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I got problem with my encryption functions. They have a repeating series of ones and zeros. It is 128-bit symmetric cipher.

Let's consider numbers divisible by $2.$ Let's count how many times are they divided by $2$. If number is divisible by $2$ exactly $n$ times, then make a block of $n$ zeros or $n$ ones.

Now put it into encrypted blocks. Every encrypting number of the form $2k$ which is even and divisible by $2$ just $n$ times will got first $n$ bits as $0$. And every encrypting number of the form $2k+1$ which is odd and $2k$ is divisible by $2$ $n$ times will got first n bits as $1$. Let's assume that all the rest of bits is indistinguishable from random. In these scheme zero-block always go into zero-block. And number $8$ will always got first three zeros and rest of bits indistinguishable from random.

Now let's shift this regularities aside. Let's say every encrypting number of the form $2k+a$ which is even and divisible by $2$ just $n$ times will got first $n$ bits as $0$ and every encrypting number of the form $2k+b+1$ which is odd and $2k+b$ is divisible by $2$ just $n$ times will got first $n$ bits as $1$. Numbers $a$ and $b$ are secret and can be understand as keys (every round got different pair).

Now let's move this regularities perpendicularly. Let's move every block by $m$ bits (with wrapping). So for example number $8$ can have first or last three zeros or somewhere in the middle. What's more until we don't know key $a$, we don't know how many zeros will there be in this block.

It is easy to find differentials if $a$, $b$ and $m$ are equal to zero. It is harder or impossible if we will choose $a$, $b$ and $m$ randomly. What is best differential attack against such vulnerabilities? And what is best differential probability? I was thinking about implementing $20$ rounds and according to my preliminary findings it should be enough if we are talking about differential attacks. But I have no idea if this can be attacked efficiently with linear cryptanalysis. Can it be?

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  • $\begingroup$ a bit of mathematical language may help frame your question concretely. $\endgroup$ – kodlu Nov 22 '20 at 12:01

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