Affiliation:
1. National Key Laboratory of Security Communication , Chengdu 610041 , China
Abstract
Abstract
Transparency order (
TO
{\mathcal{TO}}
) is one of the indicators used to measure the resistance of
(
n
,
m
)
\left(n,m)
-function to differential power analysis. At present, there are three definitions:
TO
{\mathcal{TO}}
, redefined transparency order (
ℛTO
{\mathcal{ {\mathcal R} TO}}
), and modified transparency order (
ℳTO
{\mathcal{ {\mathcal M} TO}}
). For the first time, we give one necessary and sufficient condition for
(
n
,
m
)
\left(n,m)
-function reaching
TO
=
m
{\mathcal{TO}}=m
and completely characterize
(
n
,
m
)
\left(n,m)
-functions reaching
TO
=
m
{\mathcal{TO}}=m
for any
n
n
and
m
m
. We find that any
(
n
,
1
)
\left(n,1)
-function cannot reach
TO
=
m
{\mathcal{TO}}=m
for odd
n
n
. Based on the matrix product, the necessary conditions for
(
n
,
m
)
\left(n,m)
-function reaching
ℳTO
=
m
{\mathcal{ {\mathcal M} TO}}=m
or
ℛTO
=
m
{\mathcal{ {\mathcal R} TO}}=m
are given, respectively. Finally, it is proved that any balanced
(
n
,
m
)
\left(n,m)
-function cannot reach the upper bound on
TO
{\mathcal{TO}}
(or
ℛTO
{\mathcal{ {\mathcal R} TO}}
,
ℳTO
{\mathcal{ {\mathcal M} TO}}
).