RSA: Get exponent and modulus given a public key

Question

I need to encrypt some data using RSA in JavaScript. All of the libraries around ask for an exponent and a modulus, yet I get a single public.key file from my opponent.

How do you retrieve the public exponent and modulus part from an RSA file?

Answer 1

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:

-----BEGIN PUBLIC KEY----- MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAmBAjFv+29CaiQqYZIw4P J0q5Qz2gS7kbGleS3ai8Xbhu5n8PLomldxbRz0RpdCuxqd1yvaicqpDKe/TT09sR mL1h8Sx3Qa3EQmqI0TcEEqk27Ak0DTFxuVrq7c5hHB5fbJ4o7iEq5MYfdSl4pZax UxdNv4jRElymdap8/iOo3SU1RsaK6y7kox1/tm2cfWZZhMlRFYJnpoXpyNYrp+Yo CNKxmZJnMsS698kaFjDlyznLlihwMroY0mQvdD7dCeBoVlfPUGPAlamwWyqtIU+9 5xVkSp3kxcNcNb/mePSKQIPafQ1sAmBKPwycA/1I5nLzDVuQa95ZWMn0JkphtFIh HQIDAQAB -----END PUBLIC KEY----- 

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           :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   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.)