Elliptic Curves for Efficient Repeated Additions
Eun‐Jeong Lee, YoungJu Choie · Information Security and Cryptology · 1995
In spite of the good security of the cryptosystem on an elliptic curve defined over finite field, the cryptosystem on an elliptic curve is slower than that on a finite field. To be practical, we need a better method to improve a speed of the cryptosystem on an elliptic curve defined over a finite field. In 1991, Koblitz suggested to use an anomalous curve over , which is an elliptic curve with Frobenious map whose trace is 1, and reduced a speed of computation of mP. In this paper, we consider an elliptic curve defined over with Frobenious map whose trace is 3 and suggest an efficient algorithm to compute mP. On the proposed elliptic curve, we can compute multiples mP with +1 addition in worst case.