{"id":3220,"date":"2020-07-24T13:13:15","date_gmt":"2020-07-24T09:43:15","guid":{"rendered":"https:\/\/actobit.com\/actomag\/?p=3220"},"modified":"2020-11-25T18:32:02","modified_gmt":"2020-11-25T15:02:02","slug":"rsa","status":"publish","type":"post","link":"https:\/\/actobit.com\/actomag\/1399\/rsa\/","title":{"rendered":"\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 RSA \u0686\u06cc\u0633\u062a\u061f"},"content":{"rendered":"<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 <a data-toggle=\"tooltip\" data-placement=\"top\" class=\"post-tooltip tooltip-top\" title=\"Rivest\u2013Shamir\u2013Adleman\">RSA<\/a> \u0627\u0632 \u0627\u0648\u0644\u06cc\u0646 \u0634\u06cc\u0648\u0647 \u0647\u0627\u06cc \u0631\u0645\u0632\u0646\u06af\u0627\u0631\u06cc \u0628\u0647 \u0631\u0648\u0634 \u06a9\u0644\u06cc\u062f \u0639\u0645\u0648\u0645\u06cc (\u0631\u0645\u0632\u0646\u06af\u0627\u0631\u06cc \u0646\u0627\u0645\u062a\u0642\u0627\u0631\u0646) \u0627\u0633\u062a \u06a9\u0647 \u0628\u0635\u0648\u0631\u062a \u06af\u0633\u062a\u0631\u062f\u0647 \u0628\u0631\u0627\u06cc \u062a\u0627\u0645\u06cc\u0646 \u0627\u0645\u0646\u06cc\u062a \u0627\u0646\u062a\u0642\u0627\u0644 \u062f\u0627\u062f\u0647 \u0627\u0632 \u0637\u0631\u06cc\u0642 <a href=\"https:\/\/actobit.com\/actomag\/1399\/ssl\/\" target=\"_blank\" rel=\"noopener noreferrer\"><span style=\"color: #0000ff;\">SSL<\/span> <\/a>\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u0627\u06cc\u0646 \u0631\u0648\u0634\u060c \u0646\u062e\u0633\u062a\u06cc\u0646 \u0631\u0648\u0634 \u0645\u0648\u0631\u062f \u0627\u0639\u062a\u0645\u0627\u062f \u062f\u0631 \u0628\u06cc\u0646 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0631\u0645\u0632\u0646\u06af\u0627\u0631\u06cc \u062f\u06cc\u06af\u0631 \u0627\u0633\u062a \u0648 \u06cc\u06a9\u06cc \u0627\u0632 \u0628\u0632\u0631\u06af\u200c\u062a\u0631\u06cc\u0646 \u067e\u06cc\u0634\u0631\u0641\u062a\u200c\u0647\u0627 \u062f\u0631 \u0632\u0645\u06cc\u0646\u0647\u0654 \u0631\u0645\u0632\u0646\u06af\u0627\u0631\u06cc \u0628\u0647 \u062d\u0633\u0627\u0628 \u0645\u06cc\u200c\u0622\u06cc\u062f. \u0622\u0631\u0627\u0633\u200c\u0627\u06cc \u0647\u0645\u0686\u0646\u0627\u0646 \u0628\u0647 \u0635\u0648\u0631\u062a \u06af\u0633\u062a\u0631\u062f\u0647\u200c\u0627\u06cc \u062f\u0631 \u062a\u0628\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u06a9\u062a\u0631\u0648\u0646\u06cc\u06a9\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u062f\u0631 \u0635\u0648\u0631\u062a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062f\u0631\u0633\u062a \u0628\u0627 \u06a9\u0644\u06cc\u062f\u0647\u0627\u06cc \u0637\u0648\u0644\u0627\u0646\u06cc \u06a9\u0627\u0645\u0644\u0627\u064b \u0627\u0645\u0646 \u0645\u06cc \u0628\u0627\u0634\u062f.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u062d\u0631\u0648\u0641 \u0627\u0648\u0644\u06cc\u0647 RSA\u060c \u062d\u0631\u0648\u0641 \u0627\u0648\u0644\u06cc\u0647 \u0646\u0627\u0645 \u0647\u0627\u06cc \u062e\u0627\u0646\u0648\u0627\u062f\u06af\u06cc Ron RIvest \u060c Adi Shamir \u0648 Adleman \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0633\u0627\u0644 \u06f1\u06f9\u06f7\u06f7 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u0628\u0637\u0648\u0631 \u0639\u0645\u0648\u0645\u06cc \u0645\u0639\u0631\u0641\u06cc \u06a9\u0631\u062f\u0646\u062f. \u06cc\u06a9 \u0631\u06cc\u0627\u0636\u06cc \u062f\u0627\u0646 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc \u0628\u0647 \u0646\u0627\u0645 Clifford Cocks\u060c \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0633\u062a\u0627\u062f \u0627\u0631\u062a\u0628\u0627\u0637\u0627\u062a \u062f\u0648\u0644\u062a \u0628\u0631\u06cc\u062a\u0627\u0646\u06cc\u0627 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0631\u062f\u060c \u0633\u06cc\u0633\u062a\u0645\u06cc \u0645\u0639\u0627\u062f\u0644 \u0627\u06cc\u0646 \u0633\u06cc\u0633\u062a\u0645 \u0631\u0627 \u062f\u0631 \u0633\u0627\u0644 \u06f1\u06f9\u06f7\u06f3 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u06a9\u0631\u062f\u0647 \u0628\u0648\u062f\u060c \u06a9\u0647 \u062a\u0627 \u0633\u0627\u0644 \u06f1\u06f9\u06f7\u06f3 \u0628\u0635\u0648\u0631\u062a \u0645\u062d\u0631\u0645\u0627\u0646\u0647 \u0628\u0627\u0642\u06cc \u0645\u0627\u0646\u062f.<\/strong><\/span><\/p>\n<h2><strong><span style=\"color: #ff0000;\">\u0631\u0648\u0634 \u0639\u0645\u0644\u06a9\u0631\u062f RSA<\/span><\/strong><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0641\u0631\u0633\u062a\u0646\u062f\u0647 \u067e\u06cc\u0627\u0645 \u062c\u0641\u062a \u0639\u062f\u062f \u0635\u062d\u06cc\u062d \u0648 \u0628\u0632\u0631\u06af (e,n) \u0631\u0627 \u0628\u0639\u0646\u0648\u0627\u0646 \u06a9\u0644\u06cc\u062f \u0639\u0645\u0648\u0645\u06cc \u0628\u0631\u0627\u06cc \u0631\u0645\u0632\u0646\u06af\u0627\u0631\u06cc \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u062e\u0648\u062f \u062f\u0631 \u0627\u062e\u062a\u06cc\u0627\u0631 \u062f\u0627\u0631\u062f. \u062f\u0631 \u0637\u0631\u0641 \u0645\u0642\u0627\u0628\u0644 \u060c\u06af\u06cc\u0631\u0646\u062f\u0647 \u0646\u06cc\u0632 \u062c\u0641\u062a \u0639\u062f\u062f (d,n) \u0631\u0627 \u0628\u0631\u0627\u06cc \u0631\u0645\u0632\u06af\u0634\u0627\u06cc\u06cc \u067e\u06cc\u0627\u0645 \u0628\u06a9\u0627\u0631 \u0645\u06cc \u0628\u0631\u062f. \u0628\u062f\u06cc\u0647\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0648 \u062c\u0641\u062a \u0639\u062f\u062f (e,n) \u0648 (d,n) \u0628\u0627 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0627\u0631\u062a\u0628\u0627\u0637 \u0632\u06cc\u0631\u06a9\u0627\u0646\u0647 \u0627\u06cc \u062f\u0627\u0631\u0646\u062f \u0648\u0644\u06cc \u0628\u06af\u0648\u0646\u0647 \u0627\u06cc \u0646\u06cc\u0633\u062a \u06a9\u0647 \u0628\u062a\u0648\u0627\u0646 \u0628\u0627 \u062f\u0631 \u0627\u062e\u062a\u06cc\u0627\u0631 \u062f\u0627\u0634\u062a\u0646 e \u0648 n \u0628\u0631\u0627\u062d\u062a\u06cc d \u0631\u0627 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u06a9\u0631\u062f. \u0628\u0627 \u0641\u0631\u0636 \u0648\u062c\u0648\u062f \u0686\u0646\u06cc\u0646 \u06a9\u0644\u06cc\u062f \u0647\u0627\u06cc\u06cc\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 RSA \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u0633\u0627\u062f\u06af\u06cc \u0628\u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/strong><\/span><\/p>\n<ul>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u067e\u06cc\u0627\u0645\u06cc \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0631\u0645\u0632 \u0634\u0648\u062f \u0628\u0647 \u0628\u0644\u0648\u06a9\u0647\u0627\u06cc K \u06a9\u0627\u0631\u0627\u06a9\u062a\u0631\u06cc (k \u0628\u0627\u06cc\u062a\u06cc) \u062a\u0642\u0633\u06cc\u0645 \u0628\u0646\u062f\u06cc \u0645\u06cc \u0634\u0648\u062f.<\/strong><\/span><\/li>\n<li style=\"text-align: justify;\"><strong style=\"color: #000000;\">\u0647\u0631 \u0628\u0644\u0648\u06a9 \u0637\u0628\u0642 \u0642\u0627\u0639\u062f\u0647 \u0627\u06cc \u06a9\u0627\u0645\u0644\u0627 \u062f\u0644\u062e\u0648\u0627\u0647 \u0628\u0647 \u06cc\u06a9 \u0639\u062f\u062f \u0635\u062d\u06cc\u062d \u0628\u0647 \u0646\u0627\u0645 Pi \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc \u06af\u0631\u062f\u062f.<\/strong><\/li>\n<li style=\"text-align: justify;\"><strong style=\"color: #000000;\">\u0628\u0627 \u062c\u0641\u062a \u0639\u062f\u062f (e,n) \u0628\u0647 \u0627\u0632\u0627\u06cc \u06cc\u06a9\u0627\u06cc\u06a9 \u0628\u0644\u0648\u06a9\u0647\u0627\u06cc Pi \u0627\u0639\u062f\u0627\u062f \u062c\u062f\u06cc\u062f\u06cc \u0637\u0628\u0642 \u0631\u0627\u0628\u0637\u0647 \u0632\u06cc\u0631 \u0628\u062f\u0633\u062a \u0645\u06cc \u0622\u06cc\u0646\u062f:<\/strong><\/li>\n<\/ul>\n<p dir=\"ltr\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Ci = (Pi )e mod n<\/strong><\/span><\/p>\n<ul>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u06a9\u062f\u0647\u0627\u06cc Ci \u0628\u062c\u0627\u06cc \u06a9\u062f\u0647\u0627\u06cc \u0627\u0635\u0644\u06cc Pi \u0627\u0631\u0633\u0627\u0644 \u0645\u06cc \u0634\u0648\u0646\u062f.<\/strong><\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u0631\u0648\u0634 \u0631\u0645\u0632\u06af\u0634\u0627\u06cc\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627 \u062f\u0642\u06cc\u0642\u0627 \u0645\u062b\u0644 \u0631\u0648\u0634 \u0631\u0645\u0632\u0646\u06af\u0627\u0631\u06cc \u0627\u0633\u062a \u06cc\u0639\u0646\u06cc \u0628\u0627 \u062f\u0627\u0634\u062a\u0646 \u062c\u0641\u062a \u0639\u062f\u062f (d,n) \u0628\u0644\u0648\u06a9\u0647\u0627\u06cc \u0631\u0645\u0632 \u0634\u062f\u0647 \u0628\u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0627\u0632 \u0631\u0645\u0632 \u062e\u0627\u0631\u062c \u0645\u06cc \u0634\u0648\u0646\u062f:<\/strong><\/span><\/p>\n<p dir=\"ltr\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Pi = ( Ci )d mod n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u062f\u0631 RSA\u060c \u0628\u0647 \u062c\u0641\u062a \u0639\u062f\u062f (e,n) \u06a9\u0647 \u0645\u062a\u0646 \u0628\u0647 \u06a9\u0645\u06a9 \u0622\u0646 \u0631\u0645\u0632 \u0645\u06cc \u0634\u0648\u062f\u060c \u0627\u0635\u0637\u0644\u0627\u062d\u0627 \u06a9\u0644\u06cc\u062f \u0639\u0645\u0648\u0645\u06cc (public key) \u0648 \u0628\u0647 \u062c\u0641\u062a \u0639\u062f\u062f (d,n) \u06a9\u0647 \u0645\u062a\u0646 \u0628\u0648\u0633\u06cc\u0644\u0647 \u0622\u0646 \u0627\u0632 \u0631\u0645\u0632 \u062f\u0631 \u0645\u06cc \u0622\u06cc\u062f\u060c \u06a9\u0644\u06cc\u062f \u062e\u0635\u0648\u0635\u06cc (private key) \u06af\u0641\u062a\u0647 \u0645\u06cc \u0634\u0648\u062f. \u0646\u06a9\u062a\u0647 \u0627\u0633\u0627\u0633\u06cc \u062f\u0631 RSA \u0622\u0646 \u0627\u0633\u062a \u06a9\u0647 \u062c\u0647\u062a \u062a\u0636\u0645\u06cc\u0646 \u0648\u0627\u0631\u0648\u0646 \u067e\u0630\u06cc\u0631\u06cc \u0631\u0648\u0634 \u0631\u0645\u0632\u060c \u0627\u0639\u062f\u0627\u062f \u0628\u0627\u06cc\u0633\u062a\u06cc \u062f\u0631 \u0631\u0627\u0628\u0637\u0647 \u0632\u06cc\u0631 \u0635\u062f\u0642 \u06a9\u0646\u0646\u062f \u0644\u0630\u0627 \u0628\u0627\u06cc\u062f \u062f\u0631 \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u0639\u062f\u0627\u062f \u062f\u0642\u062a \u06a9\u0631\u062f:<\/strong><\/span><\/p>\n<p dir=\"ltr\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(x)e.d mod n = x<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u0627\u0635\u0644 \u0627\u0633\u0627\u0633\u06cc \u062f\u06cc\u06af\u0631\u06cc \u06a9\u0647 \u0628\u0627\u06cc\u062f \u062f\u0631 \u0631\u0645\u0632\u0646\u06af\u0627\u0631\u06cc RSA \u062d\u062a\u0645\u0627 \u0631\u0639\u0627\u06cc\u062a \u0634\u0648\u062f \u0622\u0646 \u0627\u0633\u062a \u06a9\u0647 \u06a9\u062f\u0647\u0627\u06cc Pi \u06a9\u0647 \u0628\u0647 \u0647\u0631 \u0628\u0644\u0648\u06a9 \u0646\u0633\u0628\u062a \u0645\u06cc \u062f\u0647\u06cc\u0645 \u0628\u0627\u06cc\u062f \u062f\u0631 \u0634\u0631\u0637 \u0632\u06cc\u0631 \u0635\u062f\u0642 \u06a9\u0646\u062f:<\/strong><\/span><\/p>\n<p dir=\"ltr\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u0660 \u2264 Pi&lt; n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong> \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0627\u06af\u0631 \u0628\u0644\u0648\u06a9 \u0647\u0627 \u0628\u0635\u0648\u0631\u062a \u0631\u0634\u062a\u0647 \u0647\u0627\u06cc k \u0628\u06cc\u062a\u06cc \u0645\u062f\u0644 \u0634\u0648\u0646\u062f\u060c \u0628\u0627\u06cc\u062f \u0634\u0631\u0637 \u0662K&lt; n \u0628\u0631\u0642\u0631\u0627\u0631 \u0628\u0627\u0634\u062f. \u062f\u0644\u06cc\u0644 \u0627\u06cc\u0646 \u0627\u0645\u0631 \u0622\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u0627\u062d\u062a\u06cc \u0628\u062a\u0648\u0627\u0646 \u06af\u0632\u0627\u0631\u0647 Pi mod n = Pi \u0631\u0627 \u0646\u0648\u0634\u062a \u0648\u06af\u0631\u0646\u0647 \u062f\u0631 \u062d\u0627\u0644\u062a \u06a9\u0644\u06cc \u0627\u06cc\u0646 \u06af\u0632\u0627\u0631\u0647 \u062f\u0631\u0633\u062a \u0646\u0645\u06cc \u0628\u0627\u0634\u062f \u0648 \u062f\u0631 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0631\u0645\u0632\u06af\u0634\u0627\u06cc\u06cc \u0635\u062d\u06cc\u062d \u062f\u0627\u062f\u0647 \u0647\u0627 \u062a\u0636\u0645\u06cc\u0646 \u0646\u062e\u0648\u0627\u0647\u062f \u0634\u062f.<\/strong><\/span><\/p>\n\n\t\t<div class=\"clearfix\"><\/div>\n\t\t<hr style=\"margin-top:20px; margin-bottom:20px;\" class=\"divider divider-solid\">\n\t\n<h4><span style=\"color: #0000ff;\"><strong>\u0628\u06cc\u0634\u062a\u0631 \u0628\u062f\u0627\u0646\u06cc\u062f:<\/strong><\/span><\/h4>\n<ul>\n<li>\n<p class=\"post-title entry-title\"><a href=\"https:\/\/actobit.com\/actomag\/1399\/diffiehellman\/\" target=\"_blank\" rel=\"noopener noreferrer\"><span style=\"color: #0000ff;\"><strong>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u06cc\u0641\u06cc-\u0647\u0644\u0645\u0646<\/strong><\/span><\/a><\/p>\n<\/li>\n<li><a href=\"https:\/\/actobit.com\/actomag\/1399\/symmetric-vs-asymmetric-encryption\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong><span style=\"color: #0000ff;\">\u062a\u0641\u0627\u0648\u062a \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc Symmetric \u0648 Asymmetric \u062f\u0631 \u0686\u06cc\u0633\u062a\u061f<\/span><\/strong><\/a><\/li>\n<\/ul>\n\n\t\t<div class=\"clearfix\"><\/div>\n\t\t<hr style=\"margin-top:20px; margin-bottom:20px;\" class=\"divider divider-solid\">\n\t\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u0631\u0648\u0634 \u0627\u0646\u062a\u062e\u0627\u0628 e \u0648 d \u06a9\u0647 \u062a\u0648\u0633\u0637 \u0627\u0628\u062f\u0627\u0639 \u06a9\u0646\u0646\u062f\u06af\u0627\u0646 RSA \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u0634\u062f\u0647\u060c \u0639\u0628\u0627\u0631\u062a \u0627\u0633\u062a \u0627\u0632:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u0627\u0644\u0641) \u062f\u0648 \u0639\u062f\u062f \u062f\u0644\u062e\u0648\u0627\u0647 (\u0627\u0645\u0627 \u0628\u0632\u0631\u06af) p \u0648 q \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc \u0634\u0648\u062f.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u0628) \u0627\u0639\u062f\u0627\u062f n \u0648 z \u0631\u0627 \u0637\u0628\u0642 \u062f\u0648 \u0631\u0627\u0628\u0637\u0647 \u0632\u06cc\u0631 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u06af\u0631\u062f\u062f:<\/strong><\/span><\/p>\n<p dir=\"ltr\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>n = p * q<\/strong><\/span><\/p>\n<p dir=\"ltr\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>z = (p-\u0661) * (q-\u0661)<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u062c) \u0639\u062f\u062f d \u0637\u0648\u0631\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u0646\u0633\u0628\u062a \u0628\u0647 z \u0627\u0648\u0644 \u0628\u0627\u0634\u062f \u06cc\u0639\u0646\u06cc \u0647\u06cc\u0686 \u0639\u0627\u0645\u0644 \u0645\u0634\u062a\u0631\u06a9\u06cc \u06a9\u0647 \u0647\u0631 \u062f\u0648 \u0628\u0631 \u0622\u0646 \u0628\u062e\u0634\u067e\u0630\u06cc\u0631 \u0628\u0627\u0634\u0646\u062f \u06cc\u0627\u0641\u062a \u0646\u0634\u0648\u062f.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u062f) \u0628\u0631 \u0627\u0633\u0627\u0633 d\u060c \u0639\u062f\u062f e \u0637\u0648\u0631\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u0631\u0627\u0628\u0637\u0647 \u0632\u06cc\u0631 \u0628\u0631\u0642\u0631\u0627\u0631 \u0628\u0627\u0634\u062f: (\u0628\u0639\u0628\u0627\u0631\u062a\u06cc \u0645\u0639\u06a9\u0648\u0633 \u0636\u0631\u0628\u06cc d \u062f\u0631 \u067e\u06cc\u0645\u0627\u0646\u0647 z \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647 \u0648 e \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.)<\/strong><\/span><\/p>\n<p dir=\"ltr\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>( e * d ) mod z = \u0661<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u0622\u0646\u0686\u0647 \u06a9\u0647 \u0645\u0634\u062e\u0635 \u0627\u0633\u062a \u062f\u0631 \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u0639\u0645\u0644\u06cc\u060c \u0627\u0639\u062f\u0627\u062f p \u0648 q \u062d\u062f\u0627\u0642\u0644 \u0635\u062f \u0631\u0642\u0645\u06cc (\u0635\u062f \u0631\u0642\u0645 \u062f\u0631 \u0645\u0628\u0646\u0627\u06cc \u062f\u0647) \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc \u0634\u0648\u0646\u062f \u06cc\u0639\u0646\u06cc \u0627\u06cc\u0646 \u062f\u0648 \u0639\u062f\u062f \u062d\u062f\u0627\u0642\u0644 \u0627\u0632 \u0645\u0631\u062a\u0628\u0647 \u0661\u0660\u0661\u0660\u0660 \u0647\u0633\u062a\u0646\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u062d\u0627\u0644\u062a \u0639\u062f\u062f \u0635\u062d\u06cc\u062d \u0645\u062a\u0646\u0627\u0638\u0631 \u0628\u0627 \u0628\u0644\u0648\u06a9\u0647\u0627\u06cc Pi \u06a9\u0647 \u0637\u0628\u0642 \u0634\u0631\u0637 \u0641\u0648\u0642 \u0628\u0627\u06cc\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 n \u0628\u0627\u0634\u0646\u062f\u060c \u0646\u0628\u0627\u06cc\u0633\u062a\u06cc \u0627\u0632 \u0668\u0663 \u06a9\u0627\u0631\u0627\u06a9\u062a\u0631 \u0628\u06cc\u0634\u062a\u0631 \u0628\u0627\u0634\u0646\u062f\u060c \u0632\u06cc\u0631\u0627:<\/strong><\/span><\/p>\n<p dir=\"ltr\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>p , q \u2248 \u0661\u0660\u0661\u0660\u0660 \u2192 n = p * q \u2248 \u0661\u0660\u0662\u0660\u0660 \u2192 (Pi &lt;(\u0662\u0666\u0666\u0664\u2248\u0661\u0660\u0662\u0660\u0660)) \u2192 Pi &lt;\u0662\u0666\u0666\u0664<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u067e\u0633 \u0647\u0631 \u0628\u0644\u0648\u06a9 \u0645\u062a\u0646 \u0628\u0627\u06cc\u0633\u062a\u06cc \u062d\u062f\u0627\u06a9\u062b\u0631 \u0666\u0666\u0664 \u0628\u06cc\u062a \u06cc\u0627 \u0668\u0663 \u06a9\u0627\u0631\u0627\u06a9\u062a\u0631 \u0647\u0634\u062a \u0628\u06cc\u062a\u06cc \u0628\u0627\u0634\u062f.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u0646\u06a9\u062a\u0647 \u0638\u0631\u06cc\u0641 \u0644\u0627\u0632\u0645 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 Ae mod n \u0644\u0627\u0632\u0645 \u0646\u06cc\u0633\u062a \u06a9\u0647 A \u0628\u0647 \u062a\u0639\u062f\u0627\u062f e \u0628\u0627\u0631 \u062f\u0631 \u062e\u0648\u062f\u0634 \u0636\u0631\u0628 \u0648 \u0633\u067e\u0633 \u0628\u0627\u0642\u06cc\u0645\u0627\u062f\u0647 \u0627\u0634 \u0628\u0631 n \u067e\u06cc\u062f\u0627 \u0634\u0648\u062f \u0632\u06cc\u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0628\u0631\u062e\u06cc \u062e\u0648\u0627\u0635 \u0631\u06cc\u0627\u0636\u06cc \u0646\u062a\u06cc\u062c\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0647\u06cc\u0686\u06af\u0627\u0647 \u0627\u0632 n \u0641\u0631\u0627\u062a\u0631 \u0646\u0645\u06cc \u0631\u0648\u062f.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u062d\u0627\u0644 \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u06cc\u06a9 \u0646\u0641\u0630\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u062f \u0628\u0627 \u062f\u0631 \u0627\u062e\u062a\u06cc\u0627\u0631 \u062f\u0627\u0634\u062a\u0646 \u06a9\u0644\u06cc\u062f \u0639\u0645\u0648\u0645\u06cc (e,n)\u060c \u0631\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f. \u062f\u0631 \u0627\u06cc\u0646\u0635\u0648\u0631\u062a \u0628\u0627\u06cc\u062f \u062f\u0631 \u0648\u0647\u0644\u0647 \u0627\u0648\u0644 n \u0631\u0627 \u0628\u0647 \u062f\u0648 \u0639\u0627\u0645\u0644 \u0627\u0648\u0644 \u0622\u0646 \u06cc\u0639\u0646\u06cc p \u0648 q \u062a\u062c\u0632\u06cc\u0647 \u06a9\u0646\u062f \u062a\u0627 \u0628\u062a\u0648\u0627\u0646\u062f z \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0631\u062f\u0647 \u0648 \u0633\u067e\u0633 d \u0631\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f. \u0628\u0631\u0627\u06cc \u062a\u062c\u0632\u06cc\u0647 \u0627\u0639\u062f\u0627\u062f \u0628\u0647 \u0639\u0648\u0627\u0645\u0644 \u0627\u0648\u0644 \u0622\u0646 \u0647\u06cc\u0686 \u0631\u0627\u0647\u06cc \u0628\u062c\u0632 \u062c\u0633\u062a\u062c\u0648 \u0648 \u0622\u0632\u0645\u0648\u0646 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f \u0648 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u06a9\u0647 n \u062d\u062f\u0627\u0642\u0644 \u062f\u0648\u06cc\u0633\u062a \u0631\u0642\u0645\u06cc \u0627\u0633\u062a\u060c \u062a\u062c\u0632\u06cc\u0647 \u0686\u0646\u06cc\u0646 \u0627\u0639\u062f\u0627\u062f\u06cc \u062d\u062a\u06cc \u0628\u0647 \u06a9\u0645\u06a9 \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631 \u0647\u0632\u0627\u0631\u0627\u0646 \u0633\u0627\u0644 \u0637\u0648\u0644 \u062e\u0648\u0627\u0647\u062f \u06a9\u0634\u06cc\u062f.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u0627\u06af\u0631 \u0686\u0647 \u062a\u062d\u0642\u06cc\u0642 \u0628\u0631 \u0631\u0648\u06cc \u0645\u0633\u0626\u0644\u0647 \u062a\u062c\u0632\u06cc\u0647 \u0627\u0639\u062f\u0627\u062f \u0628\u0632\u0631\u06af \u0628\u0647 \u0639\u0648\u0627\u0645\u0644 \u0622\u0646 \u0647\u0646\u0648\u0632 \u0627\u062f\u0627\u0645\u0647 \u062f\u0627\u0631\u062f \u0627\u0645\u0627 \u0647\u0646\u0648\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06a9\u0627\u0631\u0622\u0645\u062f\u06cc \u06a9\u0647 \u0628\u062a\u0648\u0627\u0646\u062f \u0627\u0639\u062f\u0627\u062f \u0628\u0632\u0631\u06af \u0631\u0627 \u0628\u0627 \u0647\u0631 \u0637\u0648\u0644\u06cc \u062f\u0631 \u0632\u0645\u0627\u0646 \u062b\u0627\u0628\u062a \u06cc\u0627 \u062f\u0631 \u062d\u062f \u0645\u062a\u0639\u0627\u0631\u0641 \u06a9\u0648\u0686\u06a9\u06cc \u0628\u0647 \u0639\u0648\u0627\u0645\u0644 \u0627\u0648\u0644 \u0622\u0646 \u062a\u062c\u0632\u06cc\u0647 \u06a9\u0646\u062f\u060c \u06cc\u0627\u0641\u062a \u0646\u0634\u062f\u0647 \u0627\u0633\u062a\u060c \u0644\u0630\u0627 \u0628\u0627 \u06af\u0630\u0634\u062a \u0663\u0660 \u0633\u0627\u0644 \u0627\u0632 \u0645\u0639\u0631\u0641\u06cc RSA \u0647\u0646\u0648\u0632 \u0627\u0632 \u0634\u0627\u0646 \u0622\u0646 \u06a9\u0627\u0633\u062a\u0647 \u0646\u0634\u062f\u0647 \u0627\u0633\u062a \u0628\u0644\u06a9\u0647 \u0641\u0642\u0637 \u06a9\u0644\u06cc\u062f\u0647\u0627 \u0628\u0647 \u062c\u0647\u062a \u0645\u062d\u06a9\u0645 \u06a9\u0627\u0631\u06cc \u0628\u0632\u0631\u06af\u062a\u0631 \u0634\u062f\u0647 \u0627\u0646\u062f.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>\u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u0627\u0639\u062f\u0627\u062f \u0627\u0648\u0644 \u0647\u06cc\u0686 \u0646\u0638\u0645 \u0634\u0646\u0627\u062e\u062a\u0647 \u0634\u062f\u0647 \u0627\u06cc \u0646\u062f\u0627\u0631\u0646\u062f \u0644\u0630\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u0639\u062f\u0627\u062f \u0627\u0648\u0644 \u0628\u0633\u06cc\u0627\u0631 \u0628\u0632\u0631\u06af p \u0648 q \u06cc\u06a9\u06cc \u0627\u0632 \u0686\u0627\u0644\u0634 \u0647\u0627\u06cc \u0628\u0632\u0631\u06af RSA \u0627\u0633\u062a \u0632\u06cc\u0631\u0627 \u0628\u0631\u0627\u06cc \u0627\u062b\u0628\u0627\u062a \u0627\u0648\u0644 \u0628\u0648\u062f\u0646 \u0639\u062f\u062f\u06cc \u0645\u062b\u0644 p \u0628\u0627\u06cc\u062f \u0645\u062d\u062f\u0648\u062f\u0647 \u0627\u0639\u062f\u0627\u062f\u06a9\u0645\u062a\u0631 \u06cc\u0627 \u0645\u0633\u0627\u0648\u06cc p \u221a \u0628\u0631\u0631\u0633\u06cc \u0648 \u0628\u062e\u0634 \u0646\u0627\u067e\u0630\u06cc\u0631\u06cc p \u0628\u0631 \u0622\u0646\u0647\u0627 \u0645\u0637\u0627\u0644\u0639\u0647 \u06af\u0631\u062f\u062f \u06a9\u0647 \u0647\u0631\u0686\u0647 p \u0628\u0632\u0631\u06af\u062a\u0631 \u0628\u0627\u0634\u062f \u0645\u062d\u062f\u0648\u062f\u0647 \u062c\u0633\u062a\u062c\u0648\u06cc p \u221a 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