Encryption using blinded key

Question

I was wondering whether there are any "blinded" encryption schemas, such as the following:

We encrypt message $m$ using $f(k)$, where $f()$ is some blinding function and $c = \text{Enc}(f(k), m)$, while the decryption works as $m' = \text{Dec}(k, c)$ and $m' = m$.

One possible option is, of course, public-key encryption schemas, but I was thinking about more efficient (in terms of performance) symmetric key encryption schemas which have this property.

Answer 1

Would it be a requirement that, given $f(k)$ and $c$, it is hard to rederive $m$?

If so, then what you are effectively asking for is a public key encryption system; your public key is $f(k)$, and your private key is $k$. Such a method can be constructed from any public key encryption algorithm (but isn't any more efficient than the underlying pk algorithm).

If not, then it is easy; here is one construction:

• Let $f(k)$ be a randomized function $f(k) = r || \text{hash}( r, k )$.
• To encrypt, you compute $\text{Enc}(f(k), m) = r || \text{AES}( \text{hash}(r, k), m )$.
• To decrypt, you compute $\text{Dec}(k, (r || c)) = \text{AES}^{-1}( \text{hash}(r, k), c )$