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<HTML><HEAD><TITLE>Sample Private Key in TXT format (2048 bits)</TITLE><METANAME="GENERATOR"CONTENT="Modular DocBook HTML Stylesheet Version 1.55"><LINKREL="HOME"TITLE="The Open–source PKI Book"HREF="ospki-book.htm"><LINKREL="UP"TITLE="Sample Certificate Documents"HREF="sample-openssl-usage.htm"><LINKREL="PREVIOUS"TITLE="Sample Private Key in PEM format (2048 bits)"HREF="sample-priv-key.htm"><LINKREL="NEXT"TITLE="Sample CA Certificate in PEM format"HREF="sample-ca-cert.htm"></HEAD><BODYCLASS="SECT1"BGCOLOR="#FFFFFF"TEXT="#000000"LINK="#0000FF"VLINK="#840084"ALINK="#0000FF"><DIVCLASS="NAVHEADER"><TABLEWIDTH="100%"BORDER="0"CELLPADDING="0"CELLSPACING="0"><TR><THCOLSPAN="3"ALIGN="center">The Open–source PKI Book: A guide to PKIs and Open–source Implementations</TH></TR><TR><TDWIDTH="10%"ALIGN="left"VALIGN="bottom"><AHREF="sample-priv-key.htm">Prev</A></TD><TDWIDTH="80%"ALIGN="center"VALIGN="bottom">Appendix B. Sample Certificate Documents</TD><TDWIDTH="10%"ALIGN="right"VALIGN="bottom"><AHREF="sample-ca-cert.htm">Next</A></TD></TR></TABLE><HRALIGN="LEFT"WIDTH="100%"></DIV><DIVCLASS="SECT1"><H1CLASS="SECT1"><ANAME="SAMPLE-KEY-COMPONENTS">Sample Private Key in TXT format (2048 bits)</A></H1><P> This is a sample private key in TXT format. </P><P> <TABLEBORDER="0"BGCOLOR="#E0E0E0"WIDTH="100%"><TR><TD><PRECLASS="PROGRAMLISTING">Private-Key: (2048 bit)modulus: 00:dd:3c:f6:9a:be:d2:66:20:0c:7d:0c:ae:bc:18: cc:f4:e8:89:8d:16:b3:5c:16:75:06:33:f9:08:4f: d6:9b:f4:6b:e7:4d:0f:44:af:8b:87:dc:79:78:93: e8:e4:20:19:df:f0:0d:04:4d:2c:4c:ad:19:b0:31: 8c:6a:4d:a6:d6:0e:e8:ae:e2:37:75:8d:d5:1e:a2: 31:15:3c:f4:4d:ad:5d:f8:d0:23:c2:72:de:e2:73: 9b:ef:f7:84:25:b0:cf:92:4d:39:4a:18:41:ac:91: 81:28:ac:5b:f2:7d:74:e2:8f:f9:a7:c1:c0:b1:93: dd:cd:b1:4c:23:23:63:27:30:4c:da:8e:72:e4:0d: 77:c2:22:e2:b4:43:bb:9d:ca:36:59:fc:98:91:0c: da:c4:2c:34:03:0c:e5:91:51:e2:23:20:ae:68:5e: 30:8f:9e:f5:a5:2c:e4:bf:ab:2f:fb:82:03:31:b4: ff:5e:90:a8:f0:be:b0:4d:aa:f3:af:2c:27:42:c8: 7e:7a:d2:c3:e8:5b:53:8d:86:db:ae:f6:7c:45:03: 35:b6:52:9d:a0:c1:e0:da:ac:6b:68:05:7e:f8:73: 41:62:63:56:b3:47:6e:11:d8:d4:6c:92:be:65:aa: f2:a5:72:3d:4e:d9:d2:e2:8d:42:92:3e:cf:39:f9: 63:89publicExponent: 65537 (0x10001)privateExponent: 5c:a2:77:1b:6a:45:0c:af:e4:aa:c3:91:b2:7e:ab: ea:ec:27:14:25:6a:2a:67:d8:ce:25:1a:e4:09:11: f2:31:10:b1:43:c9:dd:d7:a7:13:d7:14:21:91:c5: 15:27:ff:cd:8d:64:d5:e5:3e:64:48:a2:95:ec:d9: 3f:75:8e:22:d9:11:42:90:c3:e9:fb:de:3d:ba:69: d4:db:b5:eb:84:68:f1:92:ad:36:71:04:b4:4a:f6: 03:2f:5f:6c:ac:b0:ed:30:5a:89:94:c8:82:ea:55: eb:62:e8:09:0b:d0:d2:40:b8:a7:2e:70:71:aa:59: 58:14:21:ae:20:d6:16:84:d2:29:5c:9b:a7:56:50: 3a:10:0b:c6:70:2b:97:dd:f8:fa:73:74:22:5f:d6: ce:0d:75:45:8a:61:5d:86:25:cb:ad:19:06:fe:8e: a4:f9:0d:35:2a:02:04:93:ec:df:0c:db:ca:f0:8c: ae:a7:54:c2:37:a1:11:7b:9f:40:54:a4:fd:31:a4: f9:ee:60:3c:8f:3b:0e:b1:e2:10:6d:f0:36:50:63: 27:6e:cc:85:c1:5d:10:4a:36:23:5d:bf:c7:ee:9b: af:3f:e6:49:47:c6:9e:b8:00:b0:d9:d2:de:07:46: 43:14:2f:de:7c:51:57:a5:8d:4b:13:04:54:25:3b: d5prime1: 00:fd:5a:b3:5d:5c:e5:cf:c2:b7:e9:54:93:30:f1: 21:07:9c:c1:01:35:64:7e:90:93:a7:13:d1:89:7b: 58:2b:56:29:61:5e:3f:8d:25:23:be:f4:f8:84:ff: 2e:a1:83:42:f8:19:44:32:2f:7c:2e:d9:f1:64:88: 74:57:8a:ea:1c:3b:12:70:0a:be:86:28:3b:4c:d5: 72:79:22:c7:d2:5a:0a:31:98:29:c0:51:26:6c:42: 03:9c:43:83:d2:72:ab:7d:3f:fd:2b:db:0f:62:0b: c1:e3:7c:2c:2c:4b:54:ba:36:98:c3:75:b1:8f:69: 4b:5b:62:e2:cb:45:8a:98:1fprime2: 00:df:8c:67:d5:09:4e:3a:11:c1:9f:d6:7c:a9:88: e8:0d:88:6f:72:3f:9a:f3:db:43:f5:e3:0f:85:eb: 1f:40:5c:26:6f:31:49:82:4a:ec:7c:67:17:22:89: c5:99:67:55:ca:06:de:e8:3a:22:85:cf:86:21:82: 2a:fd:03:f8:8e:03:24:b0:4d:40:0e:f7:33:25:29: 1e:f7:66:5f:13:68:b6:d2:5b:a8:54:17:e2:b4:1a: 50:11:13:49:3b:40:65:69:b7:cf:00:bb:39:36:cb: 0a:36:62:e4:59:2d:94:d8:11:c2:6e:fe:03:cc:35: f0:89:00:77:ec:a3:ce:2f:57exponent1: 00:c2:f9:01:1d:f1:76:fe:1b:48:b3:6d:1d:d5:45: 4b:f8:f2:be:69:72:b0:82:e2:3a:6f:12:c6:67:7a: 1f:d1:41:fe:98:6b:12:97:49:a4:a7:b9:18:64:29: 89:b6:4c:30:c6:83:93:42:d7:de:46:a3:fc:ac:34: 82:ec:38:00:90:77:39:6a:36:2a:87:4e:00:cc:d1: 5a:c6:34:68:f8:cd:c8:18:80:94:68:e7:4a:9d:77: 74:15:d6:b3:64:ca:50:85:14:30:7e:86:97:e1:09: 51:4e:02:ea:6f:b0:0d:65:3c:cc:f5:66:e6:9d:8a: 17:af:1d:7b:91:99:53:de:5bexponent2: 00:9b:be:7b:5c:8d:d6:25:58:d7:98:1f:5b:cc:d5: a8:2e:3d:7e:bf:8f:16:ca:8c:59:a5:c6:a2:ba:ff: 5b:4f:80:a3:fa:55:d1:4b:e8:1d:28:72:be:48:7e: c9:df:1d:82:44:75:52:f9:61:ff:49:50:92:b7:67: b3:c1:80:f1:bb:26:ef:79:b0:e8:4f:44:e4:2a:20: a3:05:64:1a:1b:30:9a:26:a6:5a:f8:f3:87:2b:49: 25:bd:2f:bd:96:7d:3f:ea:4e:77:f6:9f:79:b5:f5: f1:50:80:c7:6c:65:f8:4c:2c:db:54:6e:be:80:98: 97:d3:2b:33:61:f7:a1:9f:93coefficient: 00:90:c8:8a:b9:61:c2:b1:5c:82:69:bd:d1:51:fe: 97:03:d8:1d:de:a6:23:be:61:0b:02:d7:c2:4c:81: ad:4b:5b:51:e4:f8:05:21:5f:86:7a:78:22:56:85: 9c:fe:19:23:f1:20:47:67:3d:67:d7:12:cd:ec:a0: df:f3:24:94:d3:a3:03:82:00:74:0b:68:1d:5b:88: 49:fa:05:c9:2b:2f:a0:7f:79:85:e4:a9:a3:0e:d9: 29:8c:61:d0:cc:f1:7a:bc:e7:bd:d3:bc:b9:35:02: ef:54:51:97:52:af:c5:20:96:71:07:c9:17:00:6d: ab:7d:27:c9:74:71:26:d8:ce </PRE></TD></TR></TABLE> </P><DIVCLASS="NOTE"><P></P><TABLECLASS="NOTE"WIDTH="100%"BORDER="0"><TR><TDWIDTH="25"ALIGN="CENTER"VALIGN="TOP"><IMGSRC="stylesheet-images/note.gif"HSPACE="5"ALT="Note"></TD><TDALIGN="LEFT"VALIGN="TOP"><P> The numbers are in hexadecimal notation where each couple of digits represents 8 bits. </P></TD></TR></TABLE></DIV><P> In decimal, the modulus <SPANCLASS="ACRONYM">n</SPAN> is: <TABLEBORDER="0"BGCOLOR="#E0E0E0"WIDTH="100%"><TR><TD><PRECLASS="PROGRAMLISTING"> 27928727520532098560054510086934803266769027328779773633 51762493251995978285544035350906266382585272722398629867 67263282027760422651274751164233304322779357458680526177 93594651686619933029730312573799176384081348734718092523 53476550057243981913102899068449856388885987417785575633 66522578044678796800808595716146657069948593436088106761 86674067708949755093039975941211253008157978789036441127 01109572656021257137086334620169063315388954284609394192 32250643688514600699603929824545296848370051254650037973 10139479221307918200583851065828489354285517184240655579 54933738674003130224949637988279936009837240188474132980 1 </PRE></TD></TR></TABLE> </P><P> If an adversary managed to factorise the modulus, she would come up with the factors <SPANCLASS="ACRONYM">p</SPAN> and <SPANCLASS="ACRONYM">q</SPAN>, where <SPANCLASS="ACRONYM">p</SPAN> is: <TABLEBORDER="0"BGCOLOR="#E0E0E0"WIDTH="100%"><TR><TD><PRECLASS="PROGRAMLISTING"> 17791143933509595918127954499653383601218835098160342274 21719349464132778400846891474457120589082133325302604179 82181001327467441044697854896458761089076165690493808885 78606941384914032562858753139200694087767527290102835209 36343115102676302117059691295229400834867089684114302209 27632138221540171427701495839 </PRE></TD></TR></TABLE> and <SPANCLASS="ACRONYM">q</SPAN> is: <TABLEBORDER="0"BGCOLOR="#E0E0E0"WIDTH="100%"><TR><TD><PRECLASS="PROGRAMLISTING"> 15698106667513592225651910118661853088086996081175911345 49581990193390503622003253143718326860723480921952218366 69795595987275285870475032000847646645415387334949112223 81409068648841957504994872889663428380162653646162371919 71899699949089072105502530930366392712822832371160724348 51400420434671809603239292759 </PRE></TD></TR></TABLE> </P><P> The coefficient and the exponents 1 and 2 are used to increase the performance of those operations of RSA that make use of the private key. That is, they are used by the owner of the key and they are only visible to her. </P><DIVCLASS="NOTE"><P></P><TABLECLASS="NOTE"WIDTH="100%"BORDER="0"><TR><TDWIDTH="25"ALIGN="CENTER"VALIGN="TOP"><IMGSRC="stylesheet-images/note.gif"HSPACE="5"ALT="Note"></TD><TDALIGN="LEFT"VALIGN="TOP"><P> For information on software that works with natural numbers of arbitrary size, you may find the <AHREF="http://www.swox.com/gmp/"TARGET="_top">GMP library</A> quite useful. </P></TD></TR></TABLE></DIV></DIV><DIVCLASS="NAVFOOTER"><HRALIGN="LEFT"WIDTH="100%"><TABLEWIDTH="100%"BORDER="0"CELLPADDING="0"CELLSPACING="0"><TR><TDWIDTH="33%"ALIGN="left"VALIGN="top"><AHREF="sample-priv-key.htm">Prev</A></TD><TDWIDTH="34%"ALIGN="center"VALIGN="top"><AHREF="ospki-book.htm">Home</A></TD><TDWIDTH="33%"ALIGN="right"VALIGN="top"><AHREF="sample-ca-cert.htm">Next</A></TD></TR><TR><TDWIDTH="33%"ALIGN="left"VALIGN="top">Sample Private Key in PEM format (2048 bits)</TD><TDWIDTH="34%"ALIGN="center"VALIGN="top"><AHREF="sample-openssl-usage.htm">Up</A></TD><TDWIDTH="33%"ALIGN="right"VALIGN="top">Sample CA Certificate in PEM format</TD></TR></TABLE></DIV></BODY></HTML>⌨️ 快捷键说明
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