# How many queries can you do (concretely, not asymptotically) for a balanced Feistel network with 7 rounds?

In this paper Patarin says that: "for every $$\epsilon > 0$$, when $$m \ll 2^{n(1 - \epsilon)}$$ ... for 7 rounds or more it is secure against all adaptive chosen plaintext attacks" where m is the number of queries that the adversary can evaluate.

What concretely is meant by $$m \ll 2^{n(1 - \epsilon)}$$?

For instance, to have statistical security $$2^{-\sigma}$$ (e.g. $$\sigma = 40$$) concretely how many queries can be evaluated?

• define statistical security – kodlu Apr 25 '20 at 4:15
• How would you even define << concretely? It's sort an asymptotic idea. – Adrian Self Apr 26 '20 at 1:00
• @kodlu Where statistical security is the advantage of an adversary has in the Chosen Plaintext Attack game, when they are able to make $m$ queries and have unlimited computational resources. – Daniel-耶稣活着 Apr 26 '20 at 2:24
• ok so you want the advantage to be upper bounded by $2^{-40}.$ – kodlu Apr 26 '20 at 3:22
• @kodlu Yes, exactly. – Daniel-耶稣活着 Apr 26 '20 at 3:32

The linked paper is missing a lot of proof details. In any case, it seems impossible to say anything concrete for finite $$n$$ due to the existence of terms in $$O(\cdot)$$ notation in the bounds. You simply do not know how large those implied constants are.
• Yeah--the missing proof details is a lot of the problem... In principle if the details of the proof were there I should be able to go through and figure out what the constants are in the $\mathcal{O}()$ notation. But since they are omitted, I was hoping someone out there might know of a place that someone had gone through and calculated the constants. Or if not, a place where I can find the full proof so I can go through and try to figure out the constants myself. – Daniel-耶稣活着 Apr 26 '20 at 2:28