Combining point operations for efficient elliptic curve cryptography scalar multiplication

Abstract

Elliptic curve cryptosystems have gained increase attention and have become an intense area of research, mainly because of their shorter key length when compared to other public key cryptosystems such as RSA. Shorter key length brings advantages such as reduced computation effort, power consumption and storage requirements, making it possible to increase the available security for portable devices, smartcards and other power strained devices. ECC manages to cover all the significant cryptographic operations such as key exchange and agreement or digital signature with greater efficiency than previous systems. These operations rely heavily on point multiplication which is also the most time-consuming operation. This paper evaluates point operations (doubling, tripling, quadrupling, and addition) and proposes an algorithm for combining the operations in order to achieve faster scalar multiplication when compared to the standard algorithm for scalar multiplication of double and add.