A Low-Cost and High-Performance Cryptosystem Using Tripling-Oriented Elliptic Curve

Developing a high-performance public key cryptosystem is crucial for numerous modern security applications. The Elliptic Curve Cryptosystem (ECC) has performance and resource-saving advantages compared to other types of asymmetric ciphers. However, the sequential design implementation for ECC does not satisfy the current applications' performance requirements. Therefore, several factors should be considered to boost the cryptosystem performance, including the coordinate system, the scalar multiplication algorithm, and the elliptic curve form. The tripling-oriented (3DIK) form is implemented in this work due to its minimal computational complexity compared to other elliptic curves forms. This experimental study explores the factors playing an important role in ECC performance to determine the best combination that leads to developing high-speed ECC. The proposed cryptosystem uses parallel software implementation to speed up ECC performance. To our knowledge, previous studies have no similar software implementation for 3DIK ECC. Supported by using parallel design, projective coordinates, and a fast scalar multiplication algorithm, the proposed 3DIK ECC improved the speed of the encryption process compared with other counterparts and the usual sequential implementation. The highest performance level for 3DIK ECC was achieved when it was implemented using the Non-Adjacent Form algorithm and homogenous projection. Compared to the costly hardware implementations, the proposed software implementation is cost effective and can be easily adapted to other environments. In addition, the power consumption of the proposed ECC is analyzed and compared with other known cryptosystems. thus, the current study presents a detailed overview of the design and implementation of 3DIK ECC.