{"id":398,"date":"2018-05-19T17:02:23","date_gmt":"2018-05-19T08:02:23","guid":{"rendered":"http:\/\/tamatoyaku.com\/b\/?p=398"},"modified":"2018-05-19T17:02:23","modified_gmt":"2018-05-19T08:02:23","slug":"398","status":"publish","type":"post","link":"https:\/\/p-0.me\/b\/p\/398\/","title":{"rendered":"SystemVerilog\u3067Montgomery ladder\u306e\u5b9f\u88c5"},"content":{"rendered":"<p>[mathjax]\u4ee5\u524d\u4f5c\u6210\u3057\u305f<a href=\"https:\/\/tamatoyaku.com\/b\/p\/378\">\u52a0\u7b97\u516c\u5f0f<\/a>\u3068<a href=\"https:\/\/tamatoyaku.com\/b\/p\/394\">\uff12\u500d\u7b97<\/a>\u3068\u3092\u7528\u3044\u3066Montgomery ladder\u306e\u5b9f\u88c5\u3092\u884c\u3063\u305f\uff0e<br \/>\n\u57fa\u672c\u7684\u306b\u306f\u52a0\u7b97\u516c\u5f0f\u3068\uff12\u500d\u7b97\u3092\uff0c\\(k\\)\u306e\u5404\u30d3\u30c3\u30c8\u306e\u5024\u306b\u5408\u308f\u305b\u3066\u9806\u7e70\u308a\u5b9f\u884c\u3059\u308b\uff0e<br \/>\n<!--more--><br \/>\n&nbsp;<br \/>\n<strong>1.\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9<\/strong><br \/>\n\u7279\u306b\u8907\u96d1\u306a<a href=\"https:\/\/en.wikipedia.org\/wiki\/Elliptic_curve_point_multiplication#Montgomery_ladder\">\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/a>\u3067\u306f\u306a\u3044\u306e\u3067\uff0c\u6700\u521d\u304b\u3089\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u3092\u793a\u3059\uff0e<br \/>\n\u306a\u304a\uff0c\u52a0\u7b97\u516c\u5f0f\u3068\uff12\u500d\u7b97\u306b\u3064\u3044\u3066\u306f\u30ea\u30bb\u30c3\u30c8\u95a2\u9023\u306e\u51e6\u7406\u3092\u5c11\u3057\u5909\u3048\u3066\u3044\u308b\uff0e<br \/>\n&nbsp;<br \/>\n<script src=\"https:\/\/gist.github.com\/pome1618\/93a735c40c206e415fa292a87d29247d.js\"><\/script><br \/>\n<script src=\"https:\/\/gist.github.com\/pome1618\/0969b25366e54247e3955542ad01b3c4.js\"><\/script><br \/>\n<script src=\"https:\/\/gist.github.com\/pome1618\/3cb918ce9c39920321dcafdd512306fd.js\"><\/script><br \/>\n<script src=\"https:\/\/gist.github.com\/pome1618\/ae286ba57725b6e8b514aff5b7bbb6bd.js\"><\/script><br \/>\n<script src=\"https:\/\/gist.github.com\/pome1618\/4fe9a648f06e2d496d9e1d0f54fa6c29.js\"><\/script><br \/>\n<script src=\"https:\/\/gist.github.com\/pome1618\/05bcdf422c2e29e028271b79df424f54.js\"><\/script><br \/>\n<script src=\"https:\/\/gist.github.com\/pome1618\/64e4ecbc4bb1b392ad6c199412be1d8f.js\"><\/script><br \/>\n<script src=\"https:\/\/gist.github.com\/pome1618\/0a526fc251d0f4e76825e8ab2bdf5838.js\"><\/script><br \/>\n&nbsp;<br \/>\n<strong>2.\u5fc5\u8981\u306a\u30af\u30ed\u30c3\u30af\u6570\u306b\u3064\u3044\u3066<\/strong><br \/>\n\u3053\u3053\u3067\uff0c\u52a0\u7b97\u516c\u5f0f\uff0c\uff12\u500d\u7b97\uff0cMontgomery ladder\u306e\u305d\u308c\u305e\u308c\u306b\u3064\u3044\u3066\u5fc5\u8981\u3068\u306a\u308b\u30af\u30ed\u30c3\u30af\u6570\u3092\u307e\u3068\u3081\u3066\u304a\u304f\uff0e<br \/>\n&nbsp;<br \/>\n<strong>2.1.\u52a0\u7b97\u516c\u5f0f\u306b\u5fc5\u8981\u306a\u30af\u30ed\u30c3\u30af\u6570<\/strong><\/p>\n<p style=\"padding-left: 30px;\">\u30ea\u30bb\u30c3\u30c8\u3000\uff11\u30af\u30ed\u30c3\u30af<\/p>\n<p style=\"padding-left: 30px;\">\u51e6\u7406\u3000\u3000\u3000\uff18\u30af\u30ed\u30c3\u30af<\/p>\n<p style=\"padding-left: 30px;\">\u51fa\u529b\u3000\u3000\u3000\uff11\u30af\u30ed\u30c3\u30af<\/p>\n<p style=\"padding-left: 30px;\">\u5408\u8a08\uff11\uff10\u30af\u30ed\u30c3\u30af\u3068\u306a\u308b\uff0e<\/p>\n<p style=\"padding-left: 30px;\"><a href=\"https:\/\/tamatoyaku.com\/b\/wp-content\/uploads\/2018\/05\/2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-399\" src=\"https:\/\/tamatoyaku.com\/b\/wp-content\/uploads\/2018\/05\/2-1024x280.png\" alt=\"\" width=\"1024\" height=\"280\" \/><\/a><\/p>\n<p>&nbsp;<br \/>\n&nbsp;<br \/>\n<strong>2.2.2\u500d\u7b97\u306b\u5fc5\u8981\u306a\u30af\u30ed\u30c3\u30af\u6570<\/strong><\/p>\n<p style=\"padding-left: 30px;\">\u30ea\u30bb\u30c3\u30c8\u3000\uff11\u30af\u30ed\u30c3\u30af<\/p>\n<p style=\"padding-left: 30px;\">\u51e6\u7406\u3000\u3000\u30007\u30af\u30ed\u30c3\u30af<\/p>\n<p style=\"padding-left: 30px;\">\u51fa\u529b\u3000\u3000\u3000\uff11\u30af\u30ed\u30c3\u30af<\/p>\n<p style=\"padding-left: 30px;\">\u5408\u8a089\u30af\u30ed\u30c3\u30af\u3068\u306a\u308b\uff0e<\/p>\n<p style=\"padding-left: 30px;\"><a href=\"https:\/\/tamatoyaku.com\/b\/wp-content\/uploads\/2018\/05\/3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-400\" src=\"https:\/\/tamatoyaku.com\/b\/wp-content\/uploads\/2018\/05\/3-1024x256.png\" alt=\"\" width=\"1024\" height=\"256\" \/><\/a><\/p>\n<p><strong>2.3.Montgomery ladder\u306b\u5fc5\u8981\u306a\u30af\u30ed\u30c3\u30af\u6570<\/strong><br \/>\n1\u30d3\u30c3\u30c8\u3042\u305f\u308a\u306f\uff0c<\/p>\n<p style=\"padding-left: 30px;\">\u30bb\u30c3\u30c8\u3000\u3000\uff11\u30af\u30ed\u30c3\u30af<\/p>\n<p style=\"padding-left: 30px;\">\u51e6\u7406\u3000\u3000\u3000\uff11\uff10\u30af\u30ed\u30c3\u30af<\/p>\n<p style=\"padding-left: 30px;\">\u53d6\u308a\u51fa\u3057\u3000\uff11\u30af\u30ed\u30c3\u30af<\/p>\n<p style=\"padding-left: 30px;\">\u5408\u8a08\uff11\uff12\u30af\u30ed\u30c3\u30af\u3068\u306a\u308b\uff0e<\/p>\n<p>\u3053\u3053\u3067\uff0c\u70b9\u3092\\(k\\)\u500d\u3059\u308b\u3068\u304d\u306b\uff0c\\(k\\)\u306e\u30d3\u30c3\u30c8\u6570\u3060\u3051\u51e6\u7406\u3092\u7e70\u308a\u8fd4\u3059\u306e\u3067\uff0c\\(k\\)\u306e\u30d3\u30c3\u30c8\u6570\u3092\\(b_k\\)\u3068\u3059\u308b\u3068\\(b_k\\times12\\)\u30af\u30ed\u30c3\u30af\u304b\u304b\u308b\u3053\u3068\u306b\u306a\u308b\uff0e<br \/>\n\u3055\u3089\u306b\uff0c\u7d50\u679c\u306e\u53d6\u308a\u51fa\u3057\u306b\uff11\u30af\u30ed\u30c3\u30af\u304b\u304b\u308b\u306e\u3067\uff0cMontgomery ladder\u306e\u30af\u30ed\u30c3\u30af\u6570\u306f\\(b_k\\times12+1\\)\u3068\u306a\u308b\uff0e<br \/>\nFPGA\u306e\u6700\u5927\u5468\u6ce2\u6570\u304c550MHz\u3060\u3068\u3059\u308b\u3068\uff0c\\((b_k\\times12+1)\\times1.818[ns]\\)\u3068\u306a\u308b\uff1f\uff1f\u307b\u3093\u3068\u304b\uff1f\uff1f<br \/>\n&nbsp;<br \/>\n<a href=\"https:\/\/tamatoyaku.com\/b\/wp-content\/uploads\/2018\/05\/4.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-401\" src=\"https:\/\/tamatoyaku.com\/b\/wp-content\/uploads\/2018\/05\/4-1024x287.png\" alt=\"\" width=\"1024\" height=\"287\" \/><\/a><br \/>\n&nbsp;<br \/>\n<strong>3.\u52d5\u4f5c\u78ba\u8a8d<\/strong><br \/>\n\u4eca\u56de\u30c6\u30b9\u30c8\u306b\u4f7f\u7528\u3057\u305f\u66f2\u7dda\u306f\\(y^2=x^3+84x^2+x,p=65521\\)\u3067\u3042\u308a\uff0c\u30d9\u30fc\u30b9\u30dd\u30a4\u30f3\u30c8\\(P=(58745,1)\\)\u3092<br \/>\n\\(k=12\\)\u500d\u3059\u308b\u8a08\u7b97\u3092\u30c6\u30b9\u30c8\u3068\u3057\u3066\u5b9f\u884c\u3057\u305f\uff0e\u306a\u304a\uff0c\\(12P=(48694,42622)\\)\u3067\u3042\u308b\uff0e<br \/>\n\u4ee5\u4e0b\u306bPARI\/GP\u3067\u8a08\u7b97\u3057\u305f\u7d50\u679c\u3068\u9014\u4e2d\u8a08\u7b97\u3092\u793a\u3059\uff0e<br \/>\n&nbsp;<br \/>\n<script src=\"https:\/\/gist.github.com\/pome1618\/ff654e78159767cd29d11e36247a5485.js\"><\/script><br \/>\n&nbsp;<br \/>\n\u4e0a\u8a18\u306e\u7d50\u679c\u3068\u30bf\u30a4\u30df\u30f3\u30b0\u30c1\u30e3\u30fc\u30c8\u3092\u898b\u6bd4\u3079\u308b\u3068\uff0c\u6b63\u3057\u304f\u5b9f\u884c\u3067\u304d\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308b\uff0e<br \/>\n&nbsp;<br \/>\n<strong>4.\u6b21\u56de\u3084\u308b\u3053\u3068<\/strong><br \/>\ny\u5ea7\u6a19\u306e\u5fa9\u5143<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[mathjax]\u4ee5\u524d\u4f5c\u6210\u3057\u305f\u52a0\u7b97\u516c\u5f0f\u3068\uff12\u500d\u7b97\u3068\u3092\u7528\u3044\u3066Montgomery ladder\u306e\u5b9f\u88c5\u3092\u884c\u3063\u305f\uff0e \u57fa\u672c\u7684\u306b\u306f\u52a0\u7b97\u516c\u5f0f\u3068\uff12\u500d\u7b97\u3092\uff0c\\(k\\)\u306e\u5404\u30d3\u30c3\u30c8\u306e\u5024\u306b\u5408\u308f\u305b\u3066\u9806\u7e70\u308a\u5b9f\u884c\u3059\u308b\uff0e<\/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-398","post","type-post","status-publish","format-standard","hentry","category-4"],"_links":{"self":[{"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/posts\/398","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=398"}],"version-history":[{"count":0,"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/posts\/398\/revisions"}],"wp:attachment":[{"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/media?parent=398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/categories?post=398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/p-0.me\/b\/wp-json\/wp\/v2\/tags?post=398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}