Information Technology Reference
In-Depth Information
Smart cards are small, portable, tamper-resistant devices offering users conve-
nient storage and processing capabilities, and as such they play a prominent role
in providing the required security level in banking transactions, the GSM and
UMTS cellular systems or pay TV environments, to put only a few examples.
Smart cards are amenable to cryptographic implementations, as they contain
multiple software and hardware countermeasures designed to protect sensible
information such as the keying material [7].
The two most widely used smart card platforms are Java Card [8], developed
by Sun with the support from several leading smart card providers during the
1990s, and MULTOS (a multi-application operating system controlled by the
MULTOS Consortium) [9]. Though both platforms implement cryptographic
capabilities, the public-key cryptography capabilities provided by Java Card are
more complete, specially regarding ECC functionality.
In the present work, we describe two implementations, using prime and binary
fields, of the best known encryption scheme using elliptic curves, the Elliptic
Curve Integrated Encryption Scheme (ECIES). To our knowledge, there are no
smart card implementations of this encryption scheme, so this is the first time
that ECIES is implemented, and its performance is analysed, in Java Cards. We
also provide a performance comparison of both implementations using different
combinations of plaintext lengths and key sizes.
This paper is organized as follows: Section 2 presents a brief introduction to
ECC and ECIES. Section 3 includes a summary of the ECIES support in Java
Card. Section 4 provides the main characteristics of the smart cards used in the
tests and offers some details about the applet development phase. Finally, in
Section 5 we present the experimental results of the tests along with the most
important findings and conclusions.
2 Elliptic Curve Cryptography and ECIES
An elliptic curve
E
defined over a finite field
is a plane non-singular cubic
curve with at least a rational point [10]. In practice, generic elliptic curves are
managed using the following equation, known as the Weierstrass equation in
non-homogeneous form [11], where the elements
a
1
,a
2
,a
3
,a
4
,a
6
∈
F
F
and
Δ
=0,
being
Δ
the discriminant of the curve
E
[12]:
E
:
y
2
+
a
1
xy
+
a
3
y
=
x
3
+
a
2
x
2
+
a
4
x
+
a
6
.
(1)
The homogeneous version of the Weierstrass equation implies the existence of
a special point, called the point at infinity, which is denoted as
O
and does not
have a counterpart in the ane plane.
When working with finite fields, it is possible to obtain simplified versions of
the Weierstrass equation. If the finite field is a prime field, i.e.
F
p
,where
p>
3 is a prime number, the equation defining the elliptic curve becomes:
F
=
y
2
=
x
3
+
ax
+
b.
(2)
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