Cryptography Reference
In-Depth Information
Show that Tr(
P
)
∈
E
(
F
q
). Now, suppose
P
∈
E
[
r
],
P
∈
E
(
F
q
) and Tr(
P
)
=
O
E
. Show
that
generates
E
[
r
]. Deduce that the trace map is a distortion map with respect
to
E,r,e
r
and
P
.
{
P,
Tr(
P
)
}
Exercise 26.6.7
Let notation be as in Exercise
26.6.6
. Show that if
Q
∈
E
[
r
]
∩
ker(
π
q
−
[1]) then Tr(
Q
)
=
O
E
. Hence,
deduce that the trace map is not a distortion map for the groups
G
1
or
G
2
of equation (
26.3
).
=
[
k
]
Q
. Show that if
Q
∈
E
[
r
]
∩
ker(
π
q
−
[
q
]) then Tr(
Q
)
