### Abstract

The computational performance of cryptographic protocols using an elliptic curve strongly depends on the efficiency of the scalar multiplication. Some elliptic curve based cryptographic protocols, such as signature verification, require computation of multi scalar multiplications of kP + lQ, where P and Q are points on an elliptic curve. An efficient way to compute kP + lQ is to compute two scalar multiplications simultaneously, rather than computing each scalar multiplication separately. We introduce new efficient algorithms for simultaneous scalar multiplication on an elliptic curve. We also give a detailed analysis of the computational efficiency of our proposed algorithms.

Original language | English |
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Pages (from-to) | 1135-1146 |

Number of pages | 12 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E86-A |

Issue number | 5 |

Publication status | Published - Jan 1 2003 |

### All Science Journal Classification (ASJC) codes

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics