A Survey on Hardware Implementations of Elliptic Curve Cryptosystems

In the past two decades, Elliptic Curve Cryptography (ECC) have become increasingly advanced. ECC, with much smaller key sizes, offers equivalent security when compared to other asymmetric cryptosystems. In this survey, an comprehensive overview of hardware implementations of ECC is provided. We first discuss different elliptic curves, point multiplication algorithms and underling finite field operations over binary fields F2m and prime fields Fp which are used in the literature for hardware implementation. Then methods, steps and considerations of ECC implementation are presented. The implementations of the ECC are categorized in two main groups based on implementation technologies consist of field programmable gate array (FPGA) based implementations and application specific integrated circuit (ASIC) implementations. Therefore, in these categories to have a better presentation and comparison, the implementations are presented and distinguished based on type of finite fields. The best and newest structures in the literature are described in more details for overall presentation of architectures and approaches in each group of implementations. High-speed implementation is an important factor in the ECC applications such as network servers. Also in smart cards, Wireless Sensor Networks (WSN) and Radio Frequency Identification (RFID) tags require to low-cost and lightweight implementations. Therefore, implementation methods related to these applications are explored. In addition, a classification of the previous works in terms of scalability, flexibility, performance and cost effectiveness is provided. Finally, some words and techniques about future works that should be considered are provided.