# Rekeying procedure - how “far” from bijection?

Imagine that I want to change the key in order to prevent side-channel attacks on key and to protect against big load on the one key. It is desirable that key change procedure would look like random function from key space to itself.

I want to consider the function of the type: $$F : KeySpace \to KeySpace$$ $$F(k) = E_k(k)$$ E is my block cipher, for example we can assume that encryption is in ECB mode.

I understand that this is maybe not the best decision: there are numerous of provable secure algos, but now I want to consider this one.

The natural question is: does it look like random function and is it really bijective? If not, then what is the size of this compressed range of the function? Are there any estimates?

• What do you mean by "big load on one key"? And how would rekeying prevent side-channel attacks? – forest Sep 9 at 7:52
• I mean we can use usual statistical methods such as differential and linear only if we have a lot of texts processed on one key. The derived key is "fresh" and "independent" in some sense. Side channel attacks also gives us some information about the key using electromagnetic fields and all of that stuff, so if we change the key, the information collected by adversary would not be relevant anymore – Kirill Tsar. Sep 9 at 8:26
• Rekeying to reduce the impact of key compromise is common, but for any decent cipher, you aren't going to have to worry about encrypting "too much" with one key. – forest Sep 9 at 8:30