Extract RSA private key from Cryptico.js

Question

I believe this is a pretty basic question, but I'm starting the studies in JavaScript and in RSA, so I'm a little bit lost. I just downloaded the library Cryptico, which gives me an easy to use RSA key gen/encryption/decryption. The public part of the generated RSA Key, can be extracted easily just using the command:

publicKeyString(RsaKey)

Which is:

my.publicKeyString = function(rsakey) 
{
    pubkey = my.b16to64(rsakey.n.toString(16));
    return pubkey; 
}

The rsakey.n is defined while generating the key in the function:

function RSAGenerate(B, E)
{
    var rng = new SeededRandom();
    var qs = B >> 1;
    this.e = parseInt(E, 16);
    var ee = new BigInteger(E, 16);
    for (;;)
    {
        for (;;)
        {
            this.p = new BigInteger(B - qs, 1, rng);
            if (this.p.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.p.isProbablePrime(10)) break;
        }
        for (;;)
        {
            this.q = new BigInteger(qs, 1, rng);
            if (this.q.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.q.isProbablePrime(10)) break;
        }
        if (this.p.compareTo(this.q) <= 0)
        {
            var t = this.p;
            this.p = this.q;
            this.q = t;
        }
        var p1 = this.p.subtract(BigInteger.ONE);
        var q1 = this.q.subtract(BigInteger.ONE);
        var phi = p1.multiply(q1);
        if (phi.gcd(ee).compareTo(BigInteger.ONE) == 0)
        {
            this.n = this.p.multiply(this.q);
            this.d = ee.modInverse(phi);
            this.dmp1 = this.d.mod(p1);
            this.dmq1 = this.d.mod(q1);
            this.coeff = this.q.modInverse(this.p);
            break;
        }
    }
}

But the private part of the key, I just can't understand how to extract, so I'll be able to save public/private key parts and available for later using.

Library Documentation: https://github.com/wwwtyro/cryptico

Artjom B. · Accepted Answer · 2022-10-22T13:06:12.080

6

RSA is defined in such a way that the values contained in a public key make up a subset of the values contained in the private key. So your private key is already rsakey. Other public key schemes work differently where public and private key values are completely distinct.

Furthermore rsakey.n doesn't fully define the public key. You need at least the public exponent e. It is often simply set to 65537, so this might be hardcoded if you never need to change the key or upgrade the scheme. It's the E in RSAGenerate. It is ignored in this case, because

A (seeded) random RSA key is generated with Tom Wu's RSA key generator with 3 as a hard-coded public exponent.

You can choose a similar encoding of the private key as the public key, but since it has to hold multiple values, I opted for JSON serialization:

(function(c){
    var parametersBigint = ["n", "d", "p", "q", "dmp1", "dmq1", "coeff"];

    c.privateKeyString = function(rsakey) {
        var keyObj = {};
        parametersBigint.forEach(function(parameter){
            keyObj[parameter] = c.b16to64(rsakey[parameter].toString(16));
        });
        // e is 3 implicitly
        return JSON.stringify(keyObj);
    }
    c.privateKeyFromString = function(string) {
        var keyObj = JSON.parse(string);
        var rsa = new RSAKey();
        parametersBigint.forEach(function(parameter){
            rsa[parameter] = parseBigInt(c.b64to16(keyObj[parameter].split("|")[0]), 16);
        });
        rsa.e = parseInt("03", 16);
        return rsa
    }
})(cryptico)

edited Oct 22 '22 at 13:06

answered Dec 23 '14 at 17:34

Artjom B.

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Thank you for the answer. So, do you a way to view or save the entire object 'rsakey'? Because when I save I see only [object Object]... And as I said, to use the same key later for encrypt/decrypt I need it saved somehow. – user2864778 Dec 23 '14 at 18:10
I added the private key serialiazation – Artjom B. Dec 23 '14 at 19:35
Thank you. But I still unsuccessful in this job. Right now I feel a little shame, because you did something big and I still don't know how to do this work. All I need is to save the key for posterior use, because the way it was made, I dont have the key (at least the private) in some way to save and encrypt/decrypt things later... You got me? – user2864778 Dec 23 '14 at 21:03
No, I didn't got you. So you did you generate the RSA (private) key with `cryptico.generateRSAKey(passphrase, bitlength)`? If this is a system question, then you didn't provide any detail as to whether this is executed in the browser or on the server. – Artjom B. Dec 23 '14 at 21:10
Yes I generate the key. And this is executed in the client side. But I want to have a link, for a download, poiting a variable with the key (private). This is part of a project that I'm still trying to develop, that's why I want to be able to save the private key, offering it via download. – user2864778 Dec 23 '14 at 22:11
So, your actual question is, how to download a private key file from the browser? If yes, then you should ask a new question now, but look for a duplicate beforehand and see what the file API can do. Editing your question to include your new scope is not good, because I couldn't answer it and this would somewhat diminish the value my answer. Now, do you still have a problem generating a string representation of the private key or is there something else? – Artjom B. Dec 23 '14 at 22:37

Extract RSA private key from Cryptico.js

1 Answers1