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Update README.md
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Bill Buchanan
@@ -4,16 +4,16 @@ These are a collection of CTFs related to encryption.
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Bob has encrypted this RSA key pair with 128-bit AES. But he can't remember the password he applied. All he can remember is that it might have been his favouriate colour. Can you determine the two prime numbers (in hex) which make up the modulus?
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```
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-----BEGIN ENCRYPTED PRIVATE KEY-----
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MIIBvTBXBgkqhkiG9w0BBQ0wSjApBgkqhkiG9w0BBQwwHAQIZY3Pgqla6lACAggA
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MAwGCCqGSIb3DQIJBQAwHQYJYIZIAWUDBAECBBCcN0BAWWQwD5+pgSGvnHOpBIIB
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YGdKvIl5FzpYbFa7pKWUKyQlKY/QxA4Jhh6iMNU1osXVvczb08lFf7q1tB3Q4QTz
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Z8LZaQdnfD5ZGyUbOkEAZnIGThtClqGQQoxwMx226n5efyQvkhCjSfpLFHboY2m1
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+tG3OvoO/BmRDbY5PGWURGGwXgsFCgLgV7OfqC6qCfYqPtgBFbNjVZQSM6ojC7dd
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p6x3FnU9wvEuVbkuyHjTgVgA8CegeRY+hSXAprd2SD46Y6JqjLHoCA+jbLqJtsXW
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cJo88VgUfaz08Ehr4t+gQxl0vS0bm6bevbI1Boe9rQgKGThrqqWrvTXlY17nK48m
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4W+Si67DeIIBG5JHIHWQ45Gh/zdjxZdjFXGZi+VSNfgryDPWViPZuhxvR7t1UKpo
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JQpHMvfLrgOeLzO5uH8ToAzySJxXIsJKqKXdL7Y41wyF9+C/ahbZppMzzANrjhWc
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pXVqFsHfEJRcW9zZXuxCk20=
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MIIBvTBXBgkqhkiG9w0BBQ0wSjApBgkqhkiG9w0BBQwwHAQIzZS/FkAl8o8CAggA
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MAwGCCqGSIb3DQIJBQAwHQYJYIZIAWUDBAECBBDQG9NEvzkLxz9ywcanUMSQBIIB
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YJgi4T/Ko02Uwc2rYbWtXmgElqtso2LmSSOLQ6SyTOqaNvOiCn3F+AmUpF4XGHuH
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2Oig7U9afUfnk9MAqQf+/hSi5Lc+kbyvLCJjy881Gd8URiqNDhfQM9B0PUljnPY6
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de4rGXAg9rzqIfpOxfNEggADegEEN8T1EdxWtrFLViEuZ11h1FWQ92Nsiv9HUi3T
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36dC+zRgKeeze2C0REPtd7xWugHocyQL+YtGtGGbSUnukhrTAXAFsZxNDQfy+D9U
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o8B3YhPUC1z47nhhmTNtVYiIvFgDDJCa9NOPPnOQ4G5rwcLgpbplsksXfXLM/ONj
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gCnrJ7dIt+1ZXsr9K+oynBw86hVBppiQhVar19B4ftPfWDoSieKBuihwIYW0mXqT
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P0Jn92jXdCHM0b/9NwO9XkFNvGCRetJHnXuY7oD/7HRH9WkcftloO0r/cAxW0JVl
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uvAJRPcSU9/nYqpQT6uOwXQ=
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-----END ENCRYPTED PRIVATE KEY-----
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```
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The method is defined [https://asecuritysite.com/openssl/rsa_keygen2](https://asecuritysite.com/openssl/rsa_keygen2).
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@@ -23,48 +23,48 @@ For this we can basically try with a batch file, and substitute colours. This on
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% cat 1.key | openssl rsa -passin pass:blue -text
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Private-Key: (512 bit, 2 primes)
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modulus:
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00:c3:da:b8:08:4e:88:5e:23:11:52:e0:b8:25:42:
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52:40:40:22:58:5d:80:f7:34:2b:f6:ff:5d:1f:7e:
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e3:1d:29:9f:65:77:6d:71:76:97:57:5f:f8:d7:4d:
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b8:9c:0a:4f:7e:93:ff:f5:46:8f:e8:c1:89:b5:b1:
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a2:1e:64:23:71
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00:eb:3a:72:f0:05:d5:3f:de:f9:5e:7f:77:0a:86:
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f0:a4:bd:ca:51:d1:ac:a7:6a:a7:1d:af:9b:dd:cc:
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a1:37:c5:12:0c:59:57:4d:59:d8:d4:b8:fa:7c:34:
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d8:8b:ab:e6:5b:5e:2e:f1:85:48:27:89:45:bc:cc:
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3a:1f:71:ee:31
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publicExponent: 65537 (0x10001)
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privateExponent:
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14:31:67:ca:0b:76:c9:e5:e9:b2:56:d3:05:9c:69:
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e8:8f:f4:3a:92:21:6a:db:69:31:05:31:2f:bf:20:
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61:70:2b:ef:1e:b4:a8:40:23:6b:1c:fd:58:0e:66:
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aa:0c:d4:e1:3c:47:a2:8b:08:f2:a6:5a:c2:1e:7d:
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76:d4:bd:f5
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00:b4:bc:85:21:9d:29:bb:d8:a3:fc:12:ae:31:9d:
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7a:fa:e9:84:b1:97:0c:34:da:82:ab:11:8a:0e:42:
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b3:40:b8:26:c5:9e:8a:4e:a9:9d:a2:df:a9:e6:e4:
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89:fa:6b:f1:5e:b4:14:12:60:e4:0f:89:45:b9:db:
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6c:ba:eb:45:1d
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prime1:
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00:ec:14:d3:2a:06:c3:bf:0d:68:e0:83:3f:7c:7f:
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ec:87:16:30:dd:9a:bc:57:0d:e7:0b:db:39:16:5b:
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12:4c:df
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00:f8:07:29:8d:3e:20:d4:ee:1d:0d:fd:36:cd:26:
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36:d2:15:5d:f2:3e:6b:fd:ee:2c:29:01:98:4f:a8:
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68:6f:63
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prime2:
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00:d4:61:05:b7:59:ff:93:ee:91:33:56:fb:87:86:
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68:4e:fa:82:8c:10:68:85:b3:70:9e:f2:c8:e1:a3:
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ca:49:af
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00:f2:c9:f7:bf:f2:50:e7:2a:02:8c:74:04:e0:c0:
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b2:d5:9d:b9:fb:d8:d4:eb:5b:33:53:87:ae:86:c8:
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7b:32:5b
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exponent1:
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74:62:ab:db:bb:2c:03:63:24:02:13:12:58:59:64:
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8d:10:56:94:d9:74:e2:61:fb:36:b0:23:cb:ae:a8:
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2d:f7
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5b:d0:2a:ed:82:06:1d:4c:57:ad:0a:02:f3:46:26:
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1c:f6:93:e4:4c:7f:25:6c:b9:24:24:d7:01:05:d2:
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43:09
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exponent2:
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00:9e:cf:da:85:6c:20:49:0f:d9:b6:69:71:f7:bb:
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13:5f:13:c6:f1:54:07:c5:0b:14:c9:57:45:ce:2d:
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3b:c4:73
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00:95:a8:a5:cd:6e:43:2c:9b:9a:c2:95:69:c4:59:
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44:63:a5:3c:55:e0:4d:2f:5f:22:7e:64:ee:d2:2a:
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96:b6:6d
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coefficient:
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00:95:4f:6d:16:84:7f:2b:cc:ca:c9:19:0d:81:db:
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42:b7:ef:82:3c:8c:4d:3c:96:55:32:2c:01:92:c7:
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5e:f1:69
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3f:01:70:5e:21:bc:ff:6c:a1:a9:23:ff:9f:15:76:
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ab:a0:29:f0:cb:a4:71:51:da:2f:06:cb:ac:ad:00:
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b9:75
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writing RSA key
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-----BEGIN PRIVATE KEY-----
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MIIBVQIBADANBgkqhkiG9w0BAQEFAASCAT8wggE7AgEAAkEAw9q4CE6IXiMRUuC4
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JUJSQEAiWF2A9zQr9v9dH37jHSmfZXdtcXaXV1/41024nApPfpP/9UaP6MGJtbGi
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HmQjcQIDAQABAkAUMWfKC3bJ5emyVtMFnGnoj/Q6kiFq22kxBTEvvyBhcCvvHrSo
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QCNrHP1YDmaqDNThPEeiiwjyplrCHn121L31AiEA7BTTKgbDvw1o4IM/fH/shxYw
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3Zq8Vw3nC9s5FlsSTN8CIQDUYQW3Wf+T7pEzVvuHhmhO+oKMEGiFs3Ce8sjho8pJ
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rwIgdGKr27ssA2MkAhMSWFlkjRBWlNl04mH7NrAjy66oLfcCIQCez9qFbCBJD9m2
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aXH3uxNfE8bxVAfFCxTJV0XOLTvEcwIhAJVPbRaEfyvMyskZDYHbQrfvgjyMTTyW
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VTIsAZLHXvFp
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MIIBVQIBADANBgkqhkiG9w0BAQEFAASCAT8wggE7AgEAAkEA6zpy8AXVP975Xn93
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CobwpL3KUdGsp2qnHa+b3cyhN8USDFlXTVnY1Lj6fDTYi6vmW14u8YVIJ4lFvMw6
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H3HuMQIDAQABAkEAtLyFIZ0pu9ij/BKuMZ16+umEsZcMNNqCqxGKDkKzQLgmxZ6K
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Tqmdot+p5uSJ+mvxXrQUEmDkD4lFudtsuutFHQIhAPgHKY0+INTuHQ39Ns0mNtIV
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XfI+a/3uLCkBmE+oaG9jAiEA8sn3v/JQ5yoCjHQE4MCy1Z25+9jU61szU4euhsh7
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MlsCIFvQKu2CBh1MV60KAvNGJhz2k+RMfyVsuSQk1wEF0kMJAiEAlailzW5DLJua
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wpVpxFlEY6U8VeBNL18ifmTu0iqWtm0CID8BcF4hvP9soakj/58VdqugKfDLpHFR
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2i8Gy6ytALl1
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-----END PRIVATE KEY-----
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```
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## Cracking RSA with Chinese Remainder Theory - Håstad’s Broadcast
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