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RSA：获取给定公钥的指数和模数

发布于 2024-09-07 12:33:03 字数 152 浏览 12 评论 0原文

我需要在 JavaScript 中使用 RSA 加密一些数据。周围的所有库都要求提供指数和模数，但我从对手那里得到了一个 public.key 文件。

如何从 RSA 文件中检索公共指数和模部分？

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兔姬 2024-09-14 12:33:03

这取决于您可以使用的工具。我怀疑是否有 JavaScript 可以直接在浏览器中执行此操作。它还取决于它是否是一次性的（始终相同的密钥）或是否需要编写脚本。

命令行/OpenSSL

如果您想在 unix 命令行上使用 OpenSSL 之类的东西，您可以执行以下操作。
我假设您的 public.key 文件包含类似这样的内容：

然后，命令将是：

PUBKEY=`grep -v -- ----- public.key | tr -d '\n'`

然后，您可以查看 ASN.1 结构：

echo $PUBKEY | base64 -d | openssl asn1parse -inform DER -i

这应该给您类似这样的内容：

    0:d=0  hl=4 l= 290 cons: SEQUENCE          
    4:d=1  hl=2 l=  13 cons:  SEQUENCE          
    6:d=2  hl=2 l=   9 prim:   OBJECT            :rsaEncryption
   17:d=2  hl=2 l=   0 prim:   NULL              
   19:d=1  hl=4 l= 271 prim:  BIT STRING

模数和公共指数位于最后位字符串，偏移量 19，因此使用 -strparse：

 echo $PUBKEY | base64 -d | openssl asn1parse -inform DER -i -strparse 19

这将为您提供十六进制的模数和公共指数（两个整数）：

    0:d=0  hl=4 l= 266 cons: SEQUENCE          
    4:d=1  hl=4 l= 257 prim:  INTEGER           :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
  265:d=1  hl=2 l=   3 prim:  INTEGER           :010001

如果它始终是相同的密钥，那可能没问题，但这是放入脚本可能不太方便。

或者（这可能更容易放入脚本中），

openssl rsa -pubin -inform PEM -text -noout < public.key

将返回：

Modulus (2048 bit):
    00:98:10:23:16:ff:b6:f4:26:a2:42:a6:19:23:0e:
    0f:27:4a:b9:43:3d:a0:4b:b9:1b:1a:57:92:dd:a8:
    bc:5d:b8:6e:e6:7f:0f:2e:89:a5:77:16:d1:cf:44:
    69:74:2b:b1:a9:dd:72:bd:a8:9c:aa:90:ca:7b:f4:
    d3:d3:db:11:98:bd:61:f1:2c:77:41:ad:c4:42:6a:
    88:d1:37:04:12:a9:36:ec:09:34:0d:31:71:b9:5a:
    ea:ed:ce:61:1c:1e:5f:6c:9e:28:ee:21:2a:e4:c6:
    1f:75:29:78:a5:96:b1:53:17:4d:bf:88:d1:12:5c:
    a6:75:aa:7c:fe:23:a8:dd:25:35:46:c6:8a:eb:2e:
    e4:a3:1d:7f:b6:6d:9c:7d:66:59:84:c9:51:15:82:
    67:a6:85:e9:c8:d6:2b:a7:e6:28:08:d2:b1:99:92:
    67:32:c4:ba:f7:c9:1a:16:30:e5:cb:39:cb:96:28:
    70:32:ba:18:d2:64:2f:74:3e:dd:09:e0:68:56:57:
    cf:50:63:c0:95:a9:b0:5b:2a:ad:21:4f:bd:e7:15:
    64:4a:9d:e4:c5:c3:5c:35:bf:e6:78:f4:8a:40:83:
    da:7d:0d:6c:02:60:4a:3f:0c:9c:03:fd:48:e6:72:
    f3:0d:5b:90:6b:de:59:58:c9:f4:26:4a:61:b4:52:
    21:1d
Exponent: 65537 (0x10001)

Java

这取决于输入格式。如果它是密钥库中的 X.509 证书，请使用 (RSAPublicKey)cert.getPublicKey()：此对象有两个用于模数和指数的 getter。

如果它的格式如上，您可能需要使用 BouncyCastle 及其 PEMReader阅读它。我还没有尝试过以下代码，但这或多或少看起来像这样：（

PEMReader pemReader = new PEMReader(new FileReader("file.pem"));
Object obj = pemReader.readObject();
pemReader.close();
if (obj instanceof X509Certificate) {
   // Just in case your file contains in fact an X.509 certificate,
   // useless otherwise.
   obj = ((X509Certificate)obj).getPublicKey();
}
if (obj instanceof RSAPublicKey) {
   // ... use the getters to get the BigIntegers.
}

您也可以在 C# 中类似地使用 BouncyCastle。）

It depends on the tools you can use. I doubt there is a JavaScript too that could do it directly within the browser. It also depends if it's a one-off (always the same key) or whether you need to script it.

Command-line / OpenSSL

If you want to use something like OpenSSL on a unix command line, you can do something as follows.
I'm assuming you public.key file contains something like this:

Then, the commands would be:

PUBKEY=`grep -v -- ----- public.key | tr -d '\n'`

Then, you can look into the ASN.1 structure:

echo $PUBKEY | base64 -d | openssl asn1parse -inform DER -i

This should give you something like this:

    0:d=0  hl=4 l= 290 cons: SEQUENCE          
    4:d=1  hl=2 l=  13 cons:  SEQUENCE          
    6:d=2  hl=2 l=   9 prim:   OBJECT            :rsaEncryption
   17:d=2  hl=2 l=   0 prim:   NULL              
   19:d=1  hl=4 l= 271 prim:  BIT STRING

The modulus and public exponent are in the last BIT STRING, offset 19, so use -strparse:

 echo $PUBKEY | base64 -d | openssl asn1parse -inform DER -i -strparse 19

This will give you the modulus and the public exponent, in hexadecimal (the two INTEGERs):

    0:d=0  hl=4 l= 266 cons: SEQUENCE          
    4:d=1  hl=4 l= 257 prim:  INTEGER           :98102316FFB6F426A242A619230E0F274AB9433DA04BB91B1A5792DDA8BC5DB86EE67F0F2E89A57716D1CF4469742BB1A9DD72BDA89CAA90CA7BF4D3D3DB1198BD61F12C7741ADC4426A88D1370412A936EC09340D3171B95AEAEDCE611C1E5F6C9E28EE212AE4C61F752978A596B153174DBF88D1125CA675AA7CFE23A8DD253546C68AEB2EE4A31D7FB66D9C7D665984C951158267A685E9C8D62BA7E62808D2B199926732C4BAF7C91A1630E5CB39CB96287032BA18D2642F743EDD09E0685657CF5063C095A9B05B2AAD214FBDE715644A9DE4C5C35C35BFE678F48A4083DA7D0D6C02604A3F0C9C03FD48E672F30D5B906BDE5958C9F4264A61B452211D
  265:d=1  hl=2 l=   3 prim:  INTEGER           :010001

That's probably fine if it's always the same key, but this is probably not very convenient to put in a script.

Alternatively (and this might be easier to put into a script),

openssl rsa -pubin -inform PEM -text -noout < public.key

will return this:

Modulus (2048 bit):
    00:98:10:23:16:ff:b6:f4:26:a2:42:a6:19:23:0e:
    0f:27:4a:b9:43:3d:a0:4b:b9:1b:1a:57:92:dd:a8:
    bc:5d:b8:6e:e6:7f:0f:2e:89:a5:77:16:d1:cf:44:
    69:74:2b:b1:a9:dd:72:bd:a8:9c:aa:90:ca:7b:f4:
    d3:d3:db:11:98:bd:61:f1:2c:77:41:ad:c4:42:6a:
    88:d1:37:04:12:a9:36:ec:09:34:0d:31:71:b9:5a:
    ea:ed:ce:61:1c:1e:5f:6c:9e:28:ee:21:2a:e4:c6:
    1f:75:29:78:a5:96:b1:53:17:4d:bf:88:d1:12:5c:
    a6:75:aa:7c:fe:23:a8:dd:25:35:46:c6:8a:eb:2e:
    e4:a3:1d:7f:b6:6d:9c:7d:66:59:84:c9:51:15:82:
    67:a6:85:e9:c8:d6:2b:a7:e6:28:08:d2:b1:99:92:
    67:32:c4:ba:f7:c9:1a:16:30:e5:cb:39:cb:96:28:
    70:32:ba:18:d2:64:2f:74:3e:dd:09:e0:68:56:57:
    cf:50:63:c0:95:a9:b0:5b:2a:ad:21:4f:bd:e7:15:
    64:4a:9d:e4:c5:c3:5c:35:bf:e6:78:f4:8a:40:83:
    da:7d:0d:6c:02:60:4a:3f:0c:9c:03:fd:48:e6:72:
    f3:0d:5b:90:6b:de:59:58:c9:f4:26:4a:61:b4:52:
    21:1d
Exponent: 65537 (0x10001)

Java

It depends on the input format. If it's an X.509 certificate in a keystore, use (RSAPublicKey)cert.getPublicKey(): this object has two getters for the modulus and the exponent.

If it's in the format as above, you might want to use BouncyCastle and its PEMReader to read it. I haven't tried the following code, but this would look more or less like this:

PEMReader pemReader = new PEMReader(new FileReader("file.pem"));
Object obj = pemReader.readObject();
pemReader.close();
if (obj instanceof X509Certificate) {
   // Just in case your file contains in fact an X.509 certificate,
   // useless otherwise.
   obj = ((X509Certificate)obj).getPublicKey();
}
if (obj instanceof RSAPublicKey) {
   // ... use the getters to get the BigIntegers.
}

(You can use BouncyCastle similarly in C# too.)

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弄潮 2024-09-14 12:33:03

使用时请注意模数中可能出现的前导 00：

openssl rsa -pubin -inform PEM -text -noout < public.key

示例模数包含 257 字节而不是 256 字节，因为 00 被包含在内，因为 98 中的 9 看起来像负号数字。

Beware the leading 00 that can appear in the modulus when using:

openssl rsa -pubin -inform PEM -text -noout < public.key

The example modulus contains 257 bytes rather than 256 bytes because of that 00, which is included because the 9 in 98 looks like a negative signed number.

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眼泪淡了忧伤 2024-09-14 12:33:03

主要供我自己参考，以下是如何从 ssh-keygen 生成的私钥中获取它

openssl rsa -text -noout -in ~/.ssh/id_rsa

当然，这仅适用于私钥。

Mostly for my own reference, here's how you get it from a private key generated by ssh-keygen

openssl rsa -text -noout -in ~/.ssh/id_rsa

Of course, this only works with the private key.

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日暮斜阳 2024-09-14 12:33:03

您可以通过

openssl rsa -pubin -in public_key.pem -noout -modulus

Bonus 直接打印模数：在末尾添加“| openssl md5”以获得更小的字符串以便于比较

you can directly print modulus by

openssl rsa -pubin -in public_key.pem -noout -modulus

Bonus: add " | openssl md5" at the end to get a smaller string to compare easily

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野生奥特曼 2024-09-14 12:33:03

除了上面的答案之外，我们还可以使用 asn1parse 来获取值

$ openssl asn1parse -i -in pub0.der -inform DER -offset 24
0:d=0  hl=4 l= 266 cons: SEQUENCE
4:d=1  hl=4 l= 257 prim:  INTEGER           :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
265:d=1  hl=2 l= 3 prim:  INTEGER           :010001

现在，为了获取此偏移量，我们尝试默认的 asn1parse

$ openssl asn1parse -i -in pub0.der -inform DER
 0:d=0  hl=4 l= 290 cons: SEQUENCE
 4:d=1  hl=2 l=  13 cons:  SEQUENCE
 6:d=2  hl=2 l=   9 prim:   OBJECT            :rsaEncryption
17:d=2  hl=2 l=   0 prim:   NULL
19:d=1  hl=4 l= 271 prim:  BIT STRING

我们需要获取 BIT 字符串部分，因此我们添加大小

< code>depth_0_header(4) + height_1_full_size(2 + 13) + Container_1_EOC_bit + BIT_STRING_header(4) = 24

这可以在以下位置更好地可视化：ASN.1 Parser, if you hover at tags, you will see the offsets

Another amazing resource: Microsoft 的 ASN.1 文档

Apart from the above answers, we can use asn1parse to get the values

$ openssl asn1parse -i -in pub0.der -inform DER -offset 24
0:d=0  hl=4 l= 266 cons: SEQUENCE
4:d=1  hl=4 l= 257 prim:  INTEGER           :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
265:d=1  hl=2 l= 3 prim:  INTEGER           :010001

Now, to get to this offset,we try the default asn1parse

$ openssl asn1parse -i -in pub0.der -inform DER
 0:d=0  hl=4 l= 290 cons: SEQUENCE
 4:d=1  hl=2 l=  13 cons:  SEQUENCE
 6:d=2  hl=2 l=   9 prim:   OBJECT            :rsaEncryption
17:d=2  hl=2 l=   0 prim:   NULL
19:d=1  hl=4 l= 271 prim:  BIT STRING

We need to get to the BIT String part, so we add the sizes

depth_0_header(4) + depth_1_full_size(2 + 13) + Container_1_EOC_bit + BIT_STRING_header(4) = 24

This can be better visialized at: ASN.1 Parser, if you hover at tags, you will see the offsets

Another amazing resource: Microsoft's ASN.1 Docs

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仙女山的月亮 2024-09-14 12:33:03

如果您需要解析脚本中的 ASN.1 对象，可以使用一个库： https://github.com /lapo-luchini/asn1js

为了进行数学计算，我发现 jsbn 很方便： http://www-cs-students.stanford.edu/~tjw/jsbn/

遍历 ASN.1 结构并提取 exp/mod/subject/etc。取决于你——我从来没有走到这一步！

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清浅ˋ旧时光 2024-09-14 12:33:03

我设法找到这个解决方案的答案，必须执行javascript注入以安装 atob

const atob:any = require('atob');
asn1(pem: any){
      asn1parser.Enc.base64ToBuf = function (b64:any) {
    return asn1parser.Enc.binToBuf(atob(b64));
  };
  const dertest = asn1parser.PEM.parseBlock(pem).der;
   var hex = asn1parser.Enc.bufToHex(asn1parser.PEM.parseBlock(pem).der)
   var buf = asn1parser.ASN1.parse(dertest);
  var asn1 = JSON.stringify(asn1parser.ASN1.parse(dertest), asn1parser.ASN1._replacer, 2 );

I manage to find the answer for this solution, have to do javascript injection for this to install atob

const atob:any = require('atob');
asn1(pem: any){
      asn1parser.Enc.base64ToBuf = function (b64:any) {
    return asn1parser.Enc.binToBuf(atob(b64));
  };
  const dertest = asn1parser.PEM.parseBlock(pem).der;
   var hex = asn1parser.Enc.bufToHex(asn1parser.PEM.parseBlock(pem).der)
   var buf = asn1parser.ASN1.parse(dertest);
  var asn1 = JSON.stringify(asn1parser.ASN1.parse(dertest), asn1parser.ASN1._replacer, 2 );

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