# Semantic security and indistinguishability

I have two frames f1 and f2 that are each composed of several elements noted e. Note that, an element can fall into one of those two categories: an identifier or a counter.

What I want is to find a property that verifies indistinguishability of elements between frames. For instance, given the element e as an identifier, if f1.e==f2.e the property is not verified while it is verified if f1.e!=f2.e.

For now, I only suppose that such a property includes probabilities and can be obtained via:

1. semantically secure block cipher for identifier elements;
2. PRNG for counter elements.
• What's a 'frame'? Sounds specific. I.e. is this a maths or computer science question? – Paul Uszak Jul 26 at 11:34
• @PaulUszak : A frame is a sequence of bytes. For instance, the hexadecimal representation of a frame can be 0x1242338455667798f1eeaa.... The question can be seen as a math question applied to computer science :). – Guillaume Jul 29 at 9:26

You could see a block cipher as an FPE for a specific domain with $$2^n$$ elements, where $$n$$ is the block size in bits. If you can define your domain to have that many elements (even unused ones) then yes, you could use a block cipher. This could be an issue if you cannot handle a relatively large output size (you cannot store $$2^{32}$$ bits or more, for instance).
• For instance, the probability of the field e of f2 not to be the same as e of f1. The point is that I don't know how to formalize it with mathematical formulas... – Guillaume Jul 26 at 10:21
• If the input is unique then the output is also unique for format preserving encryption. So $e \neq e' \to E(e) \neq E(e')$. The probability is zero as it is a permutation. You can only get collisions when using the same input or when using a different key. – Maarten Bodewes Jul 26 at 12:14