On Tue, Aug 15, 2017 at 10:45:17AM +0200, Stephan Mueller wrote: > Am Dienstag, 15. August 2017, 00:21:05 CEST schrieb Theodore Ts'o: > > Hi Theodore, > > > Have you looked at section 3.1.1 of the above cited paper? > > > > http://eprint.iacr.org/2012/251.pdf > > Thanks for the hint, but that does not seem to solve the mystery either. > > When I use magma with GF(2^32), I see that all polynomials are neither > primitive nor irreducible: I believe that assertion being made in that section is not that modified P(X) is primitive, but that Q(X) is primitive Q(X) = α**3 (P(X) − 1) + 1 Where multiplication by α**3 is done by a twist-table lookup. Also of interest might be this paper, which I believe totally missed when the authors made their proposal on the linux-crypto list in September 2016 (I've added them to the cc list): https://eprint.iacr.org/2017/726.pdf The date on the paper is from just 3 weeks ago or so, and it was just luck that I found it when Googling to find some other references in response to your question. (Thanks for raising the question, BTW). I don't have a huge amount invested in any of the mixing schemes, because in practice we are *not* feeding large number of zero inputs into mixing function. So while it is good to make the mixing function to have as large a cyclic length as possible, it seems unlikely that the weaknesses of the current polynomials can be leveraged into a practical attack. Stephan, if you have any comments on the proposal made by David Fontaine and Olivier Vivolo, I'd appreciate hearing them! - Ted
