如何从RSA私钥中提取私钥组件$ N $和$ D $? [英] How do I extract the private key components $N$ and $D$ from a private RSA key?
问题描述
我有一个私有RSA密钥，例如–例如:
I have a private RSA key like – for example – this one:
-----BEGIN RSA PRIVATE KEY-----
MIIBOgIBAAJBAMPMNNpbZZddeT/GTjU0PWuuN9VEGpxXJTAkmZY02o8238fQ2ynt
N40FVl08YksWBO/74XEjU30mAjuaz/FB2kkCAwEAAQJBALoMlsROSLCWD5q8EqCX
rS1e9IrgFfEtFZczkAWc33lo3FnFeFTXSMVCloNCBWU35od4zTOhdRPAWpQ1Mzxi
aCkCIQD9qjKjNvbDXjUcCNqdiJxPDlPGpa78yzyCCUA/+TNwVwIhAMWZoqZO3eWq
SCBTLelVQsg6CwJh9W7vlezvWxUni+ZfAiAopBAg3jmC66EOsMx12OFSOTVq6jiy
/8zd+KV2mnKHWQIgVpZiLZo1piQeAvwwDCUuZGr61Ap08C3QdsjUEssHhOUCIBee
72JZuJeABcv7lHhAWzsiCddVAkdnZKUo6ubaxw3u
-----END RSA PRIVATE KEY-----
此私钥RSA密钥是使用以下命令使用OpenSSL生成的:
This private RSA key was generated using OpenSSL using the following command:
openssl genrsa
现在，如何使用此密钥获取用于解密的$ N $和$ D $的值，以及密钥的格式是什么?
Now, how do I get the value of $N$ and $D$ used for decryption using this key and what format is the key in?
推荐答案
键入的格式是什么?
what format is the key in?
这是具有PEM编码的RSA私钥.我相信PEM编码来自 RFC 1421 .剥离PEM编码后，有一个ASN.1/DER编码的RSA私钥. ASN.1编码是二进制的，因此它不是人类可读的. ASN.1密钥的格式可以在 PKCS#1 中找到，或者 RFC 3447 .
That is an RSA private key with a PEM encoding. I believe the PEM encoding is from RFC 1421. After the PEM encoding is peeled off, there's an ASN.1/DER encoded RSA private key. The ASN.1 encoding is binary, so its not human readable. The format for the ASN.1 key can be found in PKCS #1 or RFC 3447.
根据RFC 3447，第A.1.2节RSA私钥语法，这是您可以期望的:
According to RFC 3447, Section A.1.2 RSA Private Key Syntax, here's what you can expect:
RSAPrivateKey ::= SEQUENCE {
version Version,
modulus INTEGER, -- n
publicExponent INTEGER, -- e
privateExponent INTEGER, -- d
prime1 INTEGER, -- p
prime2 INTEGER, -- q
exponent1 INTEGER, -- d mod (p-1)
exponent2 INTEGER, -- d mod (q-1)
coefficient INTEGER, -- (inverse of q) mod p
otherPrimeInfos OtherPrimeInfos OPTIONAL
}
您的密钥在我的Pasteboard(Linux上的剪贴板)上，所以:
Your key is on my Pasteboard (Clipboard on Linux), so:
$ pbpaste | openssl rsa -text -noout
Private-Key: (512 bit)
modulus:
00:c3:cc:34:da:5b:65:97:5d:79:3f:c6:4e:35:34:
3d:6b:ae:37:d5:44:1a:9c:57:25:30:24:99:96:34:
da:8f:36:df:c7:d0:db:29:ed:37:8d:05:56:5d:3c:
62:4b:16:04:ef:fb:e1:71:23:53:7d:26:02:3b:9a:
cf:f1:41:da:49
publicExponent: 65537 (0x10001)
privateExponent:
00:ba:0c:96:c4:4e:48:b0:96:0f:9a:bc:12:a0:97:
ad:2d:5e:f4:8a:e0:15:f1:2d:15:97:33:90:05:9c:
df:79:68:dc:59:c5:78:54:d7:48:c5:42:96:83:42:
05:65:37:e6:87:78:cd:33:a1:75:13:c0:5a:94:35:
33:3c:62:68:29
prime1:
00:fd:aa:32:a3:36:f6:c3:5e:35:1c:08:da:9d:88:
9c:4f:0e:53:c6:a5:ae:fc:cb:3c:82:09:40:3f:f9:
33:70:57
prime2:
00:c5:99:a2:a6:4e:dd:e5:aa:48:20:53:2d:e9:55:
42:c8:3a:0b:02:61:f5:6e:ef:95:ec:ef:5b:15:27:
8b:e6:5f
exponent1:
28:a4:10:20:de:39:82:eb:a1:0e:b0:cc:75:d8:e1:
52:39:35:6a:ea:38:b2:ff:cc:dd:f8:a5:76:9a:72:
87:59
exponent2:
56:96:62:2d:9a:35:a6:24:1e:02:fc:30:0c:25:2e:
64:6a:fa:d4:0a:74:f0:2d:d0:76:c8:d4:12:cb:07:
84:e5
coefficient:
17:9e:ef:62:59:b8:97:80:05:cb:fb:94:78:40:5b:
3b:22:09:d7:55:02:47:67:64:a5:28:ea:e6:da:c7:
0d:ee
...如何使用此密钥获取用于解密的$ N $和$ D $的值
... how do I get the value of $N$ and $D$ used for decryption using this key
这应该为您做到:
$ pbpaste | /usr/local/ssl/macosx-x64/bin/openssl rsa -noout -modulus
Modulus=C3CC34DA5B65975D793FC64E35343D6BAE37D5441A9C57253024999634DA8F36DFC7D0DB
29ED378D05565D3C624B1604EFFBE17123537D26023B9ACFF141DA49
不幸的是，没有-d或-privateExponent开关.您必须使用其他方法来解析它.
Unfortunately, there's no -d or -privateExponent switch. You'll have to parse that using some other method.
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