Scalar multiplication algorithm based on wNAF improvement

A technology of scalar multiplication and algorithm, which is applied in the field of scalar multiplication algorithm, can solve the problems of precomputation that consumes too many resources and is not applicable

Pending Publication Date: 2022-07-01
HARBIN UNIV OF SCI & TECH
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  • Claims
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Problems solved by technology

Among them, the most widely studied is the wNAF algorithm. Although this method reduces the computational complexity, the precomputation consumes too many resources and is not suitable for large windows.

Method used

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  • Scalar multiplication algorithm based on wNAF improvement
  • Scalar multiplication algorithm based on wNAF improvement
  • Scalar multiplication algorithm based on wNAF improvement

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Embodiment Construction

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

[0022] The invention provides an improved scalar multiplication algorithm based on wNAF to reduce the computational complexity of scalar multiplication, combined with the attached figure 1 , including the following steps.

[0023] 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 precompute {2 0 P,2 1 P,...,2 w P} and {3P,5P,....,(2 w-2 -1)P};

[0025] The third step is to use the wNAF algorithm to determine the value in the k chain, and determine whether the remainder of k to 2 is 0. If it is 0, then e i =0, if not 0, then e i =k mod 2 w+1 , judge e i Is it greater than 2 w , if greater than e i =e i -2 w+1 , k=k-e i , k=k / 2, this round of operation ends, the next round continues to judge whether the remainder of k versus 2 is 0, until the entire k chain is obtained;

[...

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Abstract

The invention relates to a scalar multiplication algorithm based on wNAF improvement. The invention provides an algorithm for reducing the complexity of elliptic curve scalar multiplication calculation, which comprises the following steps of: 1, inputting a scalar k and a window width w; step 2, pre-calculating {20P, 21P,..., 2wP} and {3P, 5P,..., (2w-2-1) P}; 3, determining values in the k chain by using a wNAF algorithm, judging whether the remainder of k to 2 is 0, if so, ei = 0, if not, ei = k mod 2w + 1, judging whether ei is greater than 2w, if so, ei = ei-2w + 1, k = k-ei and k = k/2, ending the operation of this round, and continuously judging whether the remainder of k to 2 is 0 in the next round until the whole k chain is obtained; 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 a wNAF scalar multiplication algorithm, the algorithm not only reduces the number of pre-calculations, but also reduces the calculation complexity, and facilitates the effective implementation of an elliptic curve cryptosystem.

Description

technical field [0001] The scalar multiplication algorithm involved in the present invention is an algorithm that can reduce the computational complexity of scalar multiplication. Background technique [0002] The main advantage of Elliptic Curve Cryptography (ECC) is the small key size, replacing the 1024-bit key of RSA with a 160-bit key, and providing the same level of security, ECC also has outstanding advantages such as low power consumption and fast calculation speed, It is especially suitable for WSN, PDA and other environments with limited processing power, storage space, bandwidth, and power consumption. [0003] In recent years, many researchers in the field of cryptography have been very interested in elliptic curve scalar multiplication over finite fields, and the main research direction is to understand how elliptic curve cryptography is implemented and how to reduce its complexity. Among them, the most widely studied is the wNAF algorithm. Although this method...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H04L9/30H04L9/06
CPCH04L9/3066H04L9/0631
Inventor 杨晓秋孙海旭田新雨
Owner HARBIN UNIV OF SCI & TECH
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