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copied!<p>What you're describing here seems to be the opposite of a one-way function: it's easy to invert but super difficult to apply. One option would be to use a standard, off-the-shelf public-key encryption algorithm where you fix a (secret, randomly-chosen) public key that you keep a secret and a private key that you share with the world. That way, your function F(x) would be the encryption of x using the public key. You could then easily decrypt F(x) back to x by using the private decryption key. Notice that the roles of the public and private key are reversed here - you give out the private key to everyone so that they can decrypt the function, but keep the public key secret on your server. That way:</p> <ol> <li>The function is a bijection, so it's invertible.</li> <li>Given F(x), x is efficiently computable.</li> <li>Given x and F(x), it is extremely difficult to compute F(y) from y, since without the public key (assuming you use a cryptographically strong encryption scheme) there is no feasible way to encrypt the data, even if the private decryption key is known.</li> </ol> <p>This has many advantages. First, you can rest assured that the crypto system is safe, since if you use a well-established algorithm like RSA then you don't need to worry about accidental insecurity. Second, there are already libraries out there to do this, so you don't need to code much up and can be immune to side-channel attacks. Finally, you can make it possible for anyone to go and invert F(x) without anyone actually being able to compute F(x).</p> <p>One detail- you should definitely not just be using the standard int type here. Even with 64-bit integers, there are so few combinations possible that an attacker could just brute-force try inverting everything until they find the encryption F(y) for some y even if they don't have the key. I would suggest using something like a 512-bit value, since even a science fiction attack would not be able to brute-force this.</p> <p>Hope this helps!</p>

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