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SEC 2: Recommended Elliptic Curve Domain Parameters Ver. 0.6
n
=
01
00000000
00000000
00000001
5AAB561B
005413CC
D4EE99D5
h
=
02
3.6
Recommended 233-bit Elliptic Curve Domain Parameters over
F2m
This section speciﬁes the two recommended 233-bit elliptic curve domain parameters over
F 2m in this
document: parameters sect233k1 associated with a Koblitz curve, and veriﬁably random parameters
sect233r1.
Section 3.6.1 speciﬁes the elliptic curve domain parameters sect233k1, and Section 3.6.2 speciﬁes the
elliptic curve domain parameters sect233r1.
3.6.1
Recommended Parameters sect233k1
The elliptic curve domain parameters over
F 2m associated with a Koblitz curve sect233k1 are speciﬁed
by the septuple T
=
(m; f
(x);a ;b ;G;n ;h ) where m
= 233 and the representation of
F 2233 is deﬁned by:
+1
+x74
f
(x)
=
x233
The curve E: y2
+xy
= x3
+ax2
+b over
F 2m is deﬁned by:
a
=
0000
00000000
00000000
00000000
00000000
00000000
00000000
00000000
b
=
0000
00000000
00000000
00000000
00000000
00000000
00000000
00000001
The base point G in compressed form is:
G
=
020172
32BA853A
7E731AF1
29F22FF4
149563A4
19C26BF5
0A4C9D6E
EFAD6126
and in uncompressed form is:
G
=
04
017232BA
853A7E73
1AF129F2
2FF41495
63A419C2
6BF50A4C
9D6EEFAD
612601DB
537DECE8
19B7F70F
555A67C4
27A8CD9B
F18AEB9B
56E0C11056FAE6A3
Finally the order n of G and the cofactor are:
n
=
80
00000000
00000000
00000000
00069D5B
B915BCD4
6EFB1AD5
F173ABDF
h
=
04