Limitation of values in LFSR

Hi all,

I'm interested to know the reasoning behind restricting the set to {1,2,3,...,2^31 -1}

Is zero not allowed in any of S_0 to S_15 on the basis that this will rule out the one problem of ALL elements being zero ?

Thank you
James

A fundamental feature of the ZUC design is that the registers operate over the field with (2^31 - 1) elements. The set of possible elements could have been represented either as {0,1,2,...,2^31 -2}
or as {1,2,3,...,2^31 -1}; the designers chose the latter.

Understood.

On page 22 of Document 4: Design and Evaluation Report, it states that "during the feedback process of the 16-stage LFSR, the value 0 should be replaced by p" and I see that in v1.5 of Document 2 this is done for the pseudo code LFSRWithInitialisationMode and LFSRWithWorkMode, but in the given example code it is only done for the C function LFSRWithInitialisationMode, and not LFSRWithWorkMode.

In v1.6 both LFSRWithInitialisationMode and LFSRWithWorkMode do not contain the expected code:

Code:

/* adjust LFSR_S15 if LFSR_S15 is zero */
if ( LFSR_S15 == 0 )
{
   LFSR_S15 = 0x7FFFFFFF;
}

Can anyone explain?

Kindest regards
James