Decrypting LFSR, knowing the beginning of the cyphertext, and nothing else I have a cipher-text in binary, I know the beginning of the plain-text. I know that it is encrypted using LFSR, and I know nothing else.
How can I attack, and decrypt it?
What I have tried;
I converted the beginning of my plain-text to binary, which had a length of 84. My ciphertext's length is 952. I've got the first 84 bits of my cipher-text, XOR'd it with the known part of plain-text in binary, assuming that this would give me the first 84 bits of my key-stream, which was not periodic.
After that, I have used the Berlekamp-Massey algorithm with that 84 bits of the key-stream, to find the smallest possible connection polynomial that could be used to get it. (I don't know if it was definitely the connection polynomial for my key-stream, knowing that the long gap is huge and the known keystream is not periodic, it probably is not)
I then tried some shenanigans but nothing worked, I couldn't take any further steps. I've tried using the known cipher-text as the initial sequence and the polynomial I've got from the BM algorithm as the connection polynomial to generate another key, but that neither worked for my known plain-text or the rest, therefore assuming this was not a correct method to continue.
What further steps can be taken to decrypt this cipher?
It's used the right tools, apparently with the right input, but missed how to use their output.
If, when given the first 84 bits of keystream, a proper Berlekamp-Massey implementation outputs a polynomial of degree 27, then it also has found a 27-bit initial state, such that the 27-bit LFSR with this initial state has output starting with the 84-bit keystream. And one can have high confidence ($p\approx1-2^{2\cdot27-84}&gt;99.9999999\%$) this is not by accident.
Next steps:

Understand where in the Berlekamp-Massey code used lies the 27-bit initial state, and output that. Basically, if the LFSR convention is that of a Fibonnaci LFSR, that initial state is the 27 first terms of the input sequence analyzed (which is why it is often not an explicit output).
Make an auxiliary program that implements this LFSR and produces keystream.
Verify correctness of the above by checking that the first 84-bit output is the input to the Berlekamp-Massey code / the known keystream. If not, fix whatever is wrong.
Generate as much keystream as needed to decipher.

Note: I recall I helped fix Berlekamp-Massey code in C. Try it online!. And someone wrote some elements of the auxiliary program (but it's non-trivial to link the two). Help on use of a particular tool is off-topic, especially for CTF or homework. And writing the auxiliary program (perhaps as an extension of the  Berlekamp-Massey code) is a simple and essential exercise.