Messages in this thread | | | Date | Mon, 14 Aug 2017 18:21:05 -0400 | From | Theodore Ts'o <> | Subject | Re: random.c: LFSR polynomials are not irreducible/primitive |
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On Mon, Aug 14, 2017 at 10:20:18AM +0200, Stephan Mueller wrote: > Hi Ted, > > drivers/char/random.c contains the following comment: > > """ > * Our mixing functions were analyzed by Lacharme, Roeck, Strubel, and > * Videau in their paper, "The Linux Pseudorandom Number Generator > * Revisited" (see: http://eprint.iacr.org/2012/251.pdf). In their > * paper, they point out that we are not using a true Twisted GFSR, > * since Matsumoto & Kurita used a trinomial feedback polynomial (that > * is, with only three taps, instead of the six that we are using). > * As a result, the resulting polynomial is neither primitive nor > * irreducible, and hence does not have a maximal period over > * GF(2**32). They suggest a slight change to the generator > * polynomial which improves the resulting TGFSR polynomial to be > * irreducible, which we have made here. > """ > > This comment leads me to belief that the current polynomial is primitive (and > irreducible). > > Strangely, this is not the case as seen with the following code that can be > used with the mathematical tool called magma. There is a free online version > of magma available to recheck it: http://magma.maths.usyd.edu.au/calc/ > > Note, the polynomials used up till 3.12 were primitive and irreducible. > > Could you please help me understanding why the current polynomials are better > than the old ones?
Have you looked at section 3.1.1 of the above cited paper?
http://eprint.iacr.org/2012/251.pdf
- Ted
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