2
Recommended Elliptic Curve Domain Parameters over
F p
Page 11
2.5.1
Recommended Parameters secp192k1
The elliptic curve domain parameters over
F p associated with a Koblitz curve secp192k1 are speciﬁed
by the sextuple T
=
(p ;a ;b ;G;n ;h ) where the ﬁnite ﬁeld
F p is deﬁned by:
p
=
FFFFFFFF
FFFFFFFF
FFFFFFFF
FFFFFFFF
FFFFFFFE
FFFFEE37
=
2192
 232
 212
 28
 27
 26
 23
 1
= x3
The curve E: y2
+ax
+b over
F p is deﬁned by:
a
=
00000000
00000000
00000000
00000000
00000000
00000000
b
=
00000000
00000000
00000000
00000000
00000000
00000003
The base point G in compressed form is:
G
=
03
DB4FF10E
C057E9AE
26B07D02
80B7F434
1DA5D1B1
EAE06C7D
and in uncompressed form is:
G
=
04
DB4FF10E
C057E9AE
26B07D02
80B7F434
1DA5D1B1
EAE06C7D
9B2F2F6D
9C5628A7
844163D0
15BE8634
4082AA88
D95E2F9D
Finally the order n of G and the cofactor are:
n
=
FFFFFFFF
FFFFFFFF
FFFFFFFE
26F2FC17
0F69466A
74DEFD8D
h
=
01
2.5.2
Recommended Parameters secp192r1
The veriﬁably random elliptic curve domain parameters over
F p secp192r1 are speciﬁed by the sex-
tuple T
=
(p ;a ;b ;G;n ;h ) where the ﬁnite ﬁeld
F p is deﬁned by:
p
=
FFFFFFFF
FFFFFFFF
FFFFFFFF
FFFFFFFE
FFFFFFFF
FFFFFFFF
=
2192
 264
 1
= x3
The curve E: y2
+ax
+b over
F p is deﬁned by:
a
=
FFFFFFFF
FFFFFFFF
FFFFFFFF
FFFFFFFE
FFFFFFFF
FFFFFFFC
b
=
64210519
E59C80E7
0FA7E9AB
72243049
FEB8DEEC
C146B9B1
E was chosen veriﬁably at random as speciﬁed in ANSI X9.62 [1] from the seed:
S
=
3045AE6F
C8422F64
ED579528
D38120EA
E12196D5
The base point G in compressed form is:
G
=
03
188DA80E
B03090F6
7CBF20EB
43A18800
F4FF0AFD
82FF1012