Stacked LFSR - why not used? New to cryptographic, weak in math. 

I have designed a PRG which consist of 33 LFSR's, each 32 bits wide.

I use one of the LFSR's as "selector", using the 5 LSB from this register to select one of the other 32 registers, from which I grab one byte and use as output. So each requested byte will thus come from one of 32 "randomly" selected registers.

My gut-feeling is that such a scheme will:


Hide the selector register from the outside world (rendering Berlekamp-Massey useless)
Expose an attacker to a very fast growing tree of possible combinations.
(If trying to sort out from which LFSR the last byte might emerge)


As it seems to me as this is an obvious way of creating a truly messy output, it surprises me that I haven't seen it described somewhere (with a name like "Rose-Morris-Nyqvist-Yang-Goldstein-scrambler"), so my conclusion is that it must be a bad solution. (Even beside the obvious hassle of seeding 33 registers and select feedback masks).

So my question is: Why not?

/Hans
Your design seems to be a byte-wise generalization of Jennings' multiplexed generator rather than the alternating step generator. 

S. M. Jennings, “Multiplexed Sequences: Some Properties of the Minimum Polynomial,” Lecture Notes in Computer Science, vol. 149, 1983.

I believe designs like hers [may even be byte based for efficiency] have been used in satellite TV encryption in the 1980s-1990s, but can't find the reference now.

There has been cryptanalysis showing such schemes may not be as strong as first thought.

Jovan Dj. Goliv, Mahmoud Salmasizadeh, Ed Dawson: Statistical Weakness of Multiplexed Sequences, Finite Fields and Their Applications 8(4):420-433, 2002.