Generate RSA activation code for machine code on the web page?

[CatABC]

I want to let users provide the machine code on the web page. The server backend uses the private key generated by HISE to generate an activation code for the machine code. After the user gets the activation code, he fills it in the plug-in to activate it.
But I don't know the RSA key signing logic of HISE. Can anyone help me?
This is the implementation steps I thought of：
1.Generate RSA key file in HISE and obtain PublicKey and PrivateKey
2.Put the PublicKey in the plugin
3.Put the PrivateKey on the server backend,
4.After the user logs in, fill in the machine code input box in the account
5.Click Submit Activation, the server uses PrivateKey to sign the machine code and generate an activation code
6.Fill in the activation code obtained into the activation code input box of the plug-in
7.The plugin uses the "FileSystem.decryptWithRSA(code, pubKey);" provided by HISE to verify the activation code

[Lindon]

@CatABC this looks about right....

[CatABC]

I found this in the source file of HISE. I think if I use JS to write a program with the same logic, I will give it a try.
RSA.cpp

[Christoph Hart]

@CatABC if you search the JUCE forum you‘ll find a PHP snippet that I hacked together in a previous life that does exactly that.

[CatABC]

@Christoph-Hart I think I succeeded, thanks

 const d = BigInt('0x' + dHex);
              const n = BigInt('0x' + nHex);
        
              const modulusBits = n.toString(2).length;
              const modulusBytes = Math.ceil(modulusBits / 8);
              const requiredHexLength = modulusBytes * 2; 
              
              const messageBuffer = Buffer.from(machineCode);
              
              const reversedBuffer = Buffer.from(messageBuffer).reverse();
             
              let value = BigInt('0x' + reversedBuffer.toString('hex'));
  
              let result = 0n;
              const modulus = n;
              
              while (value > 0n) {
                  
                  const remainder = value % modulus;
                  value = value / modulus; 
             
                  const encryptedChunk = modExp(remainder, d, modulus);
   
                  result = result * modulus + encryptedChunk;
              }

              let hexStr = result.toString(16).padStart(requiredHexLength, '0');
              const finalBuffer = Buffer.from(hexStr, 'hex');
              
              return { activationCode: finalBuffer.toString('hex') };

function modExp(base, exp, mod) {
    let result = 1n;
    base = base % mod;
    while (exp > 0n) {
        if (exp & 1n) 
            result = (result * base) % mod;
        exp = exp >> 1n;
        base = (base * base) % mod;
    }
    return result;
}