Encryption using blinded key

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.

• You are blinding the key, not the message. Blind the message and use CTR mode. Aug 26 '20 at 12:20
• @kelalaka Can you give me some details how blinding the message will obfuscate k?
– Ziva
Aug 26 '20 at 12:40
• If you look at RSA blinding that uses the mathematical property of RSA. A block cipher has many operations with many rounds, the only meaningful blinding, afaik, is x-or, however that brings no benefit. Aug 26 '20 at 14:44

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).
• 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 $$\text{Dec}(k, (r || c)) = \text{AES}^{-1}( \text{hash}(r, k), c )$$