The efficiency of devices performing arithmetic operations in finite field is crucial for the efficiency of ECC systems. Regarding the dependency of the system on those devices we conclude that the robustness of the system also depends on the robustness of the operators. The aim of conducted researches described in the dissertation was to propose efficient and robust against power analysis side-channel attacks hardware arithmetic operators on GF(2m) dedicated to elliptic curve cryptography (ECC) applications. We propose speed and area efficient hardware solutions for arithmetic operators on GF(2m). Designed units are flexible and operate, due to assumed applications, on large numbers (160-600 bits). Next we propose algorithmic and architectural modifications improving robustness against side-channel power analysis attacks of designed solutions. The final goal described was to find a tradeoff between security of arithmetic operators and their efficiency. We were able to perform such modifications increasing robustness of designed hardware arithmetic operators, which do not impact negatively overall performance of the operator. The attempt to protect the lowest level operations of ECC systems, the finite field operations, is a first known attempt of that type. Till now researches described in literature on the subject did not concern the finite field level operations protections. They considered only protections of curve or ECC protocol level operations. Proposed protections contribute and we may say complete already developed means of protections for ECC systems. By combining protections of all levels of operation of the ECC system it is assumed that it is possible to make the system very robust against side-channel power analysis attacks.
