Can I use asymmetric encryption with two private keys?

Question

According to wikipedia (and other sources), asymmetric encryption always works like this:

• Party A has a public and private key
• Party B encrypts stuff with A's public key
• Party A decrypts stuff with their private key

However, I don't want party A to be able to encrypt their own data and only want to them to be able to decrypt it. Using the asymmetric logic this would result in:

• Party A has a private key
• Party B has a private key (which is party A's public key)
• Party B encrypts stuff with their private key
• Party A decrypts stuff with their private key

We will be using this for some sort of license generation/checking. Our clients may not generate a license, but the license file must be readable on the client side.

Is this still asymmetric encryption or should I be looking at different methods?

Answer 1

Party A being able to encrypt messages using the public key is absolutely no problem.

Only you could decrypt them (with your private key) and since you have no reason to do so encrypting something with the public key embedded in your application would cause no harm - just a bunch of useless data the user has since he cannot decrypt it.

For the licensing you simply encrypt (or sign - that's enough and then people will be able to read the restrictions etc in the license file but not modidy them) your license file using your private key. The application then decrypts the file using the embedded public key (or validates the signature).

A user extracting the public key and signing a custom license file with it could not use it since it would only work if your private key was embedded in the application (since that's the key necessary to decrypt something encrypted with the public key).

However, he could very well replace your public key with a custom one (where he has the private key, too) and then sign/encrypt his own license file using his private key. That's not a cryptographical issue though - you simply need to add some anti-cracking/modification measures to make it harder to replace the embedded public key. You could do some checksum validations for example.

Answer 2

You have your private key in the safe, and publish your public key. When you create a license you encrypt it with your private key. The client can only decrypt it with your public key.

If you want to restrict your license to a client, ask the client to generate their keypair, and send their public key to you. You then encrypt the license with their public key, then sign it (or encrypt it again) with your private key.

When the client receives the license they will have to 1. verify the signature of (or decrypt) the license you sent them 2. decrypt the verified data using their own private key.

This ensures that 1. only you can send them the license and 2. only they can decrypt it.

Answer 3

What you'd generally do is generate you license on your side, and encrypt it with your private key. Then your client can read it using your public key. This is (very broadly speaking) how certificate schemes (such as used in secure online browsing with HTTPS) work. And yes, that still absolutely counts as asymmetric encryption.

Answer 4

Based on what you're saying, asymmetric encryption is still what you want, it just needs to be done in a different way than you're used to thinking about it.

Let's say you generate a key pair for A. You send A one half of the pair: it doesn't really matter but we'll call it the private half. You encrypt using the public half and send it on to A. Then A can decrypt it. But A won't be able to encrypt a message that appears to come from the A public key since they only have the private half of the key and you can't figure out the other half of the key if you only have half of it, no matter which half you have. So A could only encrypt messages that could be decrypted by the public key that you have kept as a secret.

Of course, as other posters have already said, there are better ways to set up this protocol. Just trying to explain why this is not really an issue once you understand the details of asymmetric encryption and look past what we like to call the key halves and how we usually use them.

Answer 5

You could have a look at Rhino licensing : http://hibernatingrhinos.com/open-source/rhino-licensing/introduction

Answer 6

The other answers already said how to do it ... here just a note that (at least with RSA) the scheme you described in your question is not secure, if it depends on B's key staying secret.

For RSA, the public and private keys are really asymmetric, and you can't simply swap them and expect the same security properties.

• If your party B (Bob) encrypts multiple messages with the same public key, an attacker which reads these (ciphertext) messages can with little effort get your public key. The attacker does not get the plaintexts or the private key, but the public key will always become really "public".
• For A (Alice), it is even possible to create the public key from the private one, without any message being encrypted with the public one.

I suppose similar caveats are there for other asymmetric cryptosystems - always use them only like they are specified, and proven.

In this case, you would combine two key pairs: B's one to sign/verify the message (to make sure the message was sent by B), and A's one to encrypt/decrypt the message (to make sure only A can read it).

Answer 7

Yes. You can do it with RSA - to do a Diffie-Hellman-like exchange, because not only do the keys from 1 associated pair commute, but keys from different keypairs can commute as well.

alice -> bob: alice.pub bob -> alice: bob.pub alice: r = random.secret() alice -> bob: ( r * (alice.priv * bob.pub) ) bob: r = ( (r * (alice.priv * bob.pub)) * (bob.priv * alice.pub) )

Notice that we did something odd here. We mixed RSA operations from different keypairs in one operation. The objects in parenthesis are effectively a new virtual RSA key, and neither one of these keys is public. Had we tried to create that RSA key directly, either alice or bob would know both keys of the pair. This keypair is effectively a secret key where you write to one end and only the other side can decrypt it, yet you cant decrypt what you wrote yourself, and nobody else can encrypt messages to the other side.

I have never seen anyone mix keypairs like this, but I tested this by writing the code. I had to do something unusual though because normally, applying the private key to the message is for 'signing'. But signing usually hashes the secret and applies the private key to a hash of it; something we do not want. So in my code, once I had the RSA components (D,E,N) extracted into arbitrary precision numbers... ie: decrypt,encrypt,modulus ... I just did:

wormholeSend(me,you,msg) = (((me ^ {me_D}) \% me_N) ^ {you_E}) \% you_N

The thing that makes it a little tricky is that E (encrypt exponent) is actually a predictable value, but the modulus N is in the public key (E,N). D is private to each party. We need to be careful here, because you and I have a different modulus N.

I did this because I wanted a system where a program is authorized to encrypt keys that can be decrypted by users. Doing this, the user cannot encrypt keys, and the program cannot decrypt them.