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So I made my own serial key generation software, using ECDSA, for use in my own applications and it works great so far! To keep the serial key short enough I use a 128 bit EC curve. My final signature (which I use as the product key) ends up containing two BigIntegers, 128-bit each, so the final key ends up being 32 bytes long. This is an ok solution and I can get my final key down to about 50 characters (not counting any delimiters like dashes) by doing some custom base conversion to convert this into a readable string.

Now I found a software called ellipter where the key for a 128 bit key strength only ends up being 30 characters (if you look at the screenshots on their page). Is this even possible? Or are they using a 64-bit curve? I can't understand how they do it. I would love to get my keys shorter also but I can't see how it can be possible?

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Perhaps they implemented BLS signatures. They only produce 2*n bit signatures for n bits of security, compared with 4*n bit signatures with ECDSA. There are also variants of Schnorr/DSA signatures that only produce 3*n bit signatures. – CodesInChaos Mar 20 '15 at 18:10
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Do they not say what algorithm they use? If they don't, I would be very wary about trusting that they're actually providing proper security. – cpast Mar 20 '15 at 18:53
    
They say they use elliptic curves on the page. It's strange, their public and private keys seems to be about the size I get so that indicates they are not using a much smaller curve. But how they get their key so short I still don't understand. – Johan O Mar 21 '15 at 7:54

The web site of https://ellipter.com says, they are using encryption.

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It seems that they do, but could you add how this explains the short product keys? – otus Oct 3 '15 at 6:04
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I don't know what encrytion algorithm is really used. But if its, for instance, ECIES, then the minimum cipher size is the blocklength of the underlying symmetric cipher (e.g. 128 bit for AES). – Cryptostasis Oct 3 '15 at 7:06

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