Let's consider 128-bit cipher. Now let's consider example keys $k_1$ to $k_{128}$:
$k_1$: 10
$k_2$: 1100
$k_3$: 11110000
...
In general every key $k_n$ can be some binary number which is consist of $n$ zeros and $n$ ones. This keys are mapping some encryption scheme. If $k_1$ is 10 it means that all least significant bits in encrypted numbers from $0$ to $2^{127}-1$ will be $1$ and all least significant bits in encrypted numbers from $2^{127}$ to $2^{128}$ will be $0$. And if $k_2$ is 0101 it means that all second least significant bits in encrypted numbers from $0$ to $2^{126}-1$ will be $0$, all second least significant bits in encrypted numbers from $2^{126}$ to $2^{127}-1$ will be $1$, all second least significant bits in encrypted numbers from $2^{127}$ to $2^{127}+2^{126}-1$ will be $0$ and all second least significant bits in encrypted numbers from $2^{127}+2^{126}-1$ to $2^{128}-1$ will be $1$. So the keys define how batch of the bits will be encrypted.
Not every state is allowed. To define all encryption secheme in one round we need $508$-bit main key and use it in specific algorithm, which is separate topic. It is not enough to determine all schemes as above. So we can define only some of states.
This is how works one round of encryption in my algorithm. I thougt about at least $10$ round of such encryption. To guess $k_1$ we need to geuss only one bit of the main key. To guess $k_1$ and $k_2$ we need to know $4$ bits of the main key. To guess $k_1$, $k_2$, $k_3$ we need $8$ bits of the main key. And in general to guess $k_1$ to $k_n$ keys we need to know $4(n-1)$ bits. So $n$-th key is defined by $4$ bits, exept first key $k_1$. Let's assume that realationship between $508$-bit main key and $k_1$ to $k_n$ keys are quite easy. So if you have $k_n$ you can find $4$ right bits in main $508$-bit key.
What do you think about that kind of encrytpion scheme? It looks like we ain't got here any differentials (as far as I study it). But we can easy imagine way to attack it in one round. For example to know $k_1$ you can only encrypt one number and then you know what are all least significant bits in all $0$ to $2^{127}-1$ numbers and in $2^{127}$ to $2^{128}-1$. Then we can try to find $k_2$ and guess bits of main key, quite easy. It looks like it is very easy to find encrytpion scheme in least signifficant bits. But to find all keys $k_1$ to $k_{128}$ we need very much plaintexts. And if we will do many rounds it isn't that easy even to find encrytpion scheme of least signifficant bits.
Do you think that there is a chance it will be resistant to known crypto attacks? What method of attack could be best to attack it? Maybe you can give some practical example?
