Structural Properties of Cryptographic Sequences - Computational Intelligence in Security for Information Systems - page 160

Java Card Implementation of the Elliptic Curve
Integrated Encryption Scheme Using Prime and
Binary Finite Fields

Avila 3

V. Gayoso Mart ınez 1 ,L.Hernandez Encinas 2 , and C. Sanchez

1 Universidad Francisco de Vitoria, Pozuelo de Alarcon (Madrid), Spain
[e-mail]
2 Department of Information Processing and Coding, Applied Physics Institute,
CSIC, Madrid, Spain
[e-mail]
3 Department of Applied Mathematics to Information Technologies,
Polytechnic University, Madrid, Spain
[e-mail]

Abstract. Elliptic Curve Cryptography (ECC) can be considered an
approach to public-key cryptography based on the arithmetic of elliptic
curves and the Elliptic Curve Discrete Logarithm Problem (ECDLP).
Regarding encryption, the best-known scheme based on ECC is the Ellip-
tic Curve Integrated Encryption Scheme (ECIES), included in standards
from ANSI, IEEE, and also ISO/IEC. In the present work, we provide
a comparison of two Java Card implementations of ECIES that we have
developed using prime and binary fields, respectively.

Keywords: Java Card, elliptic curves, public key encryption schemes.

1 Introduction

In the current world, cryptography is essential for the protection of data and
communication systems. Whitfield Die and Martin Hellman sparked off a rev-
olution when they introduced the concept of public-key cryptography in 1976.
Since that year, a great number of cryptosystems have been proposed, though
many have been proved to be unsuitable for commercial purposes due to vulner-
abilities in their designs or to their high complexity. The best-known successful
public-key cryptosystem is RSA [1,2], which was the first algorithm known to
be suitable for signing as well as encrypting data.
In 1985, Victor Miller [3] and Neil Koblitz [4] independently suggested the us-
age of elliptic curves defined over finite fields in cryptography [5]. In comparison
with other public-key cryptosystems, Elliptic Curve Cryptography (ECC) uses
significantly shorter keys. The reason for this fact is related to the hardness of
the ECDLP, which is considered to be more dicult to solve than the Integer
Factorization Problem (IFP) used by RSA or the Discrete Logarithm Problem
(DLP) which is the basis of the ElGamal encryption scheme [6].