Hi, Sorry to answer this late, but i was pretty busy, and i assume Olivier Vivolo is on vacation. For a polynomial, being primitive implies being irreducible, and the polynomial which must be primitive is Q(x), as you described it earlier, on GF(2^32). When the polynomials will be primitive,the TGFSR (LFSR on 32 bit word) will have his maximal period. If i remember well, we gived inthe paper, the magma code, and the patch for random.c. We did several tests for the propsal, and we chose those polynomials because they avoid a lot of changes on the source code, and they preserve the quality of the statistic distribution. Regards, David. 2017-08-16 14:51 GMT+02:00 Stephan Mueller <smueller@xxxxxxxxxx>: > Am Dienstag, 15. August 2017, 17:12:24 CEST schrieb Theodore Ts'o: > > Hi Theodore, > >> >> Stephan, if you have any comments on the proposal made by David >> Fontaine and Olivier Vivolo, I'd appreciate hearing them! > > I think I have some news: The magma code I used for GF(2^32) testing was not > correct. > > The corrected magma code is attached (thanks to Dr. Peter Birkner, BSI, who > helped me here). > > That magma code shows: > > - the current polynomials for Q(X) = α**3 (P(X) − 1) + 1 are irreducible but > not primitive over GF(2^32) > > - the polynomials suggested in https://eprint.iacr.org/2017/726.pdf Q(X) = > α**4 (P(X) − 1) + 1 are both, irreducible and primitive over GF(2^32) > > The use of GF(2^32) is important, because we apply the LFSR to a 32 bit word. > Hence, we have 2^32 permutations the LFSR should evenly cover. > > > Bottom line, I would recommend that random.c is patched to take the > polynomials suggested in https://eprint.iacr.org/2017/726.pdf. > > > If it is of any help, the attached magma code could be preserved somewhere > useful (in random.c?) > > Ciao > Stephan
