Elliptic curve cryptography on Windows CE devices

Abstract

Since mobile devices were conceived and commercialized, their market has grown exponentially, so as its problems related to secure data residing in them. Elliptic curve cryptography (ECC) is an approach to public key cryptography (PCK) based on the algebraic structure of elliptic curves over finite fields. It represents the most suitable choice for implementing cryptography in mobile devices since it uses smaller key sizes compared with others traditional public key cryptosystems without decreasing the security level. In this work we present the design of software modules for ECC over .Net Compact Framework (.Net CF) 3.5 well suited for mobile and embedded devices with Windows CE as operating system. The main cores are modules for finite field arithmetic and elliptic curve cryptographic schemes defined over the prime field Z p . These modules are not available neither in the programming language nor the .Net CF. We evaluated the performance of our implementations using the Personal Digital Assistant devices IPAQ 116 and Handheld HP 216, using elliptic curves over the prime field Z p with p=192, 224 and 256, which are key sizes currently recommended by NIST. Our results show that ECC could be implemented in .Net CF with a performance that should be tolerated by most of the users with a high degree of security.