Algorithm of Pre-judgment NAF Scalar Multiplication on ECC
Qingqing Huang · 2019
ECC (Elliptic Curve Cryptography) algorithm is widely used in many field such as smart card due to it's highly security. In some integrated circuits which have poor hardware resource, just like smart card, we need to use a lot of registers to store the temp value of the NAF of k on ECC when we are doing the scalar multiplication. To solve the problem, this paper proposes an algorithm called pre-judgment of NAF base on the general NAF algorithm. It not only inherits the fast computation speed of the general NAF algorithm, and also saves the registers for temp value stored through pre-judge the value of k. It doesn't need to calculate the NAF of k beforehand. It directly calculates the NAF of the k when doing the scalar mutilation in the same state machine. This can help save the hardware resource, and make the low power, low cost IC easy to develop.