Hardware Realization of High Speed Elliptic Curve Point Multiplication using Precomputation over GF(P)

In Diffi-Hellman type key agreement (Idrissi et al., 2012), Elliptic Curve Digital Signature Algorithm (Shivkumar and Umamaheswari, 2014) and Elgamal crypto systems (Jie and Kamarulhaili, 2011; Ismail and Hijazi, 2012), we use elliptic curve Point Multiplication (PM) (Hankerson et al., 2004). Several hardware solutions are already available for elliptic curve Point Multiplication, (Ghosh et al., 2007; Orlando and Paar, 2001; De Dormole and Quisquater, 2007). Our objective is to generate the scalar product kP where P is a point on an elliptic curve over a prime field Fp and k is an integer that belongs to Zp. We propose a fast hardware solution to PM which makes use of hardware Point Doubler (PD) and Point Adder (PA) modules. We describe two different schemes for fast multiplication. In the first method we relize the design for a ‘t’ bit k. Then we extend the design for binary multiples of ‘t’. In the second method multi scalar multiplication is used and the desired result is selected using appropriate multiplexers.