Page 20
GEC 1: Recommended Elliptic Curve Domain Parameters Ver. 0.5
3.2.1
Recommended Parameters sect113r1
The veriﬁably random elliptic curve domain parameters over
F 2m sect113r1 are speciﬁed by the sep-
tuple T
=
(m; f
(x);a ;b ;G;n ;h ) where m
= 113 and the representation of
F2113 is deﬁned by:
f
(x)
=
x113
+x9
+1
+xy
= x3
+ax2
The curve E: y2
+b over
F 2m is deﬁned by:
a
=
003088
250CA6E7
C7FE649C
E85820F7
b
=
00E8BE
E4D3E226
0744188B
E0E9C723
E was chosen veriﬁably at random as speciﬁed in ANSI X9.62 [1] from the seed:
S
=
10E723AB
14D696E6
76875615
1756FEBF
8FCB49A9
The base point G in compressed form is:
G
=
03009D73
616F35F4
AB1407D7
3562C10F
and in uncompressed form is:
G
=
04009D
73616F35
F4AB1407
D73562C1
0F00A528
30277958
EE84D131
5ED31886
Finally the order n of G and the cofactor are:
n
=
010000
00000000
00D9CCEC
8A39E56F
h
=
02
3.2.2
Recommended Parameters sect113r2
The veriﬁably random elliptic curve domain parameters over
F 2m sect113r2 are speciﬁed by the sep-
tuple T
=
(m; f
(x);a ;b ;G;n ;h ) where m
= 113 and the representation of
F2113 is deﬁned by:
+x9
f
(x)
=
x113
+1
+xy
= x3
+ax2
The curve E: y2
+b over
F 2m is deﬁned by:
a
=
006899
18DBEC7E
5A0DD6DF
C0AA55C7
b
=
0095E9
A9EC9B29
7BD4BF36
E059184F
E was chosen veriﬁably at random as speciﬁed in ANSI X9.62 [1] from the seed:
S
=
10C0FB15
760860DE
F1EEF4D6
96E67687
5615175D
The base point G in compressed form is:
G
=
0301A57A
6A7B26CA
5EF52FCD
B8164797