Some numerical results for elliptic curves over Fq(2^384 - 2^128 - 2^96 + 2^32 - 1). I generated curves by j-invariant using the relations:
a4 = (36 / (j0 - 1728)) a6 = (-1 / (j0 - 1728)) I've run 0 < j ~<= 210341. (Upper-bound approximate because a few curves with smaller j were still being point-counted when I stopped the process.) -- 221/210341 (about 0.1%) of the curves had prime order (cofactor 1). 4 of those curves (about 2%) had prime order on both the curve and twist. The j-invariants of the twist-secure curves I found: 145, 23041, 85522, 155663. (Some raw data here: https://github.com/coruus/sally) I was too lazy to attempt to replicate using Appendix 4 of this: http://csrc.nist.gov/groups/ST/toolkit/documents/dss/NISTReCur.pdf - David (Many thanks to Michael Hamburg for his point-counting script. Any egregious blunders are entirely mine, however.) _______________________________________________ Curves mailing list [email protected] https://moderncrypto.org/mailman/listinfo/curves
