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Secure outsourcing algorithm for large-scale matrix operation

A security outsourcing, matrix operation technology, applied in the field of cloud computing security

Active Publication Date: 2019-03-12
QINGDAO UNIV
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  • Abstract
  • Description
  • Claims
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AI Technical Summary

Problems solved by technology

[0006] For multiplication matrix calculation methods such as large-scale matrix multiplication (MM) on finite fields, large-scale matrix inversion (MIC) and large-scale matrix determinant calculation (MDC), it is necessary to solve the problem of outsourcing algorithm design

Method used

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  • Secure outsourcing algorithm for large-scale matrix operation

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Embodiment Construction

[0056] One, the relevant theory applied in the present invention

[0057] (1) Definition of finite field

[0058] Finite field or Galois Field (Galois Field), is a finite set containing q elements It defines two operations of addition (.) and multiplication (+), which satisfy the following properties

[0059] ① collection The Abelian group is formed under the addition operation, and its addition identity element is denoted as

[0060] ② collection The non-zero elements of form an Abelian group under the multiplication operation, and its multiplicative identity element is

[0061] ③ Multiplication satisfies the distributive law with respect to addition, that is, for any Satisfy

[0062] a·(b+c)=a·b+a·c and (b+c)·a=b·a+c·a

[0063] (2) Permutation and permutation matrix

[0064] Permutation functions are widely used in group theory and combinatorics. The permutation function is a bijection on the finite set {1, 2, ..., n}, which can be written as follows:

[...

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Abstract

The invention provides a secure outsourcing algorithm for large-scale matrix operation, which adopts a continuous sparse 11-module matrix transformation encryption technology with a simple structure.On the one hand, multiple sparse transformations can encrypt dense matrices continuously, thus protecting the statistical information of specific elements of the original matrices; On the other hand,the combinability of matrix multiplication and the simplicity of sparse matrix structure ensure the high efficiency of matrix encryption and decryption. In addition, the technology has good universality, suitable for outsourcing MM, MIC, MDC and other matrix operations, giving good consideration to the privacy of input and output, high efficiency verifiability and efficiency.

Description

technical field [0001] The invention belongs to the technical field of cloud computing security, and relates to a safe outsourcing method for matrix operations such as large-scale matrix product calculation, large-scale matrix inversion and large-scale matrix determinant calculation in a cloud environment. Background technique [0002] As a basic mathematical object, matrix is ​​widely used in scientific and engineering computing fields. Many different practical problems can be reduced to matrix computation problems. In every branch of physics, including classical mechanics, optics, electromagnetism, quantum mechanics, and quantum electrodynamics, matrices are used to study physical phenomena such as the motion of rigid bodies. In computer graphics, they are used to manipulate 3D models and project them onto a 2D plane. In probability theory and statistics, random matrices are used to describe sets of probabilities, for example, they are used in the PageRank algorithm for ...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/16H04L29/06
CPCH04L63/0428G06F17/16Y02P90/30
Inventor 田呈亮张胜霞
Owner QINGDAO UNIV
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