Ternary scalar multiplication method with window

A scalar multiplication and ternary technology, applied in the direction of instruments, electrical digital data processing, digital data processing components, etc., can solve time-consuming and other problems

Pending Publication Date: 2021-11-02
HARBIN UNIV OF SCI & TECH
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0004] Computing scalar multiplication is a time-consuming operation

Method used

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  • Ternary scalar multiplication method with window
  • Ternary scalar multiplication method with window
  • Ternary scalar multiplication method with window

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Embodiment Construction

[0021] The present invention will be described in more detail below in conjunction with the accompanying drawings.

[0022] A kind of windowed ternary scalar multiplication method of the present invention that reduces the computational complexity of scalar multiplication, combined with the attached figure 1 , including the following steps.

[0023] In the first step, input scalar K and window width w, the window width range of w is {2,3,4...11};

[0024] The second step is to pre-calculate

[0025] In the third step, when K is greater than 0, the loop is always executed, and the remainder b of K to 3 is judged 1 Is it 0, if b 1 If it is not 0, the scalar K is 3 w Take the remainder, the remainder is b 2 , judge the remainder b 2 Is it greater than if greater than e i =b 2 - if less than e i =b 2 . if b 1 When it is 0, then e i =0. Then K is divided by 3 and rounded up, and i is incremented by 1. At the end of the cycle, K chain is obtained;

[0026] T...

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Abstract

The invention relates to a ternary scalar multiplication method with a window. The invention provides an algorithm for reducing elliptic curve scalar multiplication complexity. The algorithm is implemented by the following steps: 1, inputting a scalar K and a window width w; 2, pre-calculating a third step; 3, determining a value in a K chain based on a ternary scalar multiplication algorithm, judging whether a remainder b1 obtained by K on 3 is 0 or not, if b1 is not 0, performing remainder on 3w by the scalar K, judging whether the remainder b2 is greater than or smaller than or equal to 0, and if b1 is 0, enabling e to be equal to 0; and 4, performing scalar multiplication calculation Q=K*P through the K chain obtained in the step 3 to obtain scalar multiplication Q. Compared with the traditional binary and ternary scalar multiplication algorithms, the algorithm has the advantages that the calculation complexity is reduced, and effective implementation of the elliptic curve cryptosystem is facilitated.

Description

technical field [0001] The windowed ternary scalar multiplication involved in the invention is a method that can reduce the computational complexity of the scalar multiplication. Background technique [0002] This algorithm is an improvement of an elliptic curve scalar multiplication algorithm. Elliptic curve scalar multiplication is a method of adding a point on a curve to itself at a time. In recent years, many researchers in the field of cryptography have a strong interest in elliptic curve scalar multiplication over finite fields. The main research direction is to understand how to implement elliptic curve cryptography and how to reduce its complexity. Efficient techniques used in elliptic curve cryptography are elliptic curve scalar multiplication using point-halving algorithm, double base (DB) chain algorithm, multi-base representation (SMBR), but these techniques have their drawbacks. Therefore, it is imperative to find a new method that can effectively implement el...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F7/491
CPCG06F7/4915
Inventor 翟继强孙海旭杨晓秋
Owner HARBIN UNIV OF SCI & TECH
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