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SEC 2: Recommended Elliptic Curve Domain Parameters Ver. 0.6
3.4.3
Recommended Parameters sect163r2
The veriﬁably random elliptic curve domain parameters over
F 2m sect163r2 are speciﬁed by the sep-
tuple T
=
(m; f
(x);a ;b ;G;n ;h ) where m
= 163 and the representation of
F2163 is deﬁned by:
+1
+x7
+x6
+x3
f
(x)
=
x163
The curve E: y2
+xy
= x3
+ax2
+b over
F 2m is deﬁned by:
a
=
00
00000000
00000000
00000000
00000000
00000001
b
=
02
0A601907
B8C953CA
1481EB10
512F7874
4A3205FD
E was chosen veriﬁably at random from the seed:
S
=
85E25BFE
5C86226C
DB12016F
7553F9D0
E693A268
E was selected from S as speciﬁed in ANSI X9.62 [1] in normal basis representation and converted into
polynomial basis representation.
The base point G in compressed form is:
G
=
0303
F0EBA162
86A2D57E
A0991168
D4994637
E8343E36
and in uncompressed form is:
G
=
0403F0
EBA16286
A2D57EA0
991168D4
994637E8
343E3600
D51FBC6C
71A0094F
A2CDD545
B11C5C0C
797324F1
Finally the order n of G and the cofactor are:
n
=
04
00000000
00000000
000292FE
77E70C12
A4234C33
h
=
02
3.5
Recommended 193-bit Elliptic Curve Domain Parameters over
F2m
This section speciﬁes the two recommended 193-bit elliptic curve domain parameters over
F 2m in this
document: veriﬁably random parameters sect193r1, and veriﬁably random parameters sect193r1.
Section 3.5.1 speciﬁes the elliptic curve domain parameters sect193r1, and Section 3.5.2 speciﬁes the
elliptic curve domain parameters sect193r2.
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:
+1
+x15
f
(x)
=
x193