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Old 2019-04-03, 00:57   #1
VBCurtis's Avatar
Feb 2005
Riverside, CA

2×5×232 Posts
Default Poly select and test-sieving for RSA232

The path for mere mortals to contribute to a factorization of RSA-896 or RSA-1024 may include getting an empirical sense for how our current tools scale for projects of 230+ digits.
As a start on this path, I spent about two core-weeks on CADO poly select for RSA-232:
n: 1009881397871923546909564894309468582818233821955573955141120516205831021338528545374366109757154363664913380084917065169921701524733294389270280234380960909804976440540711201965410747553824948672771374075011577182305398340606162079
skew: 2344396.759
type: gnfs
c0: -4444911653278229819370022568140110402793683027936
c1: -1601077621210143696221661846379560448537934
c2: 10503357361068234616583254671616966819
c3: -106292952091953896748493562554
c4: -2012141349873927583036795
c5: -21775742789901120
c6: -43338240
Y0: -48749394190388072676687368853974603055
Y1: 1395619071010682498582953
# MurphyE (Bf=5.498e+11,Bg=6.872e+10,area=8.590e+16) = 2.92e-08
# found by revision 78c3a74
I ran this through msieve: size 5.322e-17, alpha -10.267, combined = 5.391e-17 rroots = 6
On our best-polys table, an increase of 16 digits corresponds to an order-of-magnitude decrease in Murphy-E. ~4.7e-14 is the record for 184 digits, ~5.3e-15 is the record for 200 digits, and ~4.6e-16 (deg 6) is the record for 216 digits. So, this score at 5.4e-17 is a decent baseline polynomial to do some parameter-choice work. I tried to feed the polynomial from the RSA-768 factorization paper into msieve to compare scores, but it core-dumped and I couldn't figure out my mistake.
I'll report some test-sieve results using 16f next.
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