RSA: Get exponent and modulus given a public key

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           :98102316FFB6F426A242A619230E0F274AB9433DA04BB91B1A5792DDA8BC5DB86EE67F0F2E89A57716D1CF4469742BB1A9DD72BDA89