Page 22
GEC 1: Recommended Elliptic Curve Domain Parameters Ver. 0.5
3.3.2
Recommended Parameters sect131r2
The veriﬁably random elliptic curve domain parameters over
F 2m sect131r2 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
=
03
E5A88919
D7CAFCBF
415F07C2
176573B2
b
=
04
B8266A46
C55657AC
734CE38F
018F2192
E was chosen veriﬁably at random as speciﬁed in ANSI X9.62 [1] from the seed:
S
=
985BD3AD
BAD4D696
E6768756
15175A21
B43A97E3
The base point G in compressed form is:
G
=
0303
56DCD8F2
F95031AD
652D2395
1BB366A8
and in uncompressed form is:
G
=
040356
DCD8F2F9
5031AD65
2D23951B
B366A806
48F06D86
7940A536
6D9E265D
E9EB240F
Finally the order n of G and the cofactor are:
n
=
04
00000000
00000001
6954A233
049BA98F
h
=
02
3.4
Recommended 163-bit Elliptic Curve Domain Parameters over
F2m
This section speciﬁes the three recommended 163-bit elliptic curve domain parameters over
F 2m in
this document: parameters sect163k1 associated with a Koblitz curve, veriﬁably random parameters
sect163r1, and veriﬁably random parameters sect163r2.
Section 3.4.1 speciﬁes the elliptic curve domain parameters sect163k1, Section 3.4.2 speciﬁes the
elliptic curve domain parameters sect163r1, and Section 3.4.3 speciﬁes the elliptic curve domain
parameters sect163r2.
3.4.1
Recommended Parameters sect163k1
The elliptic curve domain parameters over
F 2m associated with a Koblitz curve sect163k1 are speciﬁed
by the septuple T
=
(m; f
(x);a ;b ;G;n ;h ) where m
= 163 and the representation of
F 2163 is deﬁned by:
+x7
+x6
+x3
f
(x)
=
x163
+1