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GEC 1: Recommended Elliptic Curve Domain Parameters Ver. 0.5
2.3.2
Recommended Parameters secp128r2
The veriﬁably random elliptic curve domain parameters over
F p secp128r2 are speciﬁed by the sex-
tuple T
=
(p ;a ;b ;G;n ;h ) where the ﬁnite ﬁeld
F p is deﬁned by:
p
=
FFFFFFFD
FFFFFFFF
FFFFFFFF
FFFFFFFF
=
2128
 297
 1
= x3
The curve E: y2
+ax
+b over
F p is deﬁned by:
a
=
D6031998
D1B3BBFE
BF59CC9B
BFF9AEE1
b
=
5EEEFCA3
80D02919
DC2C6558
BB6D8A5D
E was chosen veriﬁably at random as speciﬁed in ANSI X9.62 [1] from the seed:
S
=
004D696E
67687561
517512D8
F03431FC
E63B88F4
The base point G in compressed form is:
G
=
02
7B6AA5D8
5E572983
E6FB32A7
CDEBC140
and in uncompressed form is:
G
=
04
7B6AA5D8
5E572983
E6FB32A7
CDEBC140
27B6916A
894D3AEE
7106FE80
5FC34B44
Finally the order n of G and the cofactor are:
n
=
3FFFFFFF
7FFFFFFF
BE002472
0613B5A3
h
=
04
2.4
Recommended 160-bit Elliptic Curve Domain Parameters over
F p
This section speciﬁes the three recommended 160-bit elliptic curve domain parameters over
F p in this
document: parameters secp160k1 associated with a Koblitz curve, veriﬁably random parameters
secp160r1, and veriﬁably random parameters secp160r2.
Section 2.4.1 speciﬁes the elliptic curve domain parameters secp160k1, Section 2.4.2 speciﬁes the
elliptic curve domain parameters secp160r1, and Section 2.4.3 speciﬁes the elliptic curve domain
parameters secp160r2.
2.4.1
Recommended Parameters secp160k1
The elliptic curve domain parameters over
F p associated with a Koblitz curve secp160k1 are speciﬁed
by the sextuple T
=
(p ;a ;b ;G;n ;h ) where the ﬁnite ﬁeld
F p is deﬁned by: