High Efficiency of Scalar Multiplication in Elliptic Curve Cryptography

摘要

The elliptic curve cryptography is based on the addition and the subtraction of some points on an elliptic curve. The point obtained by repeating the addition and subtraction on the elliptic curve is called a scalar multiple point, and is used as a key of the elliptic curve cryptography. We call scalar multiplication when the formula Q=kP stands for two points P, Q on an elliptic curve and an integer k The scalar multiplication is repeatedly used in the procedure sequence and is the most important calculation in the elliptic curve cryptography. Therefore, the speed up of the scalar multiplication can directly cause speed up of the elliptic curve cryptography. When the elliptic curve and the base point are hardly changed, the scalar multiplication can be sped up by using the pre-calculation table. In the this report, we propose a making algorithm of the pre-calculation table mainly using Double-Triple (DT) operation that does the double and triple multiplication at the same time.