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Computer implementation method of multiplier over finite field and computer implementation method of large matrix element elimination

An implementation method and technology of finite fields, applied in the field of computer implementation of Gaussian elimination on finite fields, can solve the problems of wasting CPU working time, slow speed, and not considering the difference between computer cache and memory performance, so as to save time, The effect of increasing the speed of implementation

Inactive Publication Date: 2007-08-01
INST OF INFORMATION ENG CAS
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Problems solved by technology

[0010] And when above-mentioned existing element multiplication calculation method on the existing finite field, do not consider the difference performance problem of computer high-speed memory and memory, the size of the two-dimensional table that constructs in the multiplication calculation process often exceeds the size of high-speed cache. capacity, but have to be stored in memory
As a result, when the above two-dimensional table is called, the CPU needs to read the above two-dimensional table data in the memory, which is slow and wastes a lot of CPU working time

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  • Computer implementation method of multiplier over finite field and computer implementation method of large matrix element elimination

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Embodiment Construction

[0022] The technical solutions of the present invention will be described in further detail below with reference to the accompanying drawings and embodiments.

[0023] As shown in Figure 1, it is a flow chart of the computer-implemented method for multiplication over a finite field of the present invention, including such steps as:

[0024] Step 1. Select a subfield of the finite field according to the following conditions: the product of the number of elements in the subfield, the number of bytes required to store the elements in the subfield, and the expansion times of the finite field for the subfield is less than The capacity of the computer cache;

[0025] Step 2, selecting a set of bases of the finite field for the subfield;

[0026] Step 3, calculating the multiplication auxiliary table according to the group basis, the elements to be multiplied and the computer cache capacity, and storing the multiplication auxiliary table in the computer cache;

[0027] Step 4, quer...

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Abstract

This invention relates to one computer realization method for limit area multiplication, which comprises the following steps: selecting one sub zone according the following conditions as element number, bit number in zone and limit zone expansion product less than computer high speed buffer capacity; b, selecting limit zone set base; c, according to the base and multiplication aid list storing the aid list into computer high speed buffer; d, indexing computer high speed buffer product aid list to compute result as results value.

Description

technical field [0001] The invention relates to a computer implementation method of multiplication over finite fields and a computer implementation method of Gaussian elimination over finite fields based on the method. Background technique [0002] In many fields such as cryptography, coding theory and applied mathematics, the problem of solving the rank of linear equations and matrices over finite fields is often encountered. For example, in the design and analysis of multivariate public key ciphers and stream ciphers, the famous The key step in the XL algorithm is to solve a large-scale linear equation system; in the combinatorial design of applied mathematics, in order to distinguish the different structures of the two designs, we need to calculate the rank of the correlation matrix of the two designs and so on. Many times, we need to solve the rank of large-scale linear equations and large-scale matrices over finite fields. Gaussian elimination is a general method for s...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/10G06F1/03
Inventor 胡磊李剑宇聂旭云丁津泰
Owner INST OF INFORMATION ENG CAS
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