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GEC 1: Recommended Elliptic Curve Domain Parameters Ver. 0.5
‘Standards for Efﬁcient Cryptography’, followed by a t to denote parameters over
F 2m, followed by a
number denoting the ﬁeld size m, followed by a k to denote parameters associated with a Koblitz curve
or an r to denote veriﬁably random parameters, followed by a sequence number.
Parameters
Section
Strength
Size
RSA/DSA
Koblitz or
random
sect113r1
3.2.1
56
113
512
r
sect113r2
3.2.2
56
113
512
r
sect131r1
3.3.1
64
131
704
r
sect131r2
3.3.2
64
131
704
r
sect163k1
3.4.1
80
163
1024
k
sect163r1
3.4.2
80
163
1024
r
sect163r2
3.4.3
80
163
1024
r
sect193r1
3.5.1
96
193
1536
r
sect193r2
3.5.2
96
193
1536
r
sect233k1
3.6.1
112
233
2240
k
sect233r1
3.6.2
112
233
2240
r
sect239k1
3.7.1
115
239
2304
k
sect283k1
3.8.1
128
283
3456
k
sect283r1
3.8.2
128
283
3456
r
Table 4: Properties of Recommended Elliptic Curve Domain Parameters over
F2m
Table 4 summarizes salient properties of the recommended elliptic curve domain parameters over
F 2m.
Information is represented in Table 4 as follows. The column labelled ‘parameters’ gives the nickname of
the elliptic curve domain parameters. The column labelled ‘section’ refers to the section of this document
where the parameters are speciﬁed. The column labelled ‘strength’ gives the number of bits of security
the parameters offer. The column labelled ‘size’ gives the ﬁeld size m. The column labelled ‘RSA/DSA’
gives the approximate size of an RSA or DSA modulus at comparable strength. Finally the column
labelled ‘Koblitz or random’ indicates whether the parameters are associated with a Koblitz curve — ‘k’
— or were chosen veriﬁably at random — ‘r’.
Table 5 summarizes the status of the recommended elliptic curve domain parameters over
F 2m with re-
spect to their alignment with other standards.
Information is represented in Table 5 as follows. The column labelled ‘parameters’ gives the nickname
of the elliptic curve domain parameters. The column labelled ‘section’ refers to the section of this docu