# Symmetric stream cipher, is it known?

I am thinking on a simple symmetric stream cipher. My first idea is the following:

• The key is a set of array of random bytes ($\underline{k}_1$ ... $\underline{k}_n$), whose length is $l_1$, $l_2$, ..., $l_n$ (any pair of $l_j$, $l_k$ is relative prime).
• We encrypt/decrypt the $i$-th byte of the stream by XOR-ring with these arrays, each after the other, periodically: $enc(s_i)=(\bigoplus_{a=1}^{n}k_{a, i \bmod {l_n}}) \oplus s_i$.

I think, this algorithm is so trivial, that probably not I am the first whom it came to mind.

How strong is it? If it is known, what is its name?

Extension: is it weaker, as a Vigenère cipher with length $\prod{l}$?

• It's basically a combination of several (binary) Vigenère ciphers, applied consecutively. I don't know if it has a specific name, though. – Ilmari Karonen Sep 17 '15 at 19:05
• @IlmariKaronen Thanks! I think its strength would come from the fact, that the period length of the xors would be $\prod{l_i}$.. – peterh - Reinstate Monica Sep 17 '15 at 19:08
• Any idea, why the downvote happened? – peterh - Reinstate Monica Sep 17 '15 at 19:32
• I can't really know, but I do have a hunch. We do, with some regularity, get "questions" here that basically go "Hey everybody! I've invented this awesome new cipher, isn't it great?" Usually, those get downvoted (and often closed, since we have a policy against asking for cryptanalysis of homebrew ciphers). I don't really think your question is one of those, or at least not a typical member of the bunch, but it does look similar at a glance. I can see how someone might have downvoted it on that basis. Anyway, voting (both up and down) is really up to each individual voter. – Ilmari Karonen Sep 17 '15 at 19:43
• @IlmariKaronen Well, this is understable generally, but I think this is a known cipher and its name would be also a good answer. Or, at least some info, if it looks strong or not. Anyways, thank you! – peterh - Reinstate Monica Sep 17 '15 at 21:21