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So, here is the scheme of how this will look graphically:

GOST2 graphic model

The deal is to present distinguisher for this cipher. First of all here is my drafts:

Way 1

Assume that distinguisher displays in constant time two plaintexts of P and $\widehat{P}$ both consist of $P_1$ and $P_2$ parts respectively. The same construction either for cyphertexts C and $\widehat{C}$ with $C_1$ and $C_2$ parts.

I think following formula will be valid for my case too:

$P_2$ $\oplus$ $\widehat{P_2}$ $\oplus$ $C_2$ $\oplus$ $\widehat{C_2}$ = 0 (source) because GOST is Feistel cipher either.

So now I'm stuck here, because I assume that keys are not known as in presented model and that's why further calculations can't be applied to my model.

Maybe I did put too tough conditions about about the key uncertainty?

Way 2.

This comment give alternate vision of problem. Assume that chosen-plaintext attack is selected. This leads to one half arbitrary plaintext encryption and the other half and another side differs only in one bit. The right half will be fully changed after encryption and in the left half should have changed only in one bit that was inverted.

I do not know how to express all the things that are stated in Way 2 mathematically rigorous and would this finally be distinguisher for cipher once this statement expressed?

Anyway all tips and "to read"-links would be appreciated.

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  • $\begingroup$ The relation $P_2\oplus\widehat{P_2}\oplus{C_2}\oplus\widehat{C_2}=0$ does not match the drawing, even if you keep $P_1=\widehat{P_1}$ (which is unstated). To visualize that, highlight on the drawing what is affected by a bit toggle in $P_2$, in yellow for a demonstrably single-bit change, in red for a non-linear and possibly multi-bit change. However, you are on the right direction, and a similar relation can be devised: try the above coloring for a bit toggle in $P_1$. Using that relation, it is easy to craft a distinguisher; that's basically an experiment testing if the relation holds. $\endgroup$
    – fgrieu ♦
    Sep 11, 2015 at 4:18

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