Scalar Multiplication on Elliptic Curves Defined over Fields of Small Odd Characteristic

This paper explores elliptic curve cryptosystems over fields of small odd characteristic p = 3 or 5. We establish formulas multiplying by p a random point on an ordinary curve defined over $\mathbb{F}_{p^{n}}$, thereby improving scalar multiplication on random and special curves for p = 3 or 5 using a p-Multiply-and-Add method. We study the complexity of our method and compare it to other schemes.

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