### Speeding up Simultaneous Scalar Multiplication on Elliptic Curves

#### Abstract

Scalar multiplication is the basic and** **most** **expensive operation in elliptic curve based cryptographic protocols. It is the computation of integer multiple of a given point on the curve. Computation of scalar multiple is faster by using signed binary representation as compared to binary representation. Direct- recoding is a new and efficient algorithm for computation of signed binary representation as compared to the existing methods like NAF, MOF and complementary recoding. In this paper, we propose a novel method for speeding up simultaneous scalar multiplication using direct recoding method.

**Keywords**: Elliptic curve cryptography, simultaneous scalar multiplication, signed binary method, NAF, MOF, complementary recoding, JSF

MSC: 94A60

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