3
Recommended Elliptic Curve Domain Parameters over
F2m
Page 21
and in uncompressed form is:
G
=
0401A5
7A6A7B26
CA5EF52F
CDB81647
9700B3AD
C94ED1FE
674C06E6
95BABA1D
Finally the order n of G and the cofactor are:
n
=
010000
00000000
0108789B
2496AF93
h
=
02
3.3
Recommended 131-bit Elliptic Curve Domain Parameters over
F2m
This section speciﬁes the two recommended 131-bit elliptic curve domain parameters over
F 2m in this
document: veriﬁably random parameters sect131r1, and veriﬁably random parameters sect131r2.
Section 3.3.1 speciﬁes the elliptic curve domain parameters sect131r1, and Section 3.3.2 speciﬁes the
elliptic curve domain parameters sect131r2.
3.3.1
Recommended Parameters sect131r1
The veriﬁably random elliptic curve domain parameters over
F 2m sect131r1 are speciﬁed by the sep-
tuple T
=
(m; f
(x);a ;b ;G;n ;h ) where m
= 131 and the representation of
F2131 is deﬁned by:
+x8
+x3
+x2
f
(x)
=
x131
+1
+xy
= x3
+ax2
The curve E: y2
+b over
F 2m is deﬁned by:
a
=
07
A11B09A7
6B562144
418FF3FF
8C2570B8
b
=
02
17C05610
884B63B9
C6C72916
78F9D341
E was chosen veriﬁably at random as speciﬁed in ANSI X9.62 [1] from the seed:
S
=
4D696E67
68756151
75985BD3
ADBADA21
B43A97E2
The base point G in compressed form is:
G
=
0300
81BAF91F
DF9833C4
0F9C1813
43638399
and in uncompressed form is:
G
=
040081
BAF91FDF
9833C40F
9C181343
63839907
8C6E7EA3
8C001F73
C8134B1B
4EF9E150
Finally the order n of G and the cofactor are:
n
=
04
00000000
00000002
3123953A
9464B54D
h
=
02