3
Recommended Elliptic Curve Domain Parameters over
F2m
Page 25
3.5.1
Recommended Parameters sect193r1
The veriﬁably random elliptic curve domain parameters over
F 2m sect193r1 are speciﬁed by the sep-
tuple T
=
(m; f
(x);a ;b ;G;n ;h ) where m
= 193 and the representation of
F2193 is deﬁned by:
f
(x)
=
x193
+x15
+1
+xy
= x3
+ax2
The curve E: y2
+b over
F 2m is deﬁned by:
a
=
00
17858FEB
7A989751
69E171F7
7B4087DE
098AC8A9
11DF7B01
b
=
00
FDFB49BF
E6C3A89F
ACADAA7A
1E5BBC7C
C1C2E5D8
31478814
E was chosen veriﬁably at random as speciﬁed in ANSI X9.62 [1] from the seed:
S
=
103FAEC7
4D696E67
68756151
75777FC5
B191EF30
The base point G in compressed form is:
G
=
0301
F481BC5F
0FF84A74
AD6CDF6F
DEF4BF61
79625372
D8C0C5E1
and in uncompressed form is:
G
=
0401F4
81BC5F0F
F84A74AD
6CDF6FDE
F4BF6179
625372D8
C0C5E100
25E399F2
903712CC
F3EA9E3A
1AD17FB0
B3201B6A
F7CE1B05
Finally the order n of G and the cofactor are:
n
=
01
00000000
00000000
00000000
C7F34A77
8F443ACC
920EBA49
h
=
02
3.5.2
Recommended Parameters sect193r2
The veriﬁably random elliptic curve domain parameters over
F 2m sect193r2 are speciﬁed by the sep-
tuple T
=
(m; f
(x);a ;b ;G;n ;h ) where m
= 193 and the representation of
F2193 is deﬁned by:
+x15
f
(x)
=
x193
+1
+xy
= x3
+ax2
The curve E: y2
+b over
F 2m is deﬁned by:
a
=
01
63F35A51
37C2CE3E
A6ED8667
190B0BC4
3ECD6997
7702709B
b
=
00
C9BB9E89
27D4D64C
377E2AB2
856A5B16
E3EFB7F6
1D4316AE
E was chosen veriﬁably at random as speciﬁed in ANSI X9.62 [1] from the seed:
S
=
10B7B4D6
96E67687
56151751
37C8A16F
D0DA2211
The base point G in compressed form is:
G
=
0300
D9B67D19
2E0367C8
03F39E1A
7E82CA14
A651350A
AE617E8F