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

User · Answer

If you need to parse ASN 1 objects in script  there s a library for that  https   github com lapo-luchini asn1js  For doing the math  I found jsbn convenient  http   www-cs-students stanford edu  tjw jsbn   Walking the ASN 1 structure and extracting the exp mod subject etc  is up to you -- I never got that far

User · Answer

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  lt  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

User · Answer

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

User · Answer

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

User · Answer

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

User · Answer

Beware the leading 00 that can appear in the modulus when using    openssl rsa -pubin -inform PEM -text -noout  lt  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

[openssl] RSA: Get exponent and modulus given a public key

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