Specification of the scream stream cipher is unclear I am implementing in C++ the Scream stream cipher. The Scream family is composed of Scream-0, Scream-S and Scream-F. For this question, assume that I'm using Scream-S.

The specifications of the Scream cipher are given in the paper "Scream: a software-efficient stream cipher", but  I didn't find a reference sourcecode for this cipher which could have helped me. 

Maybe because the specs include many notations, I have some questions about the scream cipher:


In section 2 about the two 2X2 matrices : Am I right to say that $x$ and $x+1$ (from the $GaloisField(256)$) are replaced respectively by $2$ and $3$?
In section 3, it's possible to implement the function $F$ to optimize it. The author didn't define the multiplication ($u0 = M1(0,0) . S1[x]$). Is it a multiplication following $GF(256)$ with the polynomial $x^8 + x^7 + x^6 + x + 1$ (0x1C3) ?
In the algorithm of $F$ in section 3, they write 'byte0'. Does $byte_0$ refer to the MSB or LSB of an integer ?


Since $F$ is the core of the algorithm, it's important for me to know and understand these kind of details.
I've just dived into that paper for you, with the following results:


You've got that one correct.
The eight-byte input is multiplied with matrix M. There is no mention or indication of the polynomial you mention. Simply follow the paper. 

The matrices are fixed [[1,2],[2,1]] and [[1,3],[1,3]]. So, 2 and 3 are NOT replaced by x. The multiplication is on GF(256) with the polynomial specified at page 4. Thus, you have to do something like this: GF256_Multiply(2, S1[x], 0x1C3) where 2 = M1(0,1) = M1(1,0) for example. That's why they call T0 and T1 "lookup tables". These are fixed tables which imply M1 and M2 are fixed too.

(Notice: This was corrected thanks to OP's own research and the corrections OP mentioned in the comments to this answer.)
I think you got a bit confused there. MSB (= Most Significant Bit) and LSB (= Least Significant Bit) define "bits", while the paper explicitly talks about "bytes" in section 3. Therefore, they did not need to define any MSB or LSB. The paper simply defines $byte_0$ (which is, reading from left to right, the leftmost byte), and $byte_3$ (which is the rightmost byte). So you practically extract the 4 bytes into $byte_0$ up to $byte_3$ from left to right (aka "first in, first out").


Hope that helps.