{"id":1185,"date":"2019-07-22T13:44:22","date_gmt":"2019-07-22T04:44:22","guid":{"rendered":"https:\/\/vongg.com\/?p=1185"},"modified":"2019-07-22T13:45:35","modified_gmt":"2019-07-22T04:45:35","slug":"diffie-hellman","status":"publish","type":"post","link":"https:\/\/vongg.com\/?p=1185","title":{"rendered":"Diffie-Hellman"},"content":{"rendered":"\n

Diffie-Hellman<\/p>\n\n\n\n

\nhttps:\/\/qiita.com\/okajima\/items\/036d7e751234f88fbe9a\n<\/div><\/figure>\n\n\n\n

\u3000\u3053\u3053\u3067\u3084\u3063\u3068\u672c\u984c\u3067\u3059\u3002
\u3000\u3044\u307e\u3001Alice\u3068Bob\u306e2\u4eba\u304cDiffie-Hellman\u3092\u4f7f\u3063\u3066\u9375\u4ea4\u63db\u3092\u3057\u3088\u3046\u3068\u3057\u307e\u3059\u3002\u6b21\u306e\u30b9\u30c6\u30c3\u30d7\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

(1) \u5927\u304d\u306a\u7d20\u6570 pp, \u5c0f\u3055\u306a\u9069\u5f53\u306a\u6574\u6570 xx \u3092\u7528\u610f\u3057\u3066\u304a\u304f\u3002\u3053\u308c\u306f\u516c\u958b\u3057\u3066\u69cb\u308f\u306a\u3044\u3002
\n(2a) Alice\u304c\u79d8\u5bc6\u306e aa \u3092, 2 \u4ee5\u4e0a pp \u672a\u6e80\u306e\u6574\u6570\u304b\u3089\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u3076\u3002
\n(3a) Alice\u306f E=xa mod pE=xa mod p \u3092\u8a08\u7b97\u3059\u308b\uff08\u3053\u308c\u304c\u30ab\u30f3\u30bf\u30f3\u306a\u3053\u3068\u306f\u3055\u3063\u304d\u78ba\u8a8d\u3057\u307e\u3057\u305f)\u3002\u305d\u306e\u7d50\u679c\u306e EE \u3092Bob\u306b\u9001\u308b\u3002
\n(2b) Bob\u304c\u79d8\u5bc6\u306e bb \u3092, 22\u4ee5\u4e0a pp \u672a\u6e80\u306e\u6574\u6570\u304b\u3089\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u3076\u3002
\n(3b) Bob\u306f F=xb mod pF=xb mod p \u3092\u8a08\u7b97\u3059\u308b\uff08\u3053\u308c\u304c\u30ab\u30f3\u30bf\u30f3\u306a\u3053\u3068\u306f\u3055\u3063\u304d\u78ba\u8a8d\u3057\u307e\u3057\u305f)\u3002\u305d\u306e\u7d50\u679c\u306e FF \u3092Alice\u306b\u9001\u308b\u3002<\/p>\n\n\n\n

(4a) Alice\u306f\u3001Bob\u304b\u3089\u53d7\u3051\u53d6\u3063\u305f FF \u3068\u3001\u81ea\u5206\u306e\u624b\u5143\u306b\u3042\u308b aa \u3092\u4f7f\u3063\u3066\u3001 Ga=Fa mod pGa=Fa mod p \u3092\u8a08\u7b97\u3059\u308b\u3002
\n(4b) Bob\u306f\u3001Alice\u304b\u3089\u53d7\u3051\u53d6\u3063\u305f EE \u3068\u3001\u81ea\u5206\u306e\u624b\u5143\u306b\u3042\u308b bb \u3092\u4f7f\u3063\u3066\u3001 Gb=Eb mod pGb=Eb mod p \u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n

\u3000\u3055\u3066\u3053\u306e\u7d50\u679c\u3001E \u3068 F\u3092\u6c42\u3081\u305f\u3068\u304d\u306e\u624b\u9806\u3092\u898b\u308c\u3070\u3001Ga=Gb=(xab) mod pGa=Gb=(xab) mod p \u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u308c\u3092Alice\u3068Bob\u306e\u5171\u901a\u9375\u306b\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3059\u3002<\/p>\n\n\n\n

\u3000\u56f3\u306b\u3059\u308b\u3068\u3053\u3046\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u3000\u4eee\u306b\u3053\u306e\u901a\u4fe1\u3092\u508d\u53d7\u3057\u3066\u3044\u308b\u60aa\u8005\u304c\u3044\u305f\u3068\u3057\u3066\u3082\u3001\u898b\u3048\u308b\u306e\u306f x,p,E,Fx,p,E,F \u306e\u307f\u3067\u3059\u3002\u305d\u3053\u304b\u3089 aa \u3084 bb \u3092\u9006\u7b97\u3059\u308b\u306e\u304c\u56f0\u96e3\u3067\u3042\u308b\u306e\u306f\u3055\u304d\u307b\u3069\u78ba\u8a8d\u3057\u305f\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n

SSH\u306e\u5834\u5408<\/p>\n\n\n\n

\u3000\u7533\u3057\u9045\u308c\u307e\u3057\u305f\u304c\u3001\u79c1\u306fPoderosa\u3068\u3044\u3046SSH\u30af\u30e9\u30a4\u30a2\u30f3\u30c8\u3092\u958b\u767a\u3057\u3066\u304a\u308a\u3001SSH\u30d7\u30ed\u30c8\u30b3\u30eb\u306b\u306f\u5b9f\u306f\u3051\u3063\u3053\u3046\u8a73\u3057\u3044\u306e\u3067\u3059\u3002\u6614\u306b\u672a\u8e0f\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u4e8b\u696d\u306b\u63a1\u629e\u3082\u3055\u308c\u307e\u3057\u305f\u304c\u3001\u305d\u306e\u5f8c\u653e\u7f6e\u671f\u9593\u3092\u7d4c\u30662016\u5e74\u306b\u5fa9\u6d3b\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u3000SSH\u3067\u306f\u3001\u3053\u306e\u8a08\u7b97\u306b\u304a\u3044\u3066 x = 2 \u3067\u56fa\u5b9a\u3055\u308c\u305f\u5024\u3092\u4f7f\u3063\u3066\u3044\u307e\u3059\u3002p\u306b\u3064\u3044\u3066\u306f\u300116\u9032\u6570\u3067<\/p>\n\n\n\n

FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE649286651ECE65381FFFFFFFFFFFFFFFF
\n(diffie-hellman-group1-sha1)<\/p>\n\n\n\n

\u3000\u3068\u3044\u3046\u5024\u304c\u9577\u3089\u304f\u4f7f\u308f\u308c\u3066\u304d\u307e\u3057\u305f\u304c\u3001\u6700\u8fd1\u306f\u3053\u306e\u7a0b\u5ea6\u3067\u306f\u8a08\u7b97\u6a5f\u30d1\u30ef\u30fc\u3067\u529b\u305a\u304f\u3067\u89e3\u3051\u3066\u3057\u307e\u3046\u5371\u967a\u304c\u9ad8\u307e\u3063\u305f\u306e\u3067\u3055\u3089\u306b\u5927\u304d\u306a<\/p>\n\n\n\n

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
\n(diffie-hellman-group14-sha1)<\/p>\n\n\n\n

\u3068\u3044\u3046\u3082\u306e\u3082\u4f7f\u308f\u308c\u3066\u3044\u307e\u3059\u3002\u4e16\u306e\u4e2d\u306e\u307b\u3068\u3093\u3069\u3059\u3079\u3066\u306eSSH\u63a5\u7d9a\u3067\u306f\u3001\u30ed\u30b0\u30a4\u30f3\u6642\u306b\u3053\u306e\u3069\u3061\u3089\u304b\u306e p \u3092\u4f7f\u3063\u3066\u3044\u308b\u306e\u3067\u3059\u3002\u3053\u306e\u5de8\u5927\u7d20\u6570\u306f\u4e16\u754c\u5171\u901a\u306e\u8cc7\u7523\u3068\u3044\u3048\u307e\u3059\u3002<\/p>\n\n\n\n

\u307e\u3068\u3081<\/p>\n\n\n\n

Diffie-Hellman\u9375\u4ea4\u63db\u306f\u3001\u508d\u53d7\u3055\u308c\u3066\u3044\u308b\u901a\u4fe1\u8def\u3092\u4f7f\u3063\u3066\u3082\u5b89\u5168\u306b\u901a\u4fe1\u76f8\u624b\u306b\u9375\u3092\u5c4a\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b
\n\u305d\u306e\u6839\u62e0\u306f\u3001 xy=z mod pxy=z mod p (p \u306f\u5927\u304d\u306a\u7d20\u6570)\u3000\u306b\u304a\u3044\u3066\u3001(x, y, p)\u304b\u3089 z\u3092\u6c42\u3081\u308b\u306e\u306f\u7c21\u5358\u3060\u304c(x, z, p)\u304b\u3089y\u3092\u6c42\u3081\u308b\u306e\u306f\u56f0\u96e3\u3068\u3044\u3046\u8a08\u7b97\u7406\u8ad6\u4e0a\u306e\u5b9a\u7406\u3067\u3042\u308b<\/p>\n\n\n\n

\u7a74<\/p>\n\n\n\n

\u3000Diffie-Hellman\u9375\u4ea4\u63db\u304c\u62c5\u5f53\u3059\u308b\u306e\u306f\u3042\u304f\u307e\u3067\u3082\u901a\u4fe1\u306e\u508d\u53d7\u306b\u5bfe\u3059\u308b\u8010\u6027\u3067\u3059\u3002\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u306b\u304a\u3044\u3066\u306f\u5225\u306e\u554f\u984c\u3082\u3044\u308d\u3044\u308d\u3042\u308b\u306e\u3067\u3001\u6c7a\u3057\u3066\u4e07\u80fd\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u4f8b\u3048\u3070\u3001Alice\u304c\u901a\u4fe1 \u3057\u3066\u3044\u308b\u76f8\u624b\u306fBob\u3067\u306f\u306a\u304f\u300cBob\u306e\u3075\u308a\u3092\u3057\u305f\u60aa\u8005\u300d\u3060\u3063\u305f\u5834\u5408\u306f\u6975\u3081\u3066\u5371\u967a\u3067\u3059\u3002
\n\u3000\u307e\u305f\u3001\u8a08\u7b97\u7406\u8ad6\u306e\u5b9a\u7406\u3082\u5c06\u6765\u306f\u5d29\u3055\u308c\u308b\u5371\u967a\u304c\u3042\u308a\u307e\u3059\u3002\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u3088\u3046\u306a\u3001\u3053\u308c\u307e\u3067\u3068\u306f\u6b21\u5143\u306e\u7570\u306a\u308b\u8a08\u7b97\u624b\u6bb5\u304c\u5b9f\u7528\u5316\u3055\u308c\u305f\u5834\u5408\u3001\u4e00\u767a\u3067\u524d\u63d0\u304c\u3072\u3063\u304f\u308a\u8fd4\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u78ba\u7387\u306f\u3068\u3066\u3082\u4f4e\u3044\u3067\u3059\u304c\u3001\uff10\u3067\u306f\u3042\u308a\u307e\u305b\u3093\uff01<\/p>\n","protected":false},"excerpt":{"rendered":"

Diffie-Hellman \u3000\u3053\u3053\u3067\u3084\u3063\u3068\u672c\u984c\u3067\u3059\u3002 \u3000\u3044\u307e\u3001Alice\u3068Bob\u306e2\u4eba\u304cDiffie-Hel […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[142],"tags":[],"_links":{"self":[{"href":"https:\/\/vongg.com\/index.php?rest_route=\/wp\/v2\/posts\/1185"}],"collection":[{"href":"https:\/\/vongg.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vongg.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vongg.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vongg.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1185"}],"version-history":[{"count":2,"href":"https:\/\/vongg.com\/index.php?rest_route=\/wp\/v2\/posts\/1185\/revisions"}],"predecessor-version":[{"id":1187,"href":"https:\/\/vongg.com\/index.php?rest_route=\/wp\/v2\/posts\/1185\/revisions\/1187"}],"wp:attachment":[{"href":"https:\/\/vongg.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vongg.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vongg.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}