u4e0d\u53ef\u6b20\u3067\u3059\u3002<\/p>\n

    \u6709\u9650\u4f53\u306e\u4f7f\u7528\u306b\u304a\u3051\u308b\u4e00\u822c\u7684\u306a\u8ab2\u984c\u306e 1 \u3064\u306f\u3001\u6f14\u7b97\u306e\u5b9f\u884c\u306b\u4f34\u3046\u8a08\u7b97\u306e\u8907\u96d1\u3055\u3067\u3059\u3002\u3053\u306e\u8907\u96d1\u3055\u306f\u3001\u7279\u306b\u5927\u304d\u306a\u4f53\u3067\u9855\u8457\u306b\u306a\u308a\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u3053\u306e\u554f\u984c\u306f\u3001\u6709\u9650\u4f53\u3067\u306e\u591a\u9805\u5f0f\u4e57\u7b97\u306b\u30eb\u30c3\u30af\u30a2\u30c3\u30d7 \u30c6\u30fc\u30d6\u30eb\u3084\u9ad8\u901f\u30d5\u30fc\u30ea\u30a8\u5909\u63db (FFT) \u306a\u3069\u306e\u9ad8\u901f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u8efd\u6e1b\u3055\u308c\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002<\/p>\n

    \u985e\u4f3c\u6982\u5ff5\u3068\u306e\u6bd4\u8f03\u5206\u6790<\/h2>\n

    \u6709\u9650\u4f53\u3068\u4ed6\u306e\u985e\u4f3c\u306e\u6982\u5ff5\u3092\u6bd4\u8f03\u3059\u308b\u5834\u5408\u3001\u6709\u9650\u4f53\u3068\u3001\u3088\u308a\u4e00\u822c\u7684\u306a\u4ee3\u6570\u69cb\u9020\u3067\u3042\u308b\u74b0\u3084\u7fa4\u3092\u533a\u5225\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002<\/p>\n\n\n\n\n\n\n\n\n\n\n
    \u30d1\u30e9\u30e1\u30fc\u30bf<\/th>\n\u6709\u9650\u4f53<\/th>\n\u6307\u8f2a<\/th>\n\u30b0\u30eb\u30fc\u30d7<\/th>\n<\/tr>\n<\/thead>\n
    \u9589\u9396<\/td>\n\u306f\u3044<\/td>\n\u306f\u3044<\/td>\n\u306f\u3044<\/td>\n<\/tr>\n
    \u7d50\u5408\u6027<\/td>\n\u306f\u3044<\/td>\n\u306f\u3044<\/td>\n\u306f\u3044<\/td>\n<\/tr>\n
    \u30a2\u30a4\u30c7\u30f3\u30c6\u30a3\u30c6\u30a3\u8981\u7d20<\/td>\n\u306f\u3044<\/td>\n\u306f\u3044<\/td>\n\u306f\u3044<\/td>\n<\/tr>\n
    \u9006\u6570<\/td>\n\u306f\u3044<\/td>\n\u306f\u3044\uff08\u6dfb\u52a0\u7269\uff09<\/td>\n\u306f\u3044<\/td>\n<\/tr>\n
    \u53ef\u63db\u6027<\/td>\n\u306f\u3044\uff08\u4e21\u65b9\u306e\u64cd\u4f5c\uff09<\/td>\n\u306f\u3044\uff08\u8ffd\u52a0\uff09<\/td>\n\u306f\u3044<\/td>\n<\/tr>\n
    \u5206\u914d\u6027<\/td>\n\u306f\u3044<\/td>\n\u306f\u3044<\/td>\n\u3044\u3044\u3048<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u6709\u9650\u4f53\u306b\u95a2\u3059\u308b\u5c06\u6765\u5c55\u671b<\/h2>\n

    \u5c06\u6765\u306e\u30c6\u30af\u30ce\u30ed\u30b8\u30fc\u306e\u5206\u91ce\u3067\u306f\u3001\u6709\u9650\u4f53\u304c\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3059\u3053\u3068\u304c\u671f\u5f85\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30c6\u30a3\u30f3\u30b0\u306f\u3001\u7279\u306b\u91cf\u5b50\u30a8\u30e9\u30fc\u8a02\u6b63\u3084\u6697\u53f7\u5316\u30b7\u30b9\u30c6\u30e0\u306b\u304a\u3044\u3066\u3001\u6709\u9650\u4f53\u306e\u539f\u7406\u304c\u4e0d\u53ef\u6b20\u3068\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u5206\u91ce\u3067\u3059\u3002<\/p>\n

    \u3055\u3089\u306b\u3001\u6a5f\u68b0\u5b66\u7fd2\u3068\u4eba\u5de5\u77e5\u80fd\u306e\u53f0\u982d\u306b\u3088\u308a\u3001\u6709\u9650\u4f53\u306f\u3001\u6e96\u540c\u578b\u6697\u53f7\u5316\u3084\u5b89\u5168\u306a\u30de\u30eb\u30c1\u30d1\u30fc\u30c6\u30a3\u8a08\u7b97\u306a\u3069\u3001\u7279\u306b\u30d7\u30e9\u30a4\u30d0\u30b7\u30fc\u3092\u4fdd\u8b77\u3059\u308b\u30c7\u30fc\u30bf\u5206\u6790\u306b\u304a\u3044\u3066\u65b0\u305f\u306a\u7528\u9014\u3092\u898b\u3064\u3051\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n

    \u6709\u9650\u4f53\u3068\u30d7\u30ed\u30ad\u30b7\u30b5\u30fc\u30d0\u30fc<\/h2>\n

    \u6709\u9650\u4f53\u306f\u30d7\u30ed\u30ad\u30b7 \u30b5\u30fc\u30d0\u30fc\u306b\u76f4\u63a5\u9069\u7528\u3055\u308c\u306a\u3044\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u30d7\u30ed\u30ad\u30b7 \u30b5\u30fc\u30d0\u30fc\u304c\u4f9d\u5b58\u3059\u308b\u5b89\u5168\u306a\u901a\u4fe1\u306b\u4f7f\u7528\u3055\u308c\u308b\u57fa\u790e\u6280\u8853\u306b\u304a\u3044\u3066\u57fa\u672c\u7684\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002<\/p>\n

    \u305f\u3068\u3048\u3070\u3001\u30d7\u30ed\u30ad\u30b7 \u30b5\u30fc\u30d0\u30fc\u306e\u4e3b\u8981\u6a5f\u80fd\u3067\u3042\u308b\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u4e0a\u306e\u30c7\u30fc\u30bf\u8ee2\u9001\u306e\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u4fdd\u8b77\u306b\u4f7f\u7528\u3055\u308c\u308b\u591a\u304f\u306e\u6697\u53f7\u5316\u30d7\u30ed\u30c8\u30b3\u30eb\u306f\u3001\u6709\u9650\u4f53\u6f14\u7b97\u306b\u4f9d\u5b58\u3057\u3066\u3044\u307e\u3059\u3002Web \u6697\u53f7\u5316\u306b\u5e83\u304f\u4f7f\u7528\u3055\u308c\u3066\u3044\u308b Secure Sockets Layer (SSL) \u3068 Transport Layer Security (TLS) \u306f\u3001\u6697\u53f7\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u304a\u3044\u3066\u6709\u9650\u4f53\u306e\u6570\u5b66\u7684\u7279\u6027\u306b\u4f9d\u5b58\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n

    \u95a2\u9023\u30ea\u30f3\u30af<\/h2>\n
      \n
    1. \u6709\u9650\u4f53: \u7406\u8ad6\u3068\u8a08\u7b97<\/a><\/li>\n
    2. \u73fe\u4ee3\u6697\u53f7\u306b\u304a\u3051\u308b\u6709\u9650\u4f53\u306e\u5f79\u5272<\/a><\/li>\n
    3. \u6709\u9650\u4f53\u3068\u305d\u306e\u5fdc\u7528<\/a><\/li>\n
    4. \u6709\u9650\u4f53\u6f14\u7b97\u3068\u6697\u53f7\u306b\u304a\u3051\u308b\u305d\u306e\u5f79\u5272<\/a><\/li>\n<\/ol>\n

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