{"id":375,"date":"2018-05-02T11:34:55","date_gmt":"2018-05-02T02:34:55","guid":{"rendered":"http:\/\/tamatoyaku.com\/b\/?p=375"},"modified":"2018-05-02T11:34:55","modified_gmt":"2018-05-02T02:34:55","slug":"375","status":"publish","type":"post","link":"https:\/\/p-0.me\/b\/p\/375\/","title":{"rendered":"\u5b9f\u88c5\u306b\u5fc5\u8981\u3068\u306a\u308b\u6f14\u7b97\u5668\u306e\u6570"},"content":{"rendered":"

[mathjax]ECDSA\u3092FPGA\u4e0a\u3067\u5b9f\u88c5\u3059\u308b\u306b\u3042\u305f\u308a\uff0c\u5c04\u5f71\u5ea7\u6a19\u3067\u306e\u52a0\u7b97\u30682\u500d\u7b97\u306b\u5fc5\u8981\u3068\u306a\u308b\u6f14\u7b97\u5668\u306e\u6570\u306e\u691c\u8a3c\uff0e
\nMontgomery ladder\u3067\u306f\u52a0\u7b97\u30682\u500d\u7b97\u3092\u540c\u6642\u306b\u72ec\u7acb\u3057\u3066\u5b9f\u884c\u3059\u308b\u305f\u3081\uff0c\u52a0\u7b97\u30682\u500d\u7b97\u306b\u3064\u3044\u3066\u306f\u5225\u3005\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u3068\u8003\u3048\u308b\uff0e
\n\u6ce8\uff1a\u3053\u308c\u3068\u6b21\u306e\u8a18\u4e8b<\/a>\u3092\u30bc\u30df\u8cc7\u6599\u3068\u3057\u3066\u30b9\u30e9\u30a4\u30c9<\/a>\u306b\u307e\u3068\u3081\u305f\uff0e
\n
\n 
\n1.\u52a0\u7b97<\/strong>
\n\u4ee5\u4e0b\u306b\u52a0\u7b97\u306b\u3064\u3044\u3066\uff0c\\((X_{m+n},Z_{m+n})=(X_m,Z_m)+(X_n,Z_n)\\)\u306e\u5f0f\u3092\u793a\u3059\uff0e
\n 
\n$$ X_{m+n}=Z_{m-n}((X_m-Z_m)(X_n+Z_n)+(X_m+Z_m)(X_n-Z_n))^2 $$
\n$$ Z_{m+n}=X_{m-n}((X_m-Z_m)(X_n+Z_n)-(X_m+Z_m)(X_n-Z_n))^2 $$
\n 
\n\u4e0a\u8a18\u306e\u5f0f\u3092\u5143\u306b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u8003\u3048\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\uff0e\u306a\u304a\uff0c\u3053\u3053\u3067\u306fMontgomery ladder\u3067\u4f7f\u7528\u3059\u308b\u3053\u3068\u3092\u60f3\u5b9a\u3057\u3066\u3044\u308b\u305f\u3081\\(m-n=1\\)\u3068\u306a\u308a\uff0c\\(X_{m-n},Z_{m-n}\\)\u306f\\(X_1,Z_1\\)\u3068\u4eee\u5b9a\u3059\u308b\uff0e
\n\u307e\u305f\uff0c\u3053\u3053\u3067\u306f\u307e\u3060\u30ec\u30b8\u30b9\u30bf\u306b\u95a2\u3057\u3066\u306f\u8003\u3048\u306a\u3044\u305f\u3081\uff0c\u4fbf\u5b9c\u7684\u306b\\(a_1\\)\u304b\u3089\\(d_2\\)\u3092\u4f7f\u7528\u3057\u3066\u3044\u308b\uff0e
\n 
\nstep1<\/p>\n

1.1.\u00a0 \\(a_1=X_m+Z_m\\)<\/p>\n

1.2.\u00a0 \\(a_2=X_m-Z_m\\)<\/p>\n

1.3.\u00a0 \\(a_3=X_n+Z_n\\)<\/p>\n

1.4.\u00a0 \\(a_4=X_n-Z_n\\)<\/p>\n

step2<\/p>\n

2.1.\u00a0 \\(b_1=a_2*a_3\\)<\/p>\n

2.2.\u00a0 \\(b_2=a_1*a_4\\)<\/p>\n

step3<\/p>\n

3.1.\u00a0 \\(c_1=b_1+b_2\\)<\/p>\n

3.2.\u00a0 \\(c_2=b_1-b_2\\)<\/p>\n

step4<\/p>\n

4.1.\u00a0 \\(d_1=c_1*c_1\\)<\/p>\n

4.2.\u00a0 \\(d_2=c_2*c_2\\)<\/p>\n

step5<\/p>\n

5.1.\u00a0 \\(e_1=Z_1*d_1\\)<\/p>\n

5.2.\u00a0 \\(e_2=X_1*d_2\\)<\/p>\n

\u5404\u30b9\u30c6\u30c3\u30d7\u5185\u306f\u72ec\u7acb\u3057\u3066\u5b9f\u884c\u3067\u304d\u308b\uff0e\u305d\u306e\u305f\u3081\uff0c\u5404\u30b9\u30c6\u30c3\u30d7\u5185\u3092\u4e26\u5217\u306b\u52d5\u4f5c\u3055\u305b\u308b\u3053\u3068\u3067\u51e6\u7406\u306e\u9ad8\u901f\u5316\u3092\u56f3\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e
\n\u3057\u304b\u3057\uff0cLE\u6570(\u56de\u8def\u9762\u7a4d)\u306b\u306f\u5236\u9650\u304c\u3042\u308b\u305f\u3081\uff0c\u3088\u308a\u5c11\u306a\u3044\u6f14\u7b97\u5668\u306e\u500b\u6570\u3067\u3088\u308a\u9ad8\u901f\u306b\u51e6\u7406\u3092\u5b8c\u4e86\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u305f\u3044\uff0e
\n\u4ee5\u4e0b\u306b\u5404\u30b9\u30c6\u30c3\u30d7\u3054\u3068\u306b\u5fc5\u8981\u3068\u306a\u308b\u6f14\u7b97\u5668\u306e\u6570\u3092\u793a\u3059\uff0e<\/p>\n\n\n\n\n\n\n\n\n
<\/td>\n+<\/td>\n–<\/td>\n*<\/td>\n\/<\/td>\n<\/tr>\n
step1<\/td>\n2<\/td>\n2<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
step2<\/td>\n<\/td>\n<\/td>\n2<\/td>\n<\/td>\n<\/tr>\n
step3<\/td>\n1<\/td>\n1<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
step4<\/td>\n<\/td>\n<\/td>\n2<\/td>\n<\/td>\n<\/tr>\n
step5<\/td>\n<\/td>\n<\/td>\n2<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u3053\u3053\u3067\uff0c\u52a0\u6e1b\u7b97\u5668\u30922\u3064\uff0c\u4e57\u7b97\u5668\u30921\u3064\u3068\u3057\u3066\u30b9\u30b1\u30b8\u30e5\u30fc\u30eb\u3092\u8003\u3048\u3066\u307f\u308b\uff0e\u3059\u308b\u3068\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\uff0e<\/p>\n\n\n\n\n\n\n
time1<\/td>\ntime2<\/td>\ntime3<\/td>\ntime4<\/td>\ntime5<\/td>\ntime6<\/td>\ntime7<\/td>\ntime8<\/td>\n<\/tr>\n
+<\/td>\n+<\/td>\n*<\/td>\n+<\/td>\n*<\/td>\n*<\/td>\n*<\/td>\n*<\/td>\n<\/tr>\n
–<\/td>\n–<\/td>\n<\/td>\n–<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
<\/td>\n*<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u3088\u3063\u3066\uff0c\u52a0\u6e1b\u7b97\u5668\u30922\u3064\uff0c\u4e57\u7b97\u5668\u30921\u3064\u3067\u306f8\u30b9\u30c6\u30c3\u30d7\u3067\u51e6\u7406\u3092\u5b8c\u4e86\u3067\u304d\u308b\u3053\u3068\u304c\u5206\u304b\u308b\uff0e\u306a\u304a\uff0c\u52a0\u6e1b\u7b97\u5668\u30922\u3064\u3068\u4e57\u7b97\u5668\u30922\u3064\u3067\u306f5\u30b9\u30c6\u30c3\u30d7\uff0c\u52a0\u6e1b\u7b97\u5668\u30924\u3064\u3068\u4e57\u7b97\u5668\u30922\u3064\u3067\u30825\u30b9\u30c6\u30c3\u30d7\u3068\u306a\u308b\uff0e
\n\u4e57\u7b97\u5668\u306b\u3064\u3044\u3066\u306f\u5fc5\u8981\u3068\u306a\u308bLE\u6570\u304c\u591a\u304f\uff0c\u52a0\u6e1b\u7b97\u5668\u3060\u3051\u30924\u3064\u306b\u3057\u305f\u5834\u5408\u30828\u30b9\u30c6\u30c3\u30d7\u3067\u5909\u308f\u3089\u306a\u3044\u305f\u3081\uff0c\u52a0\u6e1b\u7b97\u5668\u30922\u3064\u3068\u4e57\u7b97\u5668\u30921\u3064\u3092\u4f7f\u30448\u30b9\u30c6\u30c3\u30d7\u3067\u5b9f\u884c\u3059\u308b\u3053\u3068\u304c\u9069\u3057\u3066\u3044\u308b\u3068\u8003\u3048\u308b\uff0e
\n 
\n 
\n2.2\u500d\u7b97<\/strong>
\n\u4ee5\u4e0b\u306b2\u500d\u7b97\u306b\u3064\u3044\u3066\uff0c\\((X_{2n},Z_{2n})=2(X_n,Z_n)\\)\u306e\u5f0f\u3092\u793a\u3059\uff0e
\n 
\n$$4X_nZ_n=(X_n+Z_n)^2-(X_n-Z_n)^2$$
\n$$X_{2n}=(X_n+Z_n)^2(X_n-Z_n)^2$$
\n$$Z_{2n}=4X_nZ_n((X_n-Z_n)^2+((A+2)\/4)(4X_nZ_n))$$
\n 
\n\u4e0a\u8a18\u306e\u5f0f\u3092\u5143\u306b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u8003\u3048\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\uff0e
\n 
\nstep1<\/p>\n

1.1.\u00a0 \\(a_1=X_n+Z_n\\)<\/p>\n

1.2.\u00a0 \\(a_2=X_n-Z_n\\)<\/p>\n

1.1.\u00a0 \\(a_3=A+2\\)<\/p>\n

step2<\/p>\n

2.1.\u00a0 \\(b_1=a_1*a_1\\)<\/p>\n

2.2.\u00a0 \\(b_2=a_2*a_2\\)<\/p>\n

2.3.\u00a0 \\(b_3=a_3\/4\\)<\/p>\n

step3<\/p>\n

3.1.\u00a0 \\(c_1=b_1-b_2\\)<\/p>\n

3.2.\u00a0 \\(c_2=b_1*b_2\\)<\/p>\n

step4<\/p>\n

4.1.\u00a0 \\(d_1=b_1-b_2\\)<\/p>\n

step5<\/p>\n

5.1.\u00a0 \\(e_1=b_2+d_1\\)<\/p>\n

step6<\/p>\n

6.1.\u00a0 \\(f_1=c_1*e_1\\)<\/p>\n

\u5404\u30b9\u30c6\u30c3\u30d7\u3067\u5fc5\u8981\u3068\u306a\u308b\u6f14\u7b97\u5668\u3092\u4ee5\u4e0b\u306b\u793a\u3059\uff0e<\/p>\n\n\n\n\n\n\n\n\n\n
<\/td>\n+<\/td>\n–<\/td>\n*<\/td>\n\/<\/td>\n<\/tr>\n
step1<\/td>\n2<\/td>\n1<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
step2<\/td>\n<\/td>\n<\/td>\n2<\/td>\n1<\/td>\n<\/tr>\n
step3<\/td>\n<\/td>\n1<\/td>\n1<\/td>\n<\/td>\n<\/tr>\n
step4<\/td>\n<\/td>\n<\/td>\n1<\/td>\n<\/td>\n<\/tr>\n
step3<\/td>\n1<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
step4<\/td>\n<\/td>\n<\/td>\n1<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u4e0a\u8a18\u306e\u56f3\u3092\u5143\u306b\u30b9\u30b1\u30b8\u30e5\u30fc\u30eb\u3092\u8003\u3048\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\uff0e<\/p>\n\n\n\n\n\n\n
time1<\/td>\ntime2<\/td>\ntime3<\/td>\ntime4<\/td>\ntime5<\/td>\ntime6<\/td>\ntime7<\/td>\n<\/tr>\n
+<\/td>\n+<\/td>\n*<\/td>\n–<\/td>\n*<\/td>\n+<\/td>\n*<\/td>\n<\/tr>\n
–<\/td>\n*<\/td>\n<\/td>\n*<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
<\/td>\n\/<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u3088\u3063\u3066\uff0c\u52a0\u6e1b\u7b97\u56682\u3064\uff0c\u4e57\u7b97\u56681\u3064\uff0c\u9664\u7b97\u56681\u3064\u306e\u5834\u54087\u30b9\u30c6\u30c3\u30d7\u3067\u5b8c\u4e86\u3067\u304d\u308b\uff0e
\n 
\n 
\n3.\u4eca\u5f8c\u306e\u8a71<\/strong>
\n\u4eca\u5f8c\u306f\u3053\u308c\u3092\u3082\u3068\u306b\u8a2d\u8a08\u3092\u8003\u3048\u3066\u307f\u308b\uff0e\u8a2d\u8a08\u5f8c\uff0cHDL\u3067\u8a18\u8ff0\u3092\u884c\u3044\u52a0\u7b97\u30682\u500d\u7b97\u306b\u3064\u3044\u3066\u30e2\u30b8\u30e5\u30fc\u30eb\u5316\u3092\u884c\u3044\uff0c\u30c6\u30b9\u30c8\u3092\u884c\u3046\uff0e
\n\u306a\u304a\uff0cmod p\u3084mod l\u306b\u3064\u3044\u3066\u306f\u5225\u9014\u8003\u3048\u308b\uff0emod\u306b\u3064\u3044\u3066\u306f\u6f14\u7b97\u5668\u306e\u5f8c\u308d\u306b\u3064\u304f\u3053\u3068\u306b\u306a\u308b\u304b\u3082\u3057\u308c\u306a\u3044\uff0e
\n <\/p>\n","protected":false},"excerpt":{"rendered":"

[mathjax]ECDSA\u3092FPGA\u4e0a\u3067\u5b9f\u88c5\u3059\u308b\u306b\u3042\u305f\u308a\uff0c\u5c04\u5f71\u5ea7\u6a19\u3067\u306e\u52a0\u7b97\u30682\u500d\u7b97\u306b\u5fc5\u8981\u3068\u306a\u308b\u6f14\u7b97\u5668\u306e\u6570\u306e\u691c\u8a3c\uff0e Montgomery ladder\u3067\u306f\u52a0\u7b97\u30682\u500d\u7b97\u3092\u540c\u6642\u306b\u72ec\u7acb\u3057\u3066\u5b9f\u884c\u3059\u308b\u305f\u3081\uff0c\u52a0\u7b97\u30682\u500d\u7b97\u306b\u3064\u3044\u3066\u306f\u5225 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-375","post","type-post","status-publish","format-standard","hentry","category-4"],"_links":{"self":[{"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/posts\/375","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/comments?post=375"}],"version-history":[{"count":0,"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/posts\/375\/revisions"}],"wp:attachment":[{"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/media?parent=375"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/categories?post=375"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/tags?post=375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}