Logarithmic brute-force for stream-ciphers
This way the brute-force search space is reduced logarithmically.


Well, no.

If there are $N$ possible keys, then you test $N$ keys on the first byte.  Then, you keep only those that succeed on the first byte, and test those on the second byte; that's approximately $N / 256^1$.  Then, you test those keys that succeed on both bytes, that's approximately $N / 256^2$ keys.

When you count the total number of keys you've tested (including those you tested multiple times), you come up with an expected:

$$N + N/256^1 + N/256^2 + N/256^3 + … = (256/255)N$$

And, $(256/255)N$ is not a "logarithmic reduction" over $N$...