Co-\(Z\) ECC scalar multiplications for hardware, software and hardwaresoftware co-design on embedded systems
Recent elliptic curve scalar multiplication algorithms are based on efficient co-\(Z\) arithmetics. These arithmetics were initially introduced by Meloni in 2007 where addition of projective points share the same \(Z\)-coordinate. The co-\(Z\) version algorithms are sufficiently fast and secure against a large variety of implementation attacks. This paper analyses the performance of these algorithms in hardware and then compares them against software and hardwaresoftware co-design environments on FPGA, in terms of speed, memory, power and energy consumption. Specifically, this paper presents a survey and performance comparison of implementations of co-\(Z\) versions of the Montgomery ladder and the Joyes double-add algorithm in an embedded system environment.
hardware hardwaresoftware co-design elliptic curves fpga regular ladders microblaze