Implementacão Eficiente em Software de Criptossistemas de Curvas Elípticas

Abstract

It is widely recognized that public-key cryptography is an important tool for providing security services such as condentiality, data integrity, authentication and non-repudiation, which are requirements present in almost all communications. The main advantage of elliptic curve cryptography (ECC) over competing public-key technologies such as RSA and DSA, is that signicantly smaller parameters can be used in ECC, but with equivalent levels of security. This advantage is especially important for applications on constrained environments such as smart cards, cell phones, personal device assistants, and pagers. From a practical point of view, the implementation of ECC presents various challenges. An ECC-based application requires that several choices be made including the security level, algorithms for implementing the nite eld arithmetic, algorithms for implementing the elliptic group operation, elliptic curve protocols, and the computer platform. These choices may have a signicant impact on the performance of the resulting application. This dissertation focuses on developing ecient algorithms for software implementation of ECC over F 2m. In this framework, we study dierent ways of eciently implementing arithmetic in F 2m, and computing an elliptic scalar multiplication, the central operation of public-key cryptography based on elliptic curves. We also concentrate on the software implementation of these algorithms for diferent platforms including PCs, workstations, and constrained devices such as the RIM interactive pager. This dissertation is a collection of ve papers written in English, with an introduction and conclusions written in Portuguese.